Skip to content
Work Practice Products Coding interviews Machine learning coding Quant developer HFT course Blog Method Why me About Book a call

Practice · Executive Assessment · Quantitative Reasoning

EA Quant practice questions

61 questions with worked solutions. Problem solving and data sufficiency without a calculator, including chart questions, graded easy to hard.

15 easy · 27 medium · 19 hard · EA Quantitative Reasoning

Practise timed: 14 questions · 30 min All Executive Assessment topics

1 Easy EA Quantitative Reasoning
After a 20% discount, a jacket costs £80. What was its price before the discount?
  1. £96
  2. £100
  3. £104
  4. £110
  5. £120
Show answer
Answer: B. £100
£80 is 80% of the original, so the original is 80 / 0.8 = £100. Adding 20% of £80 (giving £96) is the classic slip: the discount was taken from the original price, not the sale price.
2 Easy EA Quantitative Reasoning
If 3x−7=113x-7=11, what is the value of 2x+12x+1?
  1. 9
  2. 11
  3. 13
  4. 15
  5. 19
Show answer
Answer: C. 13
3x=183x=18, so x=6x=6 and 2x+1=132x+1=13.
3 Easy EA Quantitative Reasoning
The average (arithmetic mean) of four numbers is 15. Three of them are 12, 14 and 19. What is the fourth?
  1. 13
  2. 14
  3. 15
  4. 16
  5. 17
Show answer
Answer: C. 15
The four numbers total 4×15=604\times15=60; the three known ones total 45. The fourth is 15.
4 Easy EA Quantitative Reasoning
A car travels 150 km in 2 hours 30 minutes. What is its average speed, in km per hour?
  1. 50
  2. 55
  3. 60
  4. 65
  5. 75
Show answer
Answer: C. 60
150 / 2.5 = 60. Writing 2 hours 30 minutes as 2.3 hours, rather than 2.5, is the trap.
5 Easy EA Quantitative Reasoning
What is 15% of 40% of 500?
  1. 20
  2. 30
  3. 45
  4. 60
  5. 75
Show answer
Answer: B. 30
40% of 500 is 200, and 15% of 200 is 30. Equivalently, 0.15×0.4=0.060.15\times0.4=0.06, and 6% of 500 is 30.
6 Easy EA Quantitative Reasoning
The ratio of managers to other staff in an office is 2:92:9. There are 44 people in the office. How many are managers?
  1. 4
  2. 6
  3. 8
  4. 9
  5. 11
Show answer
Answer: C. 8
2 + 9 = 11 parts make 44 people, so a part is 4 and managers are 2×4=82\times4=8.
7 Easy EA Quantitative Reasoning
If xy=34\dfrac{x}{y}=\dfrac34 and y=20y=20, what is x+yx+y?
  1. 27
  2. 32
  3. 35
  4. 38
  5. 40
Show answer
Answer: C. 35
x=34×20=15x=\tfrac34\times20=15, so x+y=35x+y=35.
8 Easy EA Quantitative Reasoning
Quarterly revenue of a consultancy (£ million)
£0£5£10£15£20£12Q1£15Q2£18Q3£15Q4
In which quarter did revenue fall compared with the quarter before?
  1. Q1
  2. Q2
  3. Q3
  4. Q4
  5. In none of the quarters
Show answer
Answer: D. Q4
Revenue rose from 12 to 15 to 18, then fell to 15 in Q4.
9 Medium EA Quantitative Reasoning
Quarterly revenue of a consultancy (£ million)
£0£5£10£15£20£12Q1£15Q2£18Q3£15Q4
By what percent did revenue increase from Q1 to Q3?
  1. 6%
  2. 33%
  3. 50%
  4. 60%
  5. 150%
Show answer
Answer: C. 50%
From 12 to 18 is an increase of 6 on a base of 12: 50%. 150% is 18 as a percentage of 12, not the increase.
10 Medium EA Quantitative Reasoning
A shop's sales rose by 10% in one year and fell by 10% the next. What was the overall change over the two years?
  1. −2%
  2. −1%
  3. 0%
  4. +1%
  5. +2%
Show answer
Answer: B. −1%
1.1×0.9=0.991.1\times0.9=0.99, a 1% fall. The second change is applied to a larger base, so it outweighs the first.
11 Medium EA Quantitative Reasoning
How many integers from 1 to 100 inclusive are divisible by 4 or by 6?
  1. 25
  2. 29
  3. 33
  4. 41
  5. 50
Show answer
Answer: C. 33
Multiples of 4: 25. Multiples of 6: 16. Those counted twice are multiples of 12: 8. So 25+16−8=3325+16-8=33.
