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Practice · GMAT · Data Insights

GMAT Data Insights practice questions

83 questions with worked solutions. All five formats as they appear on the test: data sufficiency, graphics interpretation with drop-downs, sortable table analysis, two-part analysis and multi-source reasoning.

12 easy · 44 medium · 27 hard · Percentile levels 60th to 99th · what the levels mean

Practise timed: 20 questions · 45 min All GMAT topics

1 Easy ≈ 70th percentile
Is the integer nn odd?
  1. (1)n2+nn^2+n is even.
  2. (2)3n+13n+1 is even.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) n2+n=n(n+1)n^2+n=n(n+1) is a product of consecutive integers, so it is even for every nn: no information. (2) 3n+13n+1 even means 3n3n is odd, so nn is odd: sufficient.
2 Medium ≈ 80th percentile
If xx and yy are positive, what is the value of x+yx+y?
  1. (1)x2+2xy+y2=25x^2+2xy+y^2=25
  2. (2)x−y=1x-y=1
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(1) is (x+y)2=25(x+y)^2=25, and x+y>0x+y>0, so x+y=5x+y=5: sufficient. (2) fixes only the difference (x=2,y=1x=2,y=1 or x=5,y=4x=5,y=4): not sufficient.
3 Medium ≈ 85th percentile
What is the remainder when the positive integer nn is divided by 6?
  1. (1)When nn is divided by 3, the remainder is 2.
  2. (2)nn is even.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) allows n=2n=2 (remainder 2) or n=5n=5 (remainder 5). (2) allows remainders 0, 2 or 4. Together, n≡2(mod3)n\equiv2\pmod3 and n≡0(mod2)n\equiv0\pmod2 force n≡2(mod6)n\equiv2\pmod6: sufficient only together.
4 Medium ≈ 85th percentile
Is ∣x−2∣<3|x-2|<3?
  1. (1)∣x∣<1|x|<1
  2. (2)x>−1x>-1
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
∣x−2∣<3|x-2|<3 means −1<x<5-1<x<5. (1) gives −1<x<1-1<x<1, entirely inside that interval: always yes, sufficient. (2) allows x=0x=0 (yes) and x=10x=10 (no): not sufficient.
5 Hard ≈ 90th percentile
A list of five numbers has an average (arithmetic mean) of 10. What is the median of the list?
  1. (1)The five numbers are consecutive integers.
  2. (2)The range of the list is 0.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
(1) Five consecutive integers with mean 10 are 8, 9, 10, 11, 12: median 10. (2) Range 0 means all five are equal, so each is 10: median 10. Each alone is sufficient.
6 Hard ≈ 99th percentile
If kk is a positive integer, is kk prime?
  1. (1)kk is a factor of 35.
  2. (2)k−2k-2 and k+2k+2 are both prime.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) k∈{1,5,7,35}k\in\{1,5,7,35\}: 5 and 7 are prime, 1 and 35 are not. (2) k=5k=5 works (3 and 7) but so does k=9k=9 (7 and 11). Together: of 1, 5, 7, 35 only k=5k=5 has k±2k\pm2 both prime (for 7, k+2=9k+2=9), so k=5k=5, which is prime. Sufficient together.
7 Medium ≈ 75th percentile
If b≠0b\ne0, what is the value of ab\frac ab?
  1. (1)a+bb=4\frac{a+b}{b}=4
  2. (2)2a=6b2a=6b
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
(1) ab+1=4\tfrac ab+1=4, so ab=3\tfrac ab=3. (2) a=3ba=3b, so ab=3\tfrac ab=3. Each alone is sufficient.
8 Hard ≈ 95th percentile
Is x2>xx^2>x?
  1. (1)x<0x<0
  2. (2)x2>1x^2>1
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
x2>xx^2>x fails only for 0≤x≤10\le x\le1. (1) x<0x<0 is outside that interval: always yes. (2) x2>1x^2>1 means x>1x>1 or x<−1x<-1, also outside it: always yes. Each alone is sufficient. The trap is to test only positive values under (2).
9 Medium ≈ 80th percentile
Each of the 30 students in a class studies French, Spanish, both or neither. How many study both?
  1. (1)18 study French and 16 study Spanish.
  2. (2)At least 4 students study neither.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.
If mm study neither, then 30−m30-m study at least one, and both =18+16−(30−m)=4+m=18+16-(30-m)=4+m. (1) leaves mm unknown. (2) says only m≥4m\ge4. Together, both =8=8 if m=4m=4 and 99 if m=5m=5: not sufficient.
10 Hard ≈ 90th percentile
Is xy<0xy<0?
  1. (1)x3y5<0x^3y^5<0
  2. (2)xy<0\frac xy<0
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
Odd powers keep sign, so (1) says xx and yy have opposite signs: xy<0xy<0. (2) A quotient is negative exactly when the signs differ: xy<0xy<0. Each alone is sufficient.
11 Hard ≈ 95th percentile
What is the value of the integer nn?
  1. (1)n2<10n^2<10
  2. (2)n3>nn^3>n
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.
(1) n∈{−3,…,3}n\in\{-3,\dots,3\}. (2) For integers, n3>nn^3>n holds exactly when n≥2n\ge2 (check −2,−1,0,1-2,-1,0,1: all fail). Together n=2n=2 or n=3n=3: not sufficient.
12 Medium ≈ 85th percentile
A car rental firm charges a fixed amount per day plus a fixed amount per mile. What does a 3-day rental with 200 miles cost?
  1. (1)A 1-day rental with 100 miles costs $80.
  2. (2)A 2-day rental with 150 miles costs $140.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Let dd be the daily charge and mm the per-mile charge; we need 3d+200m3d+200m. (1) d+100m=80d+100m=80 and (2) 2d+150m=1402d+150m=140 are one equation each, and neither is a multiple of 3d+200m3d+200m. Together: d=40d=40, m=0.4m=0.4, cost 120+80=$200120+80=\$200. Sufficient together.
13 Hard ≈ 95th percentile
Is the positive integer nn divisible by 12?
  1. (1)n2n^2 is divisible by 12.
  2. (2)n2n^2 is divisible by 16.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) 4∣n24\mid n^2 forces 2∣n2\mid n and 3∣n23\mid n^2 forces 3∣n3\mid n, so 6∣n6\mid n; n=6n=6 (no) and n=12n=12 (yes). (2) 16∣n216\mid n^2 forces 4∣n4\mid n; n=4n=4 (no), n=12n=12 (yes). Together 6∣n6\mid n and 4∣n4\mid n, so 12∣n12\mid n: sufficient together.
14 Hard ≈ 90th percentile
What is the average (arithmetic mean) of xx, yy and zz?
  1. (1)x+2y+3z=20x+2y+3z=20
  2. (2)3x+2y+z=163x+2y+z=16
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Neither equation alone fixes x+y+zx+y+z. Adding them: 4x+4y+4z=364x+4y+4z=36, so x+y+z=9x+y+z=9 and the mean is 3. You never need the individual values.
15 Easy ≈ 70th percentile
Revenue by region, 2023 and 2024 ($ millions)
$0$10$20$30$40$50$60$70$40$50North$35$42South$60$54East$25$34West20232024
Which region had the greatest percentage increase in revenue from 2023 to 2024?
