A and B are positive two-digit integers such that the tens digit in A

Question

A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B. Which of the following CANNOT be the difference of A and B ?

A 72
B 45
C 33
D 27
E 9

A 72
B 45
C 33
D 27
E 9

Bunuel · Answer

A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B:

A = 10x + y
B = 10y + x

A - B = (10x + y) - (10y + x) = 9(x - y). As you can see the difference must be a multiple of 9. Only option C is not a multiple of 9.

Answer: C.

Bunuel · Answer

Similar questions to practice: s-and-t-are-two-digit-positive-integers-that-have-the-same-127393.html if-the-two-digit-integers-a-and-b-are-positive-and-have-the-163372.html?fl=similar

EMPOWERgmatRichC · Answer

Hi RudeyboyZ,

This question is based on an issue that many Accountants have to deal with (and it's something that you might have learned about in an Accounting Class).

When digits are 'transposed' incorrectly (eg. You mean to type 23, but you type 32 instead), the difference between the original two numbers will ALWAYS be a multiple of 9.

Here, we're asked which of the following is NOT a possible difference....You might notice that the 4 wrong answers are ALL multiples of 9, so they are all possible differences.

GMAT assassins aren't born, they're made,
Rich

dave13 · Answer

i didnt quite get the logic of highlighted part. Bunuel can please you give an example with real numbers

Bunuel · Answer

We got that A - B = 9*(x - y) = 9*integer = {a multiple of 9}.

For example, 91 - 19 = 72 = {a multiple of 9}.

Salsanousi · Answer

Hi  dave13

We can try examples such as the below

91 - 19 = 72
82 - 28 = 54
73 - 37 = 36
64 - 46 = 18
10 - 01 = 9

So all these are multiples of 9

Or algebraically as explained by Bunuel

Posted from my mobile device

dave13 · Answer

MASHALLAH !

THANK YOU

Salsanousi · Answer

dave13 you’re welcome

You could also do it 91 - 19, 92 - 29 etc.. The difference will be 72,63,54,45,36,27,18,9 Posted from my mobile device

TheGuyDangerous · Answer

2 integers XY & YX can be written as (10Y + X) & (10X + Y)

=> difference = 9Y - 9X = 9(X-Y)

=> The answer has to be a multiple of 9 and 33 is not.

Smash C

bumpbot · Answer

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A and B are positive two-digit integers such that the tens digit in A

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A and B are positive two-digit integers such that the tens digit in A

Prep Toolkit

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