12 Medium EA Quantitative Reasoning
Pipe A fills an empty tank in 3 hours; pipe B, open at the same time, empties a full tank in 6 hours. If both are opened when the tank is empty, how many hours does it take to fill?
  1. 2
  2. 4
  3. 4.5
  4. 6
  5. 9
Show answer
Answer: D. 6
Net rate: 13−16=16\tfrac13-\tfrac16=\tfrac16 of the tank an hour, so 6 hours.
13 Medium EA Quantitative Reasoning
£2,000 is invested for 3 years at 4% a year. How much more interest does it earn if interest is compounded annually rather than simple?
  1. £4.80
  2. £9.73
  3. £12.48
  4. £24.00
  5. £49.73
Show answer
Answer: B. £9.73
Simple interest: 3×80=£2403\times80=£240. Compound: 2000(1.043−1)=2000×0.124864=£249.732000(1.04^3-1)=2000\times0.124864=£249.73. The difference is £9.73: interest earned on earlier interest.
14 Medium EA Quantitative Reasoning
Two numbers have a sum of 40 and a difference of 12. What is their product?
  1. 280
  2. 336
  3. 364
  4. 400
  5. 480
Show answer
Answer: C. 364
The numbers are (40+12)/2=26(40+12)/2=26 and (40−12)/2=14(40-12)/2=14, and 26×14=36426\times14=364.
15 Medium EA Quantitative Reasoning
A committee of 5 is chosen from 7 people. How many different committees include one particular person?
  1. 6
  2. 15
  3. 21
  4. 35
  5. 42
Show answer
Answer: B. 15
With that person in, choose the other 4 from the remaining 6: (64)=15\binom64=15.
16 Medium EA Quantitative Reasoning
A price of £120 is increased by 25% and the new price is then reduced by 20%. What is the final price?
  1. £114
  2. £115
  3. £120
  4. £125
  5. £126
Show answer
Answer: C. £120
1.25×0.8=11.25\times0.8=1, so the price returns to £120. A 25% rise and a 20% fall cancel exactly because 54×45=1\tfrac54\times\tfrac45=1.
17 Medium EA Quantitative Reasoning
A 12-litre mixture is 25% juice. How many litres of juice must be added to make it 40% juice?
  1. 1.8
  2. 2
  3. 3
  4. 4.8
  5. 6
Show answer
Answer: C. 3
It holds 3 litres of juice. After adding xx litres, (3+x)/(12+x)=0.4(3+x)/(12+x)=0.4, so 3+x=4.8+0.4x3+x=4.8+0.4x and x=3x=3.
18 Medium EA Quantitative Reasoning
If nn is an odd integer, which of the following must be even?
  1. n+2n+2
  2. 3n3n
  3. n2\displaystyle n^2
  4. n2+1\displaystyle n^2+1
  5. 2n+12n+1
Show answer
Answer: D. n2+1\displaystyle n^2+1
An odd number squared is odd, so n2+1n^2+1 is even. The other four are all odd for odd nn.
19 Medium EA Quantitative Reasoning
What is the average (arithmetic mean) of all the integers from −10-10 to 30 inclusive?
  1. 0
  2. 10
  3. 15
  4. 20
  5. 30
Show answer
Answer: B. 10
For consecutive integers the mean is the average of the first and last: (−10+30)/2=10(-10+30)/2=10.
20 Medium EA Quantitative Reasoning
What is the units digit of 132713^{27}?
  1. 1
  2. 3
  3. 7
  4. 9
  5. 0
Show answer
Answer: C. 7
Only the units digit 3 matters. Powers of 3 end in 3, 9, 7, 1 and repeat every four. 27=4×6+327=4\times6+3, so the digit is the third in the cycle: 7.
21 Medium EA Quantitative Reasoning
Month-end share price (£), January–June
£40£45£50£55£60£65JanFebMarAprMayJun£50£55£44£48£60£57
What was the largest percentage fall in the share price from one month-end to the next?
  1. 5%
  2. 10%
  3. 12%
  4. 20%
  5. 25%
Show answer
Answer: D. 20%
The falls are February to March (55 to 44) and May to June (60 to 57). 11 on a base of 55 is 20%; 3 on 60 is 5%.
22 Medium EA Quantitative Reasoning
The length of a rectangle is increased by 20% and its width is decreased by 10%. By what percent does its area change?
  1. −2%
  2. +2%
  3. +8%
  4. +10%
  5. +30%
Show answer
Answer: C. +8%
1.2×0.9=1.081.2\times0.9=1.08: an 8% increase. Adding the percentages (10%) ignores that the second change applies to the changed quantity.