  1. North
  2. South
  3. East
  4. West
Show answer
Answer: D. West
North 1040=25%\tfrac{10}{40}=25\%, South 735=20%\tfrac7{35}=20\%, East fell 10%, West 925=36%\tfrac9{25}=36\%. The largest absolute increase (North, +10) is not the largest percentage increase.
16 Medium ≈ 80th percentile
Revenue by region, 2023 and 2024 ($ millions)
$0$10$20$30$40$50$60$70$40$50North$35$42South$60$54East$25$34West20232024
Total revenue across the four regions was what percent greater in 2024 than in 2023?
  1. 10%
  2. 12.5%
  3. 15%
  4. 20%
  5. 25%
Show answer
Answer: B. 12.5%
2023: 40+35+60+25=16040+35+60+25=160. 2024: 50+42+54+34=18050+42+54+34=180. 20160=12.5%\tfrac{20}{160}=12.5\%.
17 Medium ≈ 75th percentile
Company X: month-end share price ($), January–June
$40$45$50$55$60$65$70JanFebMarAprMayJun$50$55$48$60$66$63
Between which two consecutive month-ends was the percentage change in the share price largest in absolute value?
  1. Jan–Feb
  2. Feb–Mar
  3. Mar–Apr
  4. Apr–May
  5. May–Jun
Show answer
Answer: C. Mar–Apr
Changes: +10%+10\%, −12.7%-12.7\% (755\tfrac{7}{55}), +25%+25\% (1248\tfrac{12}{48}), +10%+10\%, −4.5%-4.5\%. March to April is largest: the same $12 move is a bigger percentage from a lower base.
18 Easy ≈ 65th percentile
Company X: month-end share price ($), January–June
$40$45$50$55$60$65$70JanFebMarAprMayJun$50$55$48$60$66$63
An investor bought at the January close and sold at the June close. Ignoring dividends and costs, what was the return?
  1. 16%
  2. 20%
  3. 23%
  4. 26%
  5. 30%
Show answer
Answer: D. 26%
63−5050=26%\tfrac{63-50}{50}=26\%. Only the two endpoints matter.
19 Medium ≈ 80th percentile
Hours of study and test score, eight students
405060708090Score0246810Hours of study
Which is closest to the slope of the least-squares line of best fit, in points per hour of study?
  1. 1.5
  2. 2.5
  3. 3.5
  4. 4.6
  5. 6.5
Show answer
Answer: D. 4.6
Rise over run from the end points is 85−529−2≈4.7\tfrac{85-52}{9-2}\approx4.7, a good estimate. Exactly: the means are 5.5 hours and 68.5 points; ∑(x−xˉ)(y−yˉ)=192\sum(x-\bar x)(y-\bar y)=192 and ∑(x−xˉ)2=42\sum(x-\bar x)^2=42, so the slope is 19242≈4.57\tfrac{192}{42}\approx4.57.
20 Hard ≈ 95th percentile
Five equity funds, most recent year
FundReturn (%)Volatility (%)Expense ratio (%)Assets ($bn)
Alder8.412.00.453.2
Birch6.17.50.205.8
Cedar10.218.00.901.4
Delta7.39.00.352.6
Elm9.015.00.604.1
Which fund has the highest ratio of return to volatility?
  1. Alder
  2. Birch
  3. Cedar
  4. Delta
  5. Elm
Show answer
Answer: B. Birch
Alder 0.700, Birch 6.17.5=0.813\tfrac{6.1}{7.5}=0.813, Cedar 0.567, Delta 7.39=0.811\tfrac{7.3}{9}=0.811, Elm 0.600. Birch edges Delta; the highest raw return (Cedar) is last.
21 Medium ≈ 75th percentile
Five equity funds, most recent year
FundReturn (%)Volatility (%)Expense ratio (%)Assets ($bn)
Alder8.412.00.453.2
Birch6.17.50.205.8
Cedar10.218.00.901.4
Delta7.39.00.352.6
Elm9.015.00.604.1
Net return is return minus expense ratio. How many of the five funds have a net return above 8%?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
Show answer
Answer: B. 2
Net returns: Alder 7.95, Birch 5.90, Cedar 9.30, Delta 6.95, Elm 8.40. Two exceed 8%. Alder, at 8.4% gross, falls just short after costs.
22 Hard ≈ 99th percentile
Five equity funds, most recent year
FundReturn (%)Volatility (%)Expense ratio (%)Assets ($bn)
Alder8.412.00.453.2
Birch6.17.50.205.8
Cedar10.218.00.901.4
Delta7.39.00.352.6
Elm9.015.00.604.1
What is the asset-weighted average expense ratio of the five funds, to the nearest hundredth of a percent?
  1. 0.38%
  2. 0.42%
  3. 0.50%
  4. 0.55%
  5. 0.60%
Show answer
Answer: B. 0.42%
Weight each ratio by assets: 3.2(0.45)+5.8(0.20)+1.4(0.90)+2.6(0.35)+4.1(0.60)=7.233.2(0.45)+5.8(0.20)+1.4(0.90)+2.6(0.35)+4.1(0.60)=7.23, over total assets 17.1: 0.4228%0.4228\%. The simple average, 0.50%, is the trap: the largest fund (Birch) is also the cheapest.
23 Easy ≈ 70th percentile
Five equity funds, most recent year
FundReturn (%)Volatility (%)Expense ratio (%)Assets ($bn)
Alder8.412.00.453.2
Birch6.17.50.205.8
Cedar10.218.00.901.4
Delta7.39.00.352.6
Elm9.015.00.604.1
If the funds are ranked from lowest to highest return, and separately from lowest to highest volatility, how many funds hold the same position in both rankings?
  1. None
  2. Only Birch
  3. Only Birch and Cedar
  4. Only Alder
  5. All five
Show answer
Answer: E. All five
By return: Birch, Delta, Alder, Elm, Cedar. By volatility: Birch (7.5), Delta (9), Alder (12), Elm (15), Cedar (18). The orders are identical.
24 Medium ≈ 75th percentile
Five equity funds, most recent year
FundReturn (%)Volatility (%)Expense ratio (%)Assets ($bn)
Alder8.412.00.453.2
Birch6.17.50.205.8
Cedar10.218.00.901.4
Delta7.39.00.352.6
Elm9.015.00.604.1
A fund's annual fee income is its expense ratio multiplied by its assets. Which fund earns the most fee income?
  1. Alder
  2. Birch
  3. Cedar
  4. Delta
  5. Elm
Show answer
Answer: E. Elm
In $ millions: Alder 14.4, Birch 11.6, Cedar 12.6, Delta 9.1, Elm 24.6. Elm, with a mid-range fee on the second-largest asset base.
25 Medium ≈ 80th percentile
If xx and yy are positive integers, is x+yx+y even?
  1. (1)x2+y2x^2+y^2 is even.
  2. (2)xyxy is odd.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
(1) A sum of two squares is even only when the two numbers have the same parity, and then x+yx+y is even: sufficient. (2) A product is odd only when both are odd, so the sum is even: sufficient.
26 Hard ≈ 90th percentile
What is the value of the positive integer nn?
  1. (1)nn has exactly three positive divisors.
  2. (2)10<n<3010<n<30
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) means n=p2n=p^2 for a prime pp: 4, 9, 25, 49, …. (2) alone leaves 19 values. Together, only 25 lies in the range: sufficient together.
27 Medium ≈ 85th percentile
A shop sold 300 items, each priced at either $8 or $12. What was the total revenue?
  1. (1)It sold twice as many $8 items as $12 items.
  2. (2)Revenue from the $12 items was $1,200.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
