A cashier mentally reversed the digits of one customer's correct amoun

Assume the correct change to be 10x + y cents
Here x = tens digit and y - units digit
Reversed change = 10y + x

9x - 9y = 45
or x - y =5
Only Option E satisfies this criteria.
Hence the correct answer.

The other way to solve this question is to simply reverse the digits of the options and subtract from the given value.
Only Option E satisfies the condition.

Question is asking you to play with the difference btwn each answer choice and its reciprocal to see which will give you $0.45.

Thus, 83-38 = 45

E is correct.

STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can solve the question algebraically, but testing the answer choices will be super fast.

If the cash register contained 45 cents more than it should have, we know that the cashier gave the customer LESS change than they were supposed to.
In other words, the correct amount of change that should have been given to the customer must be GREATER THAN the actual amount of change the cashier gave the customer.
So, we can automatically eliminate answers choices A and B, because these values result in the customer receiving MORE change then they should have.

We've already reduced the possible answers to C, D and E.
Let's now test answer choice D, the middle answer
D) 65 cents
If 65 cents is the correct amount of change, then the cashier would have given 56 cents to the customer.
Since 65 - 56 = 9, we can see that this error results in a difference of only 9 cents, and the question tells us that the difference must be 45 cents.
Eliminate choice D.

When we scan the remaining to answer choices (C and E), we see that choice E (when reversed) results in a difference of 45 cents.
Let's test it anyway.
E) 83 cents
Since 83 - 38 = 45, this error results in a difference of 45 cents, and since at the cashier gave the customer 45 cents less than they should have, the cash register contain 45 cents more than it should have. Perfect!!

Answer: E

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