23 Hard EA Quantitative Reasoning
What is the sum of the first 20 odd positive integers minus the sum of the first 20 even positive integers?
  1. −40
  2. −20
  3. 0
  4. 20
  5. 40
Show answer
Answer: B. −20
Pair them: (1−2)+(3−4)+⋯+(39−40)(1-2)+(3-4)+\dots+(39-40) is 20 pairs of −1-1, so −20-20. (The sums are 400 and 420.)
24 Hard EA Quantitative Reasoning
Two different cards are drawn at random from ten cards numbered 1 to 10. What is the probability that their numbers add up to 11?
  1. 110\displaystyle \tfrac1{10}
  2. 19\displaystyle \tfrac19
  3. 15\displaystyle \tfrac15
  4. 29\displaystyle \tfrac29
  5. 14\displaystyle \tfrac14
Show answer
Answer: B. 19\displaystyle \tfrac19
The pairs summing to 11 are (1,10), (2,9), (3,8), (4,7), (5,6): five out of (102)=45\binom{10}2=45, so 19\tfrac19. Equivalently, whatever the first card is, exactly one of the nine remaining cards completes 11.
25 Hard EA Quantitative Reasoning
A company's revenue grew by 20% and its costs by 10%, and as a result its profit (revenue minus costs) grew by 40%. What fraction of the original revenue were the original costs?
  1. 13\displaystyle \tfrac13
  2. 12\displaystyle \tfrac12
  3. 35\displaystyle \tfrac35
  4. 23\displaystyle \tfrac23
  5. 34\displaystyle \tfrac34
Show answer
Answer: D. 23\displaystyle \tfrac23
1.2R−1.1C=1.4(R−C)1.2R-1.1C=1.4(R-C), so 0.3C=0.2R0.3C=0.2R and C/R=23C/R=\tfrac23. Check with R=3R=3, C=2C=2: profit goes from 1 to 3.6−2.2=1.43.6-2.2=1.4.
26 Hard EA Quantitative Reasoning
Eight workers can finish a job in 15 days. After 5 days, 2 of them leave and the rest continue at the same rate. How many days does the whole job take?
  1. 18
  2. 18⅓
  3. 20
  4. 21
  5. 25
Show answer
Answer: B. 18⅓
The job is 8×15=1208\times15=120 worker-days. After 5 days, 40 are done and 80 remain for 6 workers: 131313\tfrac13 days. Total 181318\tfrac13.
27 Hard EA Quantitative Reasoning
How many integers xx satisfy x2−5x+6<0x^2-5x+6<0?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4
Show answer
Answer: A. 0
x2−5x+6=(x−2)(x−3)x^2-5x+6=(x-2)(x-3) is negative only for 2<x<32<x<3, which contains no integer. The answer is 0; answering 2 counts the endpoints, where the expression is 0, not negative.
28 Hard EA Quantitative Reasoning
If 2a⋅4b=642^a\cdot4^b=64 and a−b=1a-b=1, what is the value of aa?
  1. 2
  2. 83\displaystyle \tfrac83
  3. 3
  4. 103\displaystyle \tfrac{10}3
  5. 4
Show answer
Answer: B. 83\displaystyle \tfrac83
2a⋅22b=262^a\cdot2^{2b}=2^6, so a+2b=6a+2b=6. With a=b+1a=b+1: 3b+1=63b+1=6, b=53b=\tfrac53, a=83a=\tfrac83. Nothing says the exponents are integers.
29 Easy EA Quantitative Reasoning
What is the value of xx?
  1. (1)2x+5=172x+5=17
  2. (2)x2=36x^2=36
  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) gives x=6x=6. (2) allows 6 or −6. Statement (1) alone is sufficient.
30 Easy EA Quantitative Reasoning
Is the integer nn even?
  1. (1)n+1n+1 is odd.
  2. (2)3n3n 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: D. EACH statement ALONE is sufficient.
(1) n+1n+1 odd means nn is even. (2) 3 is odd, so 3n3n is even only when nn is even. Each alone is sufficient.
31 Easy EA Quantitative Reasoning
What is the remainder when the positive integer nn is divided by 5?
  1. (1)nn is odd.
  2. (2)The units digit of nn is 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: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) 1, 3, 5 give remainders 1, 3, 0: not sufficient. (2) A number ending in 3 leaves remainder 3. Statement (2) alone is sufficient.
32 Medium EA Quantitative Reasoning
What is the average (arithmetic mean) of aa and bb?
