Answer: 54. 10% = 36, 5% = 18, sum 54. Explains the shortcut. Fast.

M&A Prep › Guides

Brain teasers and mental math for finance interviews

Q: What is 17 × 24? Explain how you got it.

Answer: 408. Breaks it down, e.g. 17 × 25 = 425, minus 17. Calm, clear mental math. Fast.

Q: What's 25% of 480 plus 12% of 50?

25% of 480 = 120. 12% of 50 = 6. Answer: 126. Clear mental steps.

Q: A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much is the ball?

Answer: $0.05. Sets up ball = x, bat = x + 1.00. 2x + 1.00 = 1.10. Avoids the intuitive $0.10 trap.

Q: What's the angle between the hour and minute hands at 3:15?

Answer: 7.5 degrees. Minute hand at 90°. Hour hand moves 0.5° per minute: 90 + 7.5 = 97.5°. Difference is 7.5°.

Q: I'll pay you $1 for each dot on a die you roll, or you can re-roll once. What's the game worth?

Single roll expected value is 3.5. Re-roll if the first roll is 3 or less. EV = (4+5+6)/6 + (1/2)(3.5) = 2.5 + 1.75. Answer: $4.25.

Q: How many times a day do a clock's hour and minute hands overlap?

Answer: 22. They overlap 11 times every 12 hours. Not 24, because they don't overlap every hour. Explains the logic.

Q: You have 8 balls, one slightly heavier, and a balance scale. What's the fewest weighings to find it?

Answer: 2. Split into groups of 3, 3 and 2. Weigh 3 vs 3; then weigh within the heavier group or the 2. Explains why 1 weighing isn't enough.

Q: Estimate the size of the U.S. college textbook market.

Students × courses × spending per course. States assumptions (about 19M students, rentals and used books). Reasonable final range. Sanity check against total spending per student.

Some banks and most trading desks throw in brain teasers or quick mental math. They're testing how you think under pressure, so talk through your steps out loud even when you know the answer.

If you get stuck, set up the problem with simple variables, try a smaller version, and sanity-check your result before you say it.

Brain teasers

Basic

What is 17 × 24? Explain how you got it.

A strong answer covers

Answer: 408
Breaks it down, e.g. 17 × 25 = 425, minus 17
Calm, clear mental math
Fast

Basic

What is 15% of 360?

A strong answer covers

Answer: 54
10% = 36, 5% = 18, sum 54
Explains the shortcut
Fast

Basic

What's 25% of 480 plus 12% of 50?

A strong answer covers

25% of 480 = 120
12% of 50 = 6
Answer: 126
Clear mental steps

Intermediate

How many gas stations are there in the United States?

A strong answer covers

Structured approach (cars, fill-ups, station capacity or population per station)
States assumptions clearly
Lands on a reasonable number (the industry estimate is about 150,000 fueling sites)
Sanity-checks the result

Intermediate

A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much is the ball?

A strong answer covers

Answer: $0.05
Sets up ball = x, bat = x + 1.00
2x + 1.00 = 1.10
Avoids the intuitive $0.10 trap

Intermediate

What's the angle between the hour and minute hands at 3:15?

A strong answer covers

Answer: 7.5 degrees
Minute hand at 90°
Hour hand moves 0.5° per minute: 90 + 7.5 = 97.5°
Difference is 7.5°

Intermediate

I'll pay you $1 for each dot on a die you roll, or you can re-roll once. What's the game worth?

A strong answer covers

Single roll expected value is 3.5
Re-roll if the first roll is 3 or less
EV = (4+5+6)/6 + (1/2)(3.5) = 2.5 + 1.75
Answer: $4.25

Intermediate

How many times a day do a clock's hour and minute hands overlap?

A strong answer covers

Answer: 22
They overlap 11 times every 12 hours
Not 24, because they don't overlap every hour
Explains the logic

Advanced

You have 8 balls, one slightly heavier, and a balance scale. What's the fewest weighings to find it?

A strong answer covers

Answer: 2
Split into groups of 3, 3 and 2
Weigh 3 vs 3; then weigh within the heavier group or the 2
Explains why 1 weighing isn't enough

Advanced

Estimate the size of the U.S. college textbook market.

A strong answer covers

Students × courses × spending per course
States assumptions (about 19M students, rentals and used books)
Reasonable final range
Sanity check against total spending per student

Advanced

You flip a fair coin until you get two heads in a row. What's the expected number of flips?

A strong answer covers

Answer: 6
Sets up states: start, one head
E = 1 + ½E1 + ½E and E1 = 1 + ½·0 + ½E
Solves the equations cleanly

Quick quiz (8 questions)

Revenue grows from 80 to 100. What's the growth rate?

20%
25% ✓
80%
125%

(100 − 80) ÷ 80 = 25%.

Revenue falls from 100 to 80. What's the decline?

20% ✓
25%
80%
−25%

(100 − 80) ÷ 100 = 20%.

A business doubles in 5 years. Its annual growth rate is closest to:

10%
15% ✓
20%
40%

2^(1/5) ≈ 1.149, so about 15% a year.

What's 15% of 80?

12 ✓
8
15
18

10% is 8, 5% is 4: 12.

What's 25% of 360?

80
100
90 ✓
120

360 ÷ 4 = 90.

Sales go from 50 to 60. Growth is:

20% ✓
10%
16.7%
25%

10 ÷ 50 = 20%.

Sales go from 60 back to 50. Decline is:

16.7% ✓
20%
10%
25%

10 ÷ 60 ≈ 16.7%.

Using the Rule of 72, a market growing 8% a year doubles in about:

6 years
12 years
18 years
9 years ✓

72 ÷ 8 = 9 years.

Reading isn't practice. Answer these out loud, get scored, and track your progress for free.

Practice mental math drills →

Brain teasers and mental math for finance interviews

Brain teasers

What is 17 × 24? Explain how you got it.

What is 15% of 360?

What's 25% of 480 plus 12% of 50?

How many gas stations are there in the United States?

A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much is the ball?

What's the angle between the hour and minute hands at 3:15?

I'll pay you $1 for each dot on a die you roll, or you can re-roll once. What's the game worth?

How many times a day do a clock's hour and minute hands overlap?

You have 8 balls, one slightly heavier, and a balance scale. What's the fewest weighings to find it?

Estimate the size of the U.S. college textbook market.

You flip a fair coin until you get two heads in a row. What's the expected number of flips?

Quick quiz (8 questions)

More free guides