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by sana.noor » Sun May 12, 2013 3:53 am
If T is an integer between 10 and 100, what is the valueof T ?
(1) The positive difference between TÂ’ digits is 4.
(2) The sum of TÂ’ digits is 12.
OA is E but i guess it should be C. the official answer explians that T could be 48 or 84. but according to statement 1, the positive difference between T's digits is 4. it means it could only be 84 but not 48 because question says positive difference. please correct me if i am wrong.
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by GMATGuruNY » Sun May 12, 2013 5:25 am
sana.noor wrote:If T is an integer between 10 and 100, what is the valueof T ?
(1) The positive difference between TÂ’ digits is 4.
(2) The sum of TÂ’ digits is 12.
The POSITIVE DIFFERENCE between x and y = |x-y|.

Let x = the tens digit and y = the units digit.

Statement 1: |x-y| = 4.
It's possible that x=9 and y=5.
In this case, T=95.
It's possible that x=8 and y=4.
In this case, T=84.
Since different values for T are possible, INSUFFICIENT.

Statement 2: x+y = 12.
It's possible that x=8 and y=4.
In this case, T=84.
It's possible that x=9 and y=3.
In this case, T=93.
Since different values for T are possible, INSUFFICIENT.

Statements combined:
Statement 2 implies that x=12-y.
Substituting x=12-y into |x-y| = 4, we get:
|(12-y)-y| = 4
|12-2y| = 4.

Case 1: 12-2y = 4
-2y = -8
y=4, implying that x=8.
In this case, T = 84.

Case 2: -(12-2y) = 4
-12 + 2y = 4
2y = 16
y=8, implying that x=4.
In this case, T = 48.

Since different values for T are possible, INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Sun May 12, 2013 5:31 am
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Last edited by Brent@GMATPrepNow on Sun May 12, 2013 5:33 am, edited 1 time in total.
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by Brent@GMATPrepNow » Sun May 12, 2013 5:32 am
sana.noor wrote:If T is an integer between 10 and 100, what is the value of T ?
(1) The positive difference between T's digits is 4.
(2) The sum of T's digits is 12.
OA is E but i guess it should be C. the official answer explians that T could be 48 or 84. but according to statement 1, the positive difference between T's digits is 4. it means it could only be 84 but not 48 because question says positive difference. please correct me if i am wrong.
The positive difference between T's digits is 4 means that one of the digits is 4 greater than the other. There's nothing to indicate which value (the tens digit or the ones digit) is greater.

So . . .

Target question: What is the value of T ?

Statements 1 and 2 combined:
Given both statements, it's still possible that T = 48 or T = 84.

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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