(1) gives 200 and 100 items: revenue 1600+1200=$28001600+1200=\$2800. (2) gives 100 items at $12, so 200 at $8: the same $2,800. Each alone is sufficient.
28 Hard ≈ 95th percentile
A list of five distinct integers has median mm. Is the mean of the list greater than mm?
  1. (1)The largest number in the list is more than 2m2m.
  2. (2)The list is symmetric about mm: the two numbers below the median are as far below it as the two above are above it.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) is not enough: 1, 2, 3, 4, 100 has mean 22 above the median 3, but −100,−50,3,4,7-100,-50,3,4,7 also satisfies it and has mean −27.2-27.2, below. (2) forces the deviations to cancel, so the mean equals the median and the answer is a definite "no": sufficient.
29 Hard ≈ 95th percentile
If nn is a positive integer, is nn divisible by 9?
  1. (1)The sum of the digits of nn is divisible by 3.
  2. (2)n2n^2 is divisible by 27.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) only tells us 3∣n3\mid n. (2) If 3a3^a is the highest power of 3 dividing nn, then n2n^2 carries 32a3^{2a}, so 2a≥32a\ge3 forces a≥2a\ge2: 9∣n9\mid n. Sufficient.
30 Medium ≈ 85th percentile
Hours of study and test score, eight students
405060708090Score0246810Hours of study
Using the least-squares line, which is closest to the score it predicts for a student who studies 6 hours?
  1. 66
  2. 69
  3. 71
  4. 74
  5. 76
Show answer
Answer: C. 71
The line passes through the means, (5.5,68.5)(5.5,68.5), with slope about 4.57. At 6 hours: 68.5+0.5(4.57)≈70.868.5+0.5(4.57)\approx70.8.
31 Medium ≈ 75th percentile
Revenue by region, 2023 and 2024 ($ millions)
$0$10$20$30$40$50$60$70$40$50North$35$42South$60$54East$25$34West20232024
In 2024, revenue from North and West together was approximately what percent of total revenue?
  1. 35%
  2. 40%
  3. 43%
  4. 47%
  5. 52%
Show answer
Answer: D. 47%
(50+34)/180=84/180≈46.7%(50+34)/180=84/180\approx46.7\%.
32 Medium ≈ 85th percentile
Five equity funds, most recent year
FundReturn (%)Volatility (%)Expense ratio (%)Assets ($bn)
Alder8.412.00.453.2
Birch6.17.50.205.8
Cedar10.218.00.901.4
Delta7.39.00.352.6
Elm9.015.00.604.1
A client invests $100,000 in Cedar. What is the annual fee, in dollars?
  1. $90
  2. $350
  3. $600
  4. $900
  5. $1,800
Show answer
Answer: D. $900
The expense ratio is 0.90% of the amount invested: 0.009×100,000=9000.009\times100{,}000=900.
33 Hard ≈ 90th percentile
Five equity funds, most recent year
FundReturn (%)Volatility (%)Expense ratio (%)Assets ($bn)
Alder8.412.00.453.2
Birch6.17.50.205.8
Cedar10.218.00.901.4
Delta7.39.00.352.6
Elm9.015.00.604.1
Which fund would need the largest percentage increase in assets to reach $5bn?
  1. Alder
  2. Birch
  3. Cedar
  4. Delta
  5. Elm
Show answer
Answer: C. Cedar
Required increases: Alder 56%, Birch already above $5bn, Cedar 3.61.4≈257%\tfrac{3.6}{1.4}\approx257\%, Delta 92%, Elm 22%.
34 Medium ≈ 75th percentile
What is the value of xx?
  1. (1)2x+3y=122x+3y=12
  2. (2)4x+6y=244x+6y=24
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.
(2) is (1) multiplied by 2, so together they are still one equation in two unknowns. x=0,y=4x=0,y=4 and x=3,y=2x=3,y=2 both satisfy it. Two statements are only "two equations" if neither is a multiple of the other.
35 Hard ≈ 90th percentile
If nn is a positive integer, is nn divisible by 4?
  1. (1)n2n^2 is divisible by 8.
  2. (2)nn is even.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(1) n2n^2 has at least three factors of 2. The powers of 2 in a square come in pairs, so it has at least four, and nn has at least two: nn is divisible by 4. Sufficient. (2) n=2n=2 (no) and n=4n=4 (yes): not sufficient.
36 Easy ≈ 70th percentile
Pens cost pp dollars each and pencils cost qq dollars each. What is pp?
  1. (1)3p+2q=133p+2q=13
  2. (2)p+q=5p+q=5
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Each statement alone is one equation in two unknowns. Together, doubling (2) gives 2p+2q=102p+2q=10; subtracting from (1) leaves p=3p=3. Sufficient together only.
37 Medium ≈ 85th percentile
Is x>yx>y?
  1. (1)x2>y2x^2>y^2
  2. (2)x+y>0x+y>0
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) x=3,y=1x=3,y=1 (yes) or x=−3,y=1x=-3,y=1 (no). (2) x=2,y=1x=2,y=1 (yes) or x=1,y=2x=1,y=2 (no). Together: x2−y2=(x−y)(x+y)>0x^2-y^2=(x-y)(x+y)>0, and x+y>0x+y>0, so x−y>0x-y>0. Sufficient together.
38 Hard ≈ 90th percentile
What is the median of the five numbers xx, 3, 7, 9 and 12?
  1. (1)x<7x<7
  2. (2)x>3x>3
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(1) If x<7x<7, then 7, 9 and 12 are the three largest numbers, so 7 is in the middle whatever xx is. Sufficient. (2) x=4x=4 gives median 7, x=10x=10 gives median 9: not sufficient. Most people reach for C because the two statements look like a matched pair.
39 Medium ≈ 75th percentile
Of the 200 employees at a firm, how many have a university degree?
  1. (1)120 of the employees are men, and half of the men have a degree.
  2. (2)45% of the women have a degree.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) gives 60 men with degrees but says nothing about the women. (2) gives a percentage of an unknown number of women. Together: 80 women, of whom 36 have degrees, so 60+36=9660+36=96. Sufficient together.
40 Hard ≈ 95th percentile
If kk is an integer, is kk even?
  1. (1)k2+k+1k^2+k+1 is odd.
  2. (2)k3−kk^3-k is divisible by 4.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.
(1) k2+k=k(k+1)k^2+k=k(k+1) is always even, so k2+k+1k^2+k+1 is odd for every kk: no information. (2) k3−k=(k−1)k(k+1)k^3-k=(k-1)k(k+1). For odd kk, k−1k-1 and k+1k+1 are consecutive even numbers, so their product is divisible by 8: k=3k=3 gives 24. For even kk it holds when 4∣k4\mid k: k=4k=4 gives 60. So kk can be odd or even. Together still not sufficient.
41 Medium ≈ 75th percentile
What is the value of a+ba+b?
  1. (1)a2−b2=12a^2-b^2=12
  2. (2)a−b=3a-b=3
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) a=4,b=2a=4,b=2 gives 6; a=3.5,b=0.5a=3.5,b=0.5 gives 4. (2) fixes only the difference. Together, (a+b)(a−b)=12(a+b)(a-b)=12 and a−b=3a-b=3, so a+b=4a+b=4.
