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If the two-digit integers A and B are positive and have the same digit
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23 Aug 2021, 05:18
23 Aug 2021, 05:18
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86% (00:51) correct
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If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following CANNOT be the difference between A and B?
(A) 9
(B) 21
(C) 27
(D) 45
(E) 63
Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book
(A) 9
(B) 21
(C) 27
(D) 45
(E) 63
Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book
If the two-digit integers A and B are positive and have the same digit
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23 Aug 2021, 06:53
23 Aug 2021, 06:53
1
Given: A and B are two positive two-digit integers with their digits reversed.
Let A be of the form (10x + y), where x and y are its tens and units digits respectively.
This implies that B is of the form (10y + x), where y and x are its tens and units digits respectively.
Taking the difference between A and B:
(10x + y) - (10y + x) = 9(x - y)
Hence, the difference between A and B has to be a multiple of 9. Looking at the options, 21 is the only choice which is not a multiple of 9.
Answer B
Let A be of the form (10x + y), where x and y are its tens and units digits respectively.
This implies that B is of the form (10y + x), where y and x are its tens and units digits respectively.
Taking the difference between A and B:
(10x + y) - (10y + x) = 9(x - y)
Hence, the difference between A and B has to be a multiple of 9. Looking at the options, 21 is the only choice which is not a multiple of 9.
Answer B
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Re: If the two-digit integers A and B are positive and have the same digit
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13 Sep 2021, 23:28
13 Sep 2021, 23:28
1
Are options B, C, D and E valid in this question? I mean the step between 10x+y and 10y+x appears to be only 9. In order to select the difference of 27, 45, etc., we must be able to factor them out too