  1. (1)a+b=18a+b=18
  2. (2)a−b=4a-b=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: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(1) The average is 18/2=918/2=9. (2) fixes only the difference. Statement (1) alone is sufficient; you do not need aa and bb individually.
33 Medium EA Quantitative Reasoning
How many employees does company X have?
  1. (1)40% of the employees are managers, and there are 24 managers.
  2. (2)60% of the employees are not managers, and there are 36 employees who are not managers.
  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) 24/0.4=6024/0.4=60. (2) 36/0.6=6036/0.6=60. Each alone is sufficient.
34 Medium EA Quantitative Reasoning
Is x>0x>0?
  1. (1)x2>0x^2>0
  2. (2)x3>0x^3>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: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) holds for every non-zero xx, positive or negative. (2) A cube has the sign of its base, so x>0x>0. Statement (2) alone is sufficient.
35 Medium EA Quantitative Reasoning
Pens cost the same amount each and pencils cost the same amount each. What is the price of one pen?
  1. (1)3 pens and 2 pencils cost £7 in total.
  2. (2)2 pens and 3 pencils cost £8 in total.
  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, 3p+2q=73p+2q=7 and 2p+3q=82p+3q=8 give p=£1p=£1 (and q=£2q=£2).
36 Medium EA Quantitative Reasoning
Working alone at a constant rate, how many hours does machine A take to fill an order?
  1. (1)Machines A and B together, each at its constant rate, fill the order in 3 hours.
  2. (2)Machine B alone fills the order in 5 hours.
  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 alone gives A's rate. Together: 13−15=215\tfrac13-\tfrac15=\tfrac2{15} of the order an hour, so 7.5 hours.
37 Hard EA Quantitative Reasoning
Is the positive integer kk divisible by 6?
  1. (1)kk is divisible by 12.
  2. (2)k2k^2 is divisible by 18.
  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) Every multiple of 12 is a multiple of 6. (2) k2k^2 divisible by 2 and by 9 means kk is divisible by 2 and by 3, hence by 6. Each alone is sufficient.
38 Hard EA Quantitative Reasoning
What is the median of the five numbers 3, 8, xx, 11 and 5?
  1. (1)x>8x>8
  2. (2)x<10x<10
  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>8x>8, the three smallest values are 3, 5 and 8, so the median is 8 whatever xx is. (2) x=1x=1 gives median 5, x=9x=9 gives 8. Statement (1) alone is sufficient.
39 Hard EA Quantitative Reasoning
Is xy>0xy>0?
  1. (1)x+y>0x+y>0
  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: E. Statements (1) and (2) TOGETHER are NOT sufficient.
Together they give x>∣y∣x>|y|, so x>0x>0, but yy can be positive (x=3,y=1x=3,y=1: yes) or negative (x=3,y=−1x=3,y=-1: no). Not sufficient even together.
40 Hard EA Quantitative Reasoning
What percent of the students in a class passed an exam?
  1. (1)18 students passed.
  2. (2)12 students failed.
  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 alone gives one count but not the class size. Together, 18/30=60%18/30=60\%.
41 Hard EA Quantitative Reasoning
Is a>ba>b?
  1. (1)ab>1\dfrac ab>1
  2. (2)b>0b>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) a=3,b=2a=3,b=2 gives yes, but a=−3,b=−2a=-3,b=-2 gives no. (2) says nothing about aa. Together, multiplying ab>1\tfrac ab>1 by the positive bb gives a>ba>b.
42 Hard EA Quantitative Reasoning
What is the value of the integer nn?
  1. (1)10<3n<2010<3n<20
  2. (2)nn is 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) allows 4, 5 or 6. (2) allows any prime. Together only 5 fits.
43 Easy EA Quantitative Reasoning
A team of five has an average (arithmetic mean) age of 34. When a sixth member joins, the average rises to 35. How old is the new member?