42 Hard ≈ 90th percentile
If xx and yy are non-zero, is 1x>1y\dfrac1x>\dfrac1y?
  1. (1)x<yx<y
  2. (2)xy>0xy>0
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(1) x=1,y=2x=1,y=2 gives yes; x=−1,y=1x=-1,y=1 gives no. (2) says only that they have the same sign. Together: divide x<yx<y by the positive number xyxy to get 1y<1x\tfrac1y<\tfrac1x. Sufficient together. Taking reciprocals reverses an inequality only when both sides have the same sign.
43 Easy ≈ 65th percentile
A bag contains only red and blue marbles. What is the ratio of red to blue marbles?
  1. (1)There are 5 more blue marbles than red.
  2. (2)If 5 red marbles were added, there would be equal numbers of red and blue.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.
(2) says the same thing as (1): blue exceeds red by 5. With 5 red and 10 blue the ratio is 1:21:2; with 10 red and 15 blue it is 2:32:3. Not sufficient even together.
44 Medium ≈ 75th percentile
What is the remainder when the positive integer nn is divided by 5?
  1. (1)The units digit of nn is 7.
  2. (2)n+3n+3 is divisible by 5.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
(1) A number ending in 7 is 2 more than a number ending in 5 or 0, so the remainder is 2. (2) n+3≡0(mod5)n+3\equiv0\pmod5 means n≡2n\equiv2. Each alone is sufficient.
45 Easy ≈ 70th percentile
What is the value of xx?
  1. (1)x2=9x^2=9
  2. (2)x3=−27x^3=-27
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) allows x=3x=3 or x=−3x=-3. (2) Cubing is one-to-one, so x=−3x=-3. Statement (2) alone is sufficient.
46 Hard ≈ 90th percentile
What is the sum of the first ten terms of an arithmetic sequence?
  1. (1)The sum of the first and tenth terms is 26.
  2. (2)The sum of the fifth and sixth terms is 26.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: D. EACH statement ALONE is sufficient.
The sum of the first ten terms is 5(a1+a10)5(a_1+a_{10}). (1) gives 5×26=1305\times26=130. (2) In an arithmetic sequence, terms equally far from the ends add to the same total, so a5+a6=a1+a10a_5+a_6=a_1+a_{10} and (2) gives the same answer. Each alone is sufficient.
47 Easy ≈ 70th percentile
By what percent did the price of stock S change from Monday's close to Wednesday's close?
  1. (1)The price rose 10% from Monday's close to Tuesday's close.
  2. (2)Wednesday's close was 10% below Monday's close.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Show answer
Answer: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(2) answers the question directly: a 10% fall. (1) covers only the first day. Statement (2) alone is sufficient. The trap is to assume the answer must combine both days.
48 Hard ≈ 90th percentile
Six delivery routes, one week
RouteDeliveriesDistance (km)Fuel (litres)Late deliveries
Ashford120340426
Bexley95410512
Crayford1502903712
Dartford80360441
Erith130505609
Farnham110275335
Which route used the least fuel per kilometre?
  1. Ashford
  2. Bexley
  3. Dartford
  4. Erith
  5. Farnham
Show answer
Answer: D. Erith
Fuel per km: Ashford 0.124, Bexley 0.124, Crayford 0.128, Dartford 0.122, Erith 0.119, Farnham 0.120. Erith is lowest, just ahead of Farnham. The longest route is the most efficient here, so eyeballing the fuel column alone points the wrong way.
49 Medium ≈ 75th percentile
Six delivery routes, one week
RouteDeliveriesDistance (km)Fuel (litres)Late deliveries
Ashford120340426
Bexley95410512
Crayford1502903712
Dartford80360441
Erith130505609
Farnham110275335
Approximately what percent of all deliveries last week were late?
  1. 4.2%
  2. 5.1%
  3. 5.8%
  4. 6.4%
  5. 7.0%
Show answer
Answer: B. 5.1%
Total deliveries 120+95+150+80+130+110=685120+95+150+80+130+110=685; late deliveries 6+2+12+1+9+5=356+2+12+1+9+5=35. 35/685≈5.1%35/685\approx5.1\%. Averaging the six routes' own rates would give about 4.6%, which is wrong because the routes are different sizes.
50 Hard ≈ 90th percentile
Six delivery routes, one week
RouteDeliveriesDistance (km)Fuel (litres)Late deliveries
Ashford120340426
Bexley95410512
Crayford1502903712
Dartford80360441
Erith130505609
Farnham110275335
How many of the six routes had a late-delivery rate below the rate for all routes combined?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6
Show answer
Answer: C. 4
The combined rate is 35/685≈5.11%35/685\approx5.11\%. Route rates: Ashford 5.00%, Bexley 2.11%, Crayford 8.00%, Dartford 1.25%, Erith 6.92%, Farnham 4.55%. Below 5.11%: Ashford, Bexley, Dartford and Farnham, four routes. Ashford is the one people miss, at 5.00%.
51 Easy ≈ 60th percentile
Units sold by quarter, Product P and Product Q
05010015020012090Q1150110Q2135160Q3180150Q4Product PProduct Q
In which quarter did Product Q sell more units than Product P?
  1. Q1
  2. Q2
  3. Q3
  4. Q4
  5. None of the quarters
Show answer
Answer: C. Q3
Compare the bars quarter by quarter: Q beats P only in Q3, 160 to 135.
52 Medium ≈ 80th percentile
Units sold by quarter, Product P and Product Q
05010015020012090Q1150110Q2135160Q3180150Q4Product PProduct Q
Combined sales of the two products in Q4 were approximately what percent higher than in Q1?
  1. 50%
  2. 57%
  3. 64%
  4. 75%
  5. 120%
Show answer
Answer: B. 57%
Q1: 120+90=210120+90=210. Q4: 180+150=330180+150=330. 330/210≈1.571330/210\approx1.571, an increase of about 57%.
53 Medium ≈ 85th percentile
Units sold by quarter, Product P and Product Q
05010015020012090Q1150110Q2135160Q3180150Q4Product PProduct Q
Over the four quarters, Product P accounted for approximately what share of the two products' combined unit sales?
  1. 53.4%
  2. 54.6%
  3. 56.0%
  4. 57.1%
  5. 60.0%
Show answer
Answer: A. 53.4%
P sold 120+150+135+180=585120+150+135+180=585 and Q sold 90+110+160+150=51090+110+160+150=510. 585/1095≈53.4%585/1095\approx53.4\%.
54 Medium ≈ 75th percentile
Monthly marketing spend and new customers, 10 months
100150200250300New customers061218243036Spend (£000)
The relationship between monthly spend and new customers is (1), and each additional £1,000 of spend is associated with approximately (2) additional new customers.

