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Source: — Data Sufficiency |
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by aneesh.kg » Sun Apr 22, 2012 9:43 am
Let the number X be AB.
X = 10A + B
We need to know both A and B to answer the question. We also know that A and B can be from 0 to 9.

(1) A + B = 4
There many possible values.
So, Statement (1) is INSUFFICIENT.

(2)|B - A| = 2
(Please note that the question doesn't mention if 2 is the difference between the first and the second digit or the second and the first digit. So, we have to include both the possibilities.)
There are many possible values that satisfy the above equation.
So, Statement (2) is INSUFFICIENT.
Lets combine the two statements.

If B - A = 2,
The solution with B + A = 4 is
B = 3 and A = 1
X =31
If A - B =2
A = 3 and B = 1
X= 13

Even after combining, there is no conclusive answer.
so, (E) is he correct option.
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by Brent@GMATPrepNow » Sun Apr 22, 2012 10:01 am
klmehta03 wrote:What is the value of the two-digit number X?

1) The Sum of the two digits is 4
2) The diff. between the two digits is 2
OA later after some discussion
Statement 1: the Sum of the two digits is 4
From this information, we can tell right away that X equals 13, 22, 31 or 40
So, statement 1 is NOT SUFFICIENT

Statement 2: The difference between the two digits is 2
From this information, we can see several possible values for X: 13, 20, 24, 31, 35, etc
So, statement 2 is NOT SUFFICIENT

