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The number A is a two-digit positive integer . . . .

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by Vincen » Tue Dec 12, 2017 10:47 am
The number A is a two-digit positive integer; the number B is the two-digit positive integer formed by reversing the digits of A. if Q=10B-A, what is the value of Q?

(1) The tens digit of A is 7
(2) The tens digit of B is 6

The OA is B.

I liked this question, but I couldn't solve it. Experts, may you help me? Thanks.
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Source: — Data Sufficiency |

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by [email protected] » Tue Dec 12, 2017 2:14 pm
Hi Vincen,

We're told that the number "A" is a two-digit positive integer, the number "B" is a two-digit positive integer formed by REVERSING the digits of A and Q = (10B - A). We're asked for the value of Q. This question can be solved by TESTing VALUES...

1) The tens digit of A is 7

With the information in Fact 1, we can refer to the two integers as...
A = 7 _
B = _ 7

IF....
the missing digit is 1, then the A=71, B=17 and the answer to the question is 170 - 71 = 99
the missing digit is 2, then the A=72, B=27 and the answer to the question is 270 - 72 = 198
Fact 1 is INSUFFICIENT.

2) The tens digit of B is 6

With the information in Fact 2, we can refer to the two integers as...
A = _ 6
B = 6 _

IF....
the missing digit is 1, then the A=16, B=61 and the answer to the question is 610 - 16 = 594
the missing digit is 2, then the A=26, B=62 and the answer to the question is 620 - 26 = 594
the missing digit is 3, then the A=36, B=63 and the answer to the question is 630 - 36 = 594
This pattern repeats, regardless of what the missing digit is, so the answer to the question is ALWAYS 594
Fact 2 is SUFFICIENT.

Final Answer: B

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