(1) strongly negative · close to zero · moderately positive · strongly positive

(2) 2 · 4 · 7 · 12

Show answer
Answer: (1) strongly positive; (2) 7
The points lie almost on a straight rising line, so the relationship is strongly positive (the correlation is about 0.998). For the slope, compare the ends: spend rises from 10 to 33 (23 thousand) while customers rise from 120 to 290 (170), about 7.4 per £1,000; the least-squares slope is 7.26, so 7 is closest.
55 Medium ≈ 80th percentile
Company Y: quarter-end share price (£), Q1–Q8
£30£35£40£45£50£55£60£65Q1Q2Q3Q4Q5Q6Q7Q8£40£44£43£50£48£57£55£60
The largest quarter-on-quarter percentage increase in the price occurred from (1), and from Q1 to Q8 the price rose by (2).

(1) Q1 to Q2 · Q3 to Q4 · Q5 to Q6 · Q7 to Q8

(2) 20% · 35% · 50% · 60%

Show answer
Answer: (1) Q5 to Q6; (2) 50%
Percentage increases: Q1→Q2 10%, Q3→Q4 16.3%, Q5→Q6 18.75%, Q7→Q8 9.1%. The biggest jump in pounds (7, from 43 to 50) is not the biggest in percentage terms: 48 to 57 is 9 on a base of 48. Overall, 40 to 60 is a 50% rise.
56 Medium ≈ 85th percentile
Units sold by region (thousands), 2023 and 2024
0204060801001208072North6470South5045East120100West9099Central20232024
The region with the greatest percentage decrease from 2023 to 2024 was (1), and total units sold in 2024 were approximately (2) of the 2023 total.

(1) North · East · West · Central

(2) 88% · 92% · 96% · 104%

Show answer
Answer: (1) West; (2) 96%
Changes: North −10%, South +9.4%, East −10%, West −16.7%, Central +10%, so West fell most. Totals: 404 thousand in 2023 and 386 thousand in 2024, and 386/404 ≈ 95.5%, so about 96%.
57 Easy ≈ 70th percentile
Allocation of a £2.4 million annual budget
45%Staff45%20%Marketing20%15%IT15%12%Facilities12%8%Training8%
Staff costs exceed marketing costs by (1), and Facilities and Training together account for (2) Marketing.

(1) £480,000 · £600,000 · £720,000 · £1,080,000

(2) a smaller share than · the same share as · a larger share than

Show answer
Answer: (1) £600,000; (2) the same share as
Staff is 45% and Marketing 20%: the gap is 25% of £2.4 million, £600,000. Facilities (12%) plus Training (8%) is 20%, the same as Marketing.
58 Medium ≈ 80th percentile
Age and resale value of ten used cars of one model
04812162024Value (£000)01234567891011Age (years)
Each additional year of age is associated with a change in value of approximately (1), and (2) of the ten cars are worth more than £10,000.

(1) −£4,000 · −£2,000 · −£500 · +£1,000

(2) 4 · 5 · 6 · 7

Show answer
Answer: (1) −£2,000; (2) 6
Value falls from 24 to 6 thousand over 9 years, 2 thousand a year; the least-squares slope is −2.01. Cars above £10,000: ages 1 to 6 (24, 21, 19, 16.5, 14, 12.5). The seven-year-old car is worth exactly £10,000, which is not more than £10,000, so the count is 6.
59 Medium ≈ 75th percentile
Revenue and cost by month (£000)
100110120130140150160170JanFebMarAprMayJun120135128150142160110140120138150145RevenueCost
Profit (revenue minus cost) was greatest in (1), and cost exceeded revenue in (2) of the six months.

(1) January · March · April · June

(2) one · two · three · four

Show answer
Answer: (1) June; (2) two
Monthly profit: Jan 10, Feb −5, Mar 8, Apr 12, May −8, Jun 15. June is the largest, and February and May are the two loss-making months. Where the lines cross is where the sign changes, so reading the crossings is the quick check.
60 Medium ≈ 85th percentile
One-way commute times of 200 employees (number of employees)
0102030405060180–94610–195220–294030–392840–491650+
The median commute time lies in the interval (1) minutes, and (2) of employees commute for 40 minutes or more.

