Betty and Sally

Question:

Betty has $20 more than Sally. How much does each have given that, combined, they have $21 between them? Note: You can’t use fractions in the answer.

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C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

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Solution: Why does this problem give smart people such vapor lock? Maybe it’s reminiscent of the impossible trick questions we all received in grade school. Maybe it’s the constraint about “no fractions.”

So people struggle. The obvious solution is that Betty has $21 and Sally has $1. Like all obvious solutions, this one is incorrect. It satisfies the first condition, but not the second. Their funds add up to $22. Some candidates actually consider the correct solution—Betty has $20.50 and Sally has $0.50—and then get confused with the “no fractions” rule. But why? Who says cents are fractions?

The point of the puzzle is to give the only reasonable solution and have confidence in your response. The actual solution is that Betty has $20.50 and Sally has $0.50. For those so inclined to use a little algebra, here are the equations. Dollars are converted into cents. Let S Sally and B Betty:

B     S      2000¢

B     S      2100¢

Hence,

B   2050¢

S    50¢

But to my mind, a candidate who whips out simultaneous equations to solve this problem reveals a certain rigidity in thinking. Interviewers much prefer candidates who can noodle this puzzle out without going through all that rigmarole.

Answer: Betty has $20.50, and Sally has $0.50.

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