  1. 35
  2. 38
  3. 40
  4. 42
  5. 45
Show answer
Answer: C. 40
Total ages go from 5×34=1705\times34=170 to 6×35=2106\times35=210, so the new member is 40.
44 Easy EA Quantitative Reasoning
A recipe for 4 people uses 300 g of flour. How many grams are needed for 10 people?
  1. 600
  2. 650
  3. 700
  4. 750
  5. 800
Show answer
Answer: D. 750
75 g a person, so 10×75=75010\times75=750 g.
45 Easy EA Quantitative Reasoning
A train leaves at 09:40 and arrives at 13:10, covering 245 km. What is its average speed, in km per hour?
  1. 60
  2. 65
  3. 70
  4. 75
  5. 80
Show answer
Answer: C. 70
The journey takes 3 hours 30 minutes, 3.5 hours. 245÷3.5=70245\div3.5=70.
46 Medium EA Quantitative Reasoning
If 40% of xx is 24 more than 25% of xx, what is xx?
  1. 120
  2. 140
  3. 160
  4. 180
  5. 200
Show answer
Answer: C. 160
0.40x−0.25x=240.40x-0.25x=24, so 0.15x=240.15x=24 and x=160x=160.
47 Medium EA Quantitative Reasoning
How many two-digit positive integers have a units digit greater than their tens digit?
  1. 28
  2. 32
  3. 36
  4. 40
  5. 45
Show answer
Answer: C. 36
Tens digit 1 allows units 2 to 9 (8 numbers), tens digit 2 allows 7, and so on down to tens digit 8, which allows only 9. 8+7+⋯+1=368+7+\dots+1=36.
48 Medium EA Quantitative Reasoning
A fund grew from £80,000 to £96,800 over two years, growing by the same percentage each year. What was the annual growth rate?
  1. 8%
  2. 9%
  3. 10%
  4. 10.5%
  5. 11%
Show answer
Answer: C. 10%
96,80080,000=1.21=1.12\tfrac{96{,}800}{80{,}000}=1.21=1.1^2, so 10% a year. Splitting the total 21% in half, 10.5%, ignores compounding.
49 Medium EA Quantitative Reasoning
Two fair six-sided dice are rolled. What is the probability that their sum is a prime number?
  1. 13\displaystyle \tfrac13
  2. 512\displaystyle \tfrac5{12}
  3. 12\displaystyle \tfrac12
  4. 712\displaystyle \tfrac7{12}
  5. 23\displaystyle \tfrac23
Show answer
Answer: B. 512\displaystyle \tfrac5{12}
The prime sums are 2, 3, 5, 7 and 11, which occur in 1, 2, 4, 6 and 2 ways. That is 15 of the 36 outcomes, 512\tfrac5{12}.
50 Medium EA Quantitative Reasoning
Anna is twice as old as Ben. In 10 years she will be 1.5 times as old as he will be. How old is Anna now?
  1. 16
  2. 18
  3. 20
  4. 24
  5. 30
Show answer
Answer: C. 20
With Ben bb: 2b+10=1.5(b+10)2b+10=1.5(b+10), so 0.5b=50.5b=5 and b=10b=10. Anna is 20.
51 Hard EA Quantitative Reasoning
What is the sum of all multiples of 7 between 100 and 200?
  1. 1,960
  2. 2,037
  3. 2,107
  4. 2,170
  5. 2,240
Show answer
Answer: C. 2,107
The multiples run from 105 to 196: 196−1057+1=14\tfrac{196-105}{7}+1=14 terms. Their sum is 14×105+1962=2,10714\times\tfrac{105+196}{2}=2{,}107.
52 Hard EA Quantitative Reasoning
A security code is any string of 4 digits from 0 to 9. How many codes contain at least one repeated digit?
  1. 4,040
  2. 4,960
  3. 5,040
  4. 5,940
  5. 6,561
Show answer
Answer: B. 4,960
Count the complement. All codes: 104=10,00010^4=10{,}000. Codes with four different digits: 10×9×8×7=5,04010\times9\times8\times7=5{,}040. So 10,000−5,040=4,96010{,}000-5{,}040=4{,}960 have a repeat. 5,040 is the trap: it answers the opposite question.
53 Hard EA Quantitative Reasoning
What is the smallest positive integer that has exactly 6 positive divisors?
  1. 8
  2. 10
  3. 12
  4. 16
  5. 18
Show answer
Answer: C. 12
A number paqb⋯p^aq^b\cdots has (a+1)(b+1)⋯(a+1)(b+1)\cdots divisors. Six divisors means p5p^5 (smallest 32) or p2qp^2q (smallest 22×3=122^2\times3=12). 12 has divisors 1, 2, 3, 4, 6, 12.
54 Hard EA Quantitative Reasoning
A quantity doubles every 3 years. By roughly what factor does it grow over 10 years?