(1) 10–19 · 20–29 · 30–39 · 40–49

(2) 14% · 22% · 28% · 44%

Show answer
Answer: (1) 20–29; (2) 22%
With 200 employees the median sits between the 100th and 101st values. Running totals: 18, 64, 116, so both fall in 20–29. For 40 minutes or more: (28 + 16)/200 = 22%.
61 Medium ≈ 80th percentile
Eight stores, last financial year
StoreRevenue (£m)EmployeesFloor area (m²)Customer rating
A2.4301,8004.1
B1.8201,2004.5
C3.1422,5003.9
D1.2169004.6
E2.7252,1004.0
F2.0281,6004.3
G3.5502,8003.7
H1.5151,1004.4
For each statement, select Yes if it is true of the stores in the table and No otherwise.
YesNoStatement
The store with the highest revenue per employee also has the highest customer rating.
At least half of the stores have a floor area above 1,500 m².
The median revenue of the eight stores is above £2.2 million.
Show answer
Answer: 1: No; 2: Yes; 3: No
(1) No. Revenue per employee is highest at E (£108,000) but the highest rating is D's 4.6. (2) Yes: A, C, E, F and G, five of eight. (3) No. The sorted revenues are 1.2, 1.5, 1.8, 2.0, 2.4, 2.7, 3.1, 3.5, so the median is (2.0 + 2.4)/2 = 2.2, which is not above 2.2.
62 Medium ≈ 85th percentile
Six equity funds
Fund1-year return (%)5-year annualised return (%)Annual fee (%)Volatility (%)
Aster6.27.80.4511
Beech9.16.50.9017
Cedar4.85.90.207
Dahlia7.58.40.6514
Elm3.96.80.156
Fern8.27.10.7515
For each statement, select True if the data in the table support it, and False otherwise.
TrueFalseStatement
The fund with the highest 1-year return also has the highest 5-year annualised return.
Every fund with an annual fee above 0.5% has a volatility of at least 14%.
Ranked by 5-year annualised return minus annual fee, Cedar comes last.
Show answer
Answer: 1: False; 2: True; 3: False
(1) False: Beech leads on 1-year (9.1) but Dahlia leads on 5-year (8.4). (2) True: the funds charging more than 0.5% are Beech (17), Dahlia (14) and Fern (15). (3) False: net figures are Aster 7.35, Beech 5.60, Cedar 5.70, Dahlia 7.75, Elm 6.65, Fern 6.35. Beech is last, because its high fee eats a middling return.
63 Medium ≈ 85th percentile
Six long-haul routes from London Heathrow, one quarter
RouteFlightsOn time (%)Average delay (min)Load factor (%)
New York JFK420781486
Dubai36084982
Singapore21088790
Hong Kong180722179
Boston300811284
Chicago240692477
For each statement, select Yes if it is supported by the table and No otherwise.
YesNoStatement
The route with the most flights has the lowest on-time percentage.
Every route with an on-time rate below 80% has an average delay above 12 minutes.
More flights were late on the New York route than on the Chicago route.
Show answer
Answer: 1: No; 2: Yes; 3: Yes
(1) No: New York has the most flights (420) but Chicago has the lowest on-time rate (69%). (2) Yes: the routes below 80% are New York (14 min), Hong Kong (21) and Chicago (24). (3) Yes: late flights are 420 × 22% ≈ 92 for New York and 240 × 31% ≈ 74 for Chicago. A lower rate on a much larger base still gives more late flights.
64 Hard ≈ 90th percentile
Five factories making the same component, one quarter
FactoryUnits (000)Defective unitsDefects per 1,000 unitsCost per unit (£)
Leeds1203603.04.20
Lyon951902.04.80
Porto1405604.03.90
Brno801201.55.10
Gdańsk1102752.54.40
For each statement, select Yes if it is true according to the table and No otherwise.
YesNoStatement
Across the five factories, a lower cost per unit always goes with a higher defect rate.
Porto makes more than a third of all units.
Without Porto, the combined defect rate of the other four factories would be below 2.5 per 1,000 units.
Show answer
Answer: 1: Yes; 2: No; 3: Yes
(1) Yes: sorted by cost (Porto 3.90, Leeds 4.20, Gdańsk 4.40, Lyon 4.80, Brno 5.10) the defect rates run 4.0, 3.0, 2.5, 2.0, 1.5, strictly falling. (2) No: 140 of 545 thousand is about 26%. (3) Yes: the other four make 405 thousand units with 945 defects, 2.33 per 1,000. A combined rate is total defects over total units, not the average of the four rates.
65 Hard ≈ 90th percentile
Six master’s programmes, one admissions year
ProgrammeApplicantsOffersEnrolledAverage GMAT
P12,400480312705
P21,800270216690
P33,100372260720
P4900225135670
P51,500330198700
P62,200286229710
For each statement, select True if it is supported by the table and False otherwise.
TrueFalseStatement
The programme with the lowest offer rate (offers ÷ applicants) has the highest average GMAT.
Yield (enrolled ÷ offers) is highest for the programme with the most applicants.
At least four of the six programmes make offers to more than 15% of applicants.
Show answer
Answer: 1: True; 2: False; 3: False
(1) True: P3's offer rate is 12%, the lowest, and its average GMAT (720) is the highest. (2) False: P3 has the most applicants but its yield is 69.9%, while P6 (80.1%) and P2 (80.0%) are higher. (3) False: offer rates are 20, 15, 12, 25, 22 and 13%. Only three exceed 15%; P2 is exactly 15%.
66 Medium ≈ 85th percentile
Annual energy use of five office buildings
BuildingFloor area (m²)Electricity (MWh)Gas (MWh)Occupants
Alpha5,000600400250
Beta3,200480200180
Gamma8,000720880400
Delta2,50035015090
Epsilon6,000540660320
For each statement, select Yes if it is true according to the table and No otherwise.
YesNoStatement
Delta uses the most electricity per square metre.
Total energy use (electricity plus gas) per occupant is lowest in Gamma.
Gas makes up more than half of total energy use in exactly two buildings.
Show answer
Answer: 1: No; 2: No; 3: Yes
(1) No: electricity per m² is 0.12, 0.15, 0.09, 0.14 and 0.09 MWh, highest in Beta. (2) No: energy per occupant is 4.0, 3.78, 4.0, 5.56 and 3.75 MWh, lowest in Epsilon. (3) Yes: gas shares are 40%, 29%, 55%, 30% and 55%, above half in Gamma and Epsilon only.
67 Medium ≈ 80th percentile
A café sold 40 coffees and 25 teas on Monday for £188, and 30 coffees and 35 teas on Tuesday for £180, at unchanged prices. Select the price of a coffee and the price of a tea.
CoffeeTea
£2.40
£2.60
£2.80
£3.00
£3.20
£3.40
Show answer
Answer: Coffee: £3.20; Tea: £2.40
Multiply Monday by 3 and Tuesday by 4: 120c + 75t = 564 and 120c + 140t = 720. Subtracting, 65t = 156, so t = £2.40, and then 40c = 188 − 60 = 128 gives c = £3.20. Check Tuesday: 96 + 84 = 180.
68 Easy ≈ 70th percentile
Working together at constant rates, machines P and Q fill 1,200 bottles in 4 hours. Working alone, P fills 1,200 bottles in 6 hours. Select the number of bottles P fills per hour and the number Q fills per hour.
P per hourQ per hour
100
150
200
250
300
350
Show answer
Answer: P per hour: 200; Q per hour: 100
P's rate is 1,200/6 = 200 an hour. Together they manage 1,200/4 = 300 an hour, so Q adds 100.
69 Medium ≈ 75th percentile
Two numbers x and y, with x < y, satisfy x + y = 10 and xy = 21. Select the value of x and the value of y.
xy
1
3
5
7
9
21
Show answer
Answer: x: 3; y: 7
x and y are the roots of t² − 10t + 21 = 0, which factorises as (t − 3)(t − 7). With x < y, x = 3 and y = 7. The condition x < y is what makes the answer unique.
70 Medium ≈ 85th percentile
In a class of 30 students, 18 study French and 15 study Spanish; a student may study both, one, or neither. Select the minimum possible and the maximum possible number of students who study both languages.
MinimumMaximum
0
3
5
12
15
18
Show answer
Answer: Minimum: 3; Maximum: 15
The overlap is smallest when as few students as possible study neither: 18 + 15 − 30 = 3. It is largest when every Spanish student also studies French: 15. Everything between is possible.
71 Medium ≈ 80th percentile
Solution A is 20% acid and solution B is 50% acid. A chemist mixes them to make 30 litres that are 40% acid. Select the litres of A and the litres of B used.
Litres of ALitres of B
5
10
15
20
25
30
Show answer
Answer: Litres of A: 10; Litres of B: 20
The mixture needs 12 litres of acid. With a + b = 30 and 0.2a + 0.5b = 12, substituting b = 30 − a gives 15 − 0.3a = 12, so a = 10 and b = 20. The blend's 40% sits twice as far from 20% as from 50%, so there is twice as much B.
72 Medium ≈ 75th percentile
A retailer sets its price 50% above a unit cost of £20 and wants revenue of exactly £3,600 from one product. Select the price and the number of units it must sell.
Price (£)Units
20
30
45
90
120
180
Show answer
Answer: Price (£): 30; Units: 120
Price = 1.5 × £20 = £30. Units = 3,600 / 30 = 120.
73 Hard ≈ 90th percentile
Five meetings A to E are held on Monday to Friday of one week, one a day. B is on Wednesday; D is on the day immediately after A; C is on a later day than D; and E is not on Monday. Select the day on which A must be held and the day on which D must be held.
AD
Monday
Tuesday
Wednesday
Thursday
Friday
Show answer
Answer: A: Monday; D: Tuesday
A and D are consecutive and B holds Wednesday, so A–D is Mon–Tue or Thu–Fri. Thu–Fri leaves no later day for C. So A is Monday and D is Tuesday, with C and E on Thursday and Friday in either order. Both A and D are forced even though the full schedule is not.
74 Hard ≈ 95th percentile
A company's revenue grew from £2.0 million to £2.42 million over two years at a constant annual rate of r%. Over the same two years its costs fell from £1.6 million to £1.296 million at a constant annual rate of s%. Select r and s.
rs
5%
8%
10%
11%
20%
21%
Show answer
Answer: r: 10%; s: 10%
2.42/2.0 = 1.21 = 1.1², so revenue grew 10% a year. 1.296/1.6 = 0.81 = 0.9², so costs fell 10% a year. The two-year changes (21% up, 19% down) are the traps: compounding means you take square roots of the factors, not halves of the percentages.
75 Medium ≈ 75th percentile