  1. 7
  2. 8
  3. 10
  4. 12
  5. 16
Show answer
Answer: C. 10
10 years is 103\tfrac{10}{3} doubling periods: 210/3=23×21/3≈8×1.26≈10.12^{10/3}=2^3\times2^{1/3}\approx8\times1.26\approx10.1. Stopping at three doublings, 8, ignores the extra third of a period.
55 Hard EA Quantitative Reasoning
If x+1x=5x+\dfrac1x=5, what is the value of x2+1x2x^2+\dfrac1{x^2}?
  1. 21
  2. 23
  3. 25
  4. 27
  5. 29
Show answer
Answer: B. 23
Square both sides: x2+2+1x2=25x^2+2+\tfrac1{x^2}=25, so x2+1x2=23x^2+\tfrac1{x^2}=23. The middle term is the one people forget.
56 Easy EA Quantitative Reasoning
What is the value of 3x−y3x-y?
  1. (1)6x−2y=146x-2y=14
  2. (2)x+y=5x+y=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: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(1) is twice the expression: 3x−y=73x-y=7. Sufficient without finding xx or yy. (2) gives one equation in two unknowns, and it is not a multiple of 3x−y3x-y. A.
57 Medium EA Quantitative Reasoning
Is the positive integer nn divisible by 15?
  1. (1)nn is divisible by 5.
  2. (2)nn is divisible by 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.
Either alone allows numbers that are and are not multiples of 15 (5 and 15; 3 and 15). Together, divisible by both coprime numbers 3 and 5 means divisible by 15. C.
58 Medium EA Quantitative Reasoning
A shop sold 120 items on Monday. How many did it sell on Tuesday?
  1. (1)Tuesday's sales were 25% higher than Monday's.
  2. (2)Over the two days it sold 270 items.
  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) 1.25×120=1501.25\times120=150. (2) 270−120=150270-120=150. Each alone gives the answer. D.
59 Hard EA Quantitative Reasoning
Is the average (arithmetic mean) of aa, bb and cc greater than bb?
  1. (1)a>ba>b
  2. (2)c>bc>b
  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.
The average exceeds bb exactly when a+c>2ba+c>2b. (1) alone: aa may be just above bb while cc is far below it, or not. (2) alone, the same with the roles swapped. Together both aa and cc exceed bb, so a+c>2ba+c>2b: yes. C.
60 Hard EA Quantitative Reasoning
What is the average (arithmetic mean) salary of the 30 employees in a department?
  1. (1)The 10 managers in the department earn an average of £80,000.
  2. (2)The other 20 employees earn an average of £50,000.
  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 covers only part of the department. Together the total is 10×80,000+20×50,000=1,800,00010\times80{,}000+20\times50{,}000=1{,}800{,}000, and 1,800,000÷30=£60,0001{,}800{,}000\div30=£60{,}000. Averaging the two averages, £65,000, ignores that there are twice as many non-managers. C.
61 Medium EA Quantitative Reasoning
What is the remainder when the positive integer nn is divided by 4?
  1. (1)nn is even.
  2. (2)n−6n-6 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: B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) allows remainders 0 and 2. (2) n=4k+6=4(k+1)+2n=4k+6=4(k+1)+2, so the remainder is 2. B.

Keep practising

Integrated Reasoning

Graphics interpretation, sortable table analysis, two-part analysis and multi-source reasoning, with a calculator, as on the assessment.

30 questions →

Quant interview prep

500 questions with worked solutions, and a timed test.

Open →

GMAT practice questions

239 questions with worked solutions, and a timed test.

Open →

GRE practice questions

120 questions with worked solutions, and a timed test.

Open →

Oxbridge maths practice

90 questions with worked solutions, and a timed test.

Open →

Want someone to work through these with you? Executive MBA and MBA admissions, one to one, or book a free 20-minute call.