Operations memo

Goods are shipped from our warehouse in Leeds to three regional centres. We are considering moving to a warehouse in Birmingham. Shipping is charged per pallet per 100 km: £1.20 under the current contract, and £1.05 under the contract offered for Birmingham. Moving would cost £180,000 once.

Distances

Road distance to each centre (km)
CentreFrom LeedsFrom Birmingham
London315190
Bristol330140
Manchester70140

Monthly volumes

Pallets shipped per month
CentrePallets
London400
Bristol250
Manchester350
What is the current monthly shipping cost from Leeds?
  1. £2,330
  2. £2,796
  3. £3,105
  4. £3,520
  5. £4,190
Show answer
Answer: B. £2,796
Pallet-distance: 400 × 3.15 + 250 × 3.30 + 350 × 0.70 = 1,260 + 825 + 245 = 2,330 pallet-hundreds of km. At £1.20 each, £2,796. £2,330 is the trap: the distance total without the rate.
76 Medium ≈ 85th percentile

Operations memo

Goods are shipped from our warehouse in Leeds to three regional centres. We are considering moving to a warehouse in Birmingham. Shipping is charged per pallet per 100 km: £1.20 under the current contract, and £1.05 under the contract offered for Birmingham. Moving would cost £180,000 once.

Distances

Road distance to each centre (km)
CentreFrom LeedsFrom Birmingham
London315190
Bristol330140
Manchester70140

Monthly volumes

Pallets shipped per month
CentrePallets
London400
Bristol250
Manchester350
If the company moved to Birmingham under the new contract, approximately how many years would the monthly saving take to repay the cost of moving?
  1. 4
  2. 8
  3. 13
  4. 18
  5. 24
Show answer
Answer: C. 13
From Birmingham: 400 × 1.9 + 250 × 1.4 + 350 × 1.4 = 1,600 pallet-hundreds of km at £1.05, so £1,680 a month. Saving: 2,796 − 1,680 = £1,116 a month. 180,000 / 1,116 ≈ 161 months, about 13.4 years.
77 Medium ≈ 85th percentile

Operations memo

Goods are shipped from our warehouse in Leeds to three regional centres. We are considering moving to a warehouse in Birmingham. Shipping is charged per pallet per 100 km: £1.20 under the current contract, and £1.05 under the contract offered for Birmingham. Moving would cost £180,000 once.

Distances

Road distance to each centre (km)
CentreFrom LeedsFrom Birmingham
London315190
Bristol330140
Manchester70140

Monthly volumes

Pallets shipped per month
CentrePallets
London400
Bristol250
Manchester350
For each statement, select Yes if it follows from the information provided and No otherwise.
YesNoStatement
Moving to Birmingham shortens the distance to every regional centre.
Under the new contract, shipping to London alone would cost more than £750 a month from Birmingham.
Bristol accounts for less than a quarter of the current monthly shipping cost.
Show answer
Answer: 1: No; 2: Yes; 3: No
(1) No: Manchester goes from 70 km to 140 km. (2) Yes: 400 × 1.9 × 1.05 = £798. (3) No: Bristol costs 250 × 3.30 × 1.20 = £990 of £2,796, about 35%.
78 Easy ≈ 70th percentile

Trial design

600 patients with the same infection were assigned at random, 300 to the new drug and 300 to a placebo. The main outcome is recovery within 14 days of starting treatment. Side effects were recorded by patients' doctors.

Results

Outcomes after 14 days
GroupPatientsRecoveredSide effects reported
Drug30019542
Placebo30015018

Cost note

A course of the drug costs £240. A day in hospital costs £400. On average, a patient who recovers within 14 days leaves hospital 3 days earlier than one who does not.
By how many percentage points did the drug raise the 14-day recovery rate compared with the placebo?
  1. 5
  2. 10
  3. 15
  4. 20
  5. 30
Show answer
Answer: C. 15
Drug: 195/300 = 65%. Placebo: 150/300 = 50%. The difference is 15 percentage points. As a relative increase it would be 30%, which is the trap answer.
79 Medium ≈ 85th percentile

Trial design

600 patients with the same infection were assigned at random, 300 to the new drug and 300 to a placebo. The main outcome is recovery within 14 days of starting treatment. Side effects were recorded by patients' doctors.

Results

Outcomes after 14 days
GroupPatientsRecoveredSide effects reported
Drug30019542
Placebo30015018

Cost note

A course of the drug costs £240. A day in hospital costs £400. On average, a patient who recovers within 14 days leaves hospital 3 days earlier than one who does not.
About how many patients must be treated with the drug, rather than the placebo, for one additional patient to recover within 14 days?
  1. 3
  2. 5
  3. 7
  4. 10
  5. 15
Show answer
Answer: C. 7
The drug adds 15 recoveries per 100 patients, so one extra recovery per 100/15 ≈ 6.7 patients, about 7. This is the number needed to treat: the reciprocal of the absolute difference in rates.
80 Hard ≈ 90th percentile

Trial design

600 patients with the same infection were assigned at random, 300 to the new drug and 300 to a placebo. The main outcome is recovery within 14 days of starting treatment. Side effects were recorded by patients' doctors.

Results

Outcomes after 14 days
GroupPatientsRecoveredSide effects reported
Drug30019542
Placebo30015018

Cost note

A course of the drug costs £240. A day in hospital costs £400. On average, a patient who recovers within 14 days leaves hospital 3 days earlier than one who does not.
For each statement, select True if it follows from the information provided and False otherwise.
TrueFalseStatement
More than twice as many drug patients as placebo patients reported side effects.
For every 100 patients treated, the drug costs more than it saves in hospital days.
More than a fifth of the patients given the drug reported side effects.
Show answer
Answer: 1: True; 2: True; 3: False
(1) True: 42 is more than twice 18. (2) True: 100 courses cost £24,000, while the 15 extra recoveries save 15 × 3 × £400 = £18,000. (3) False: 42/300 = 14%.
81 Medium ≈ 75th percentile

Email from the CFO

Engineering headcount is 40 at the start of the year. We plan 18 hires. Each hire costs £12,000 in recruitment fees, and each engineer is paid £85,000 a year. New hires start on the first day of the quarter shown and are paid from that day.

Hiring schedule

Planned hires
QuarterHires
Q14
Q26
Q35
Q43

Budget

This year’s budget (£000)
ItemBudget
Recruitment fees200
Salaries of this year’s new hires900
How do this year's recruitment fees compare with the budget?
  1. £16,000 under budget
  2. Exactly on budget
  3. £16,000 over budget
  4. £24,000 over budget
  5. £36,000 over budget
Show answer
Answer: C. £16,000 over budget
18 hires × £12,000 = £216,000 against a budget of £200,000: £16,000 over.
82 Hard ≈ 90th percentile

Email from the CFO

Engineering headcount is 40 at the start of the year. We plan 18 hires. Each hire costs £12,000 in recruitment fees, and each engineer is paid £85,000 a year. New hires start on the first day of the quarter shown and are paid from that day.

Hiring schedule

Planned hires
QuarterHires
Q14
Q26
Q35
Q43

Budget

This year’s budget (£000)
ItemBudget
Recruitment fees200
Salaries of this year’s new hires900
What is this year's salary cost for the new hires?
  1. £816,000
  2. £900,000
  3. £998,750
  4. £1,020,000
  5. £1,530,000
Show answer
Answer: C. £998,750
Count engineer-quarters: Q1 hires work 4 quarters (4 × 4 = 16), Q2 hires 3 (18), Q3 hires 2 (10), Q4 hires 1 (3), 47 in all. A quarter's salary is 85,000/4 = £21,250, so 47 × 21,250 = £998,750. £1,530,000 is what you get by paying all 18 for the full year.
83 Hard ≈ 90th percentile

Email from the CFO

Engineering headcount is 40 at the start of the year. We plan 18 hires. Each hire costs £12,000 in recruitment fees, and each engineer is paid £85,000 a year. New hires start on the first day of the quarter shown and are paid from that day.

Hiring schedule

Planned hires
QuarterHires
Q14
Q26
Q35
Q43

Budget

This year’s budget (£000)
ItemBudget
Recruitment fees200
Salaries of this year’s new hires900
For each statement, select Yes if it follows from the information provided and No otherwise.
YesNoStatement
Moving all Q4 hires to Q1 would take new-hire salaries more than £150,000 over budget.
Headcount at the end of Q3 will be 57.
More than half of this year's hires start in the first half of the year.
Show answer
Answer: 1: Yes; 2: No; 3: Yes
(1) Yes: the three Q4 hires would each work 3 more quarters, 9 more engineer-quarters, so 56 × £21,250 = £1,190,000, £290,000 over the £900,000 budget. (2) No: 40 + 4 + 6 + 5 = 55. (3) Yes: 10 of the 18 start in Q1 or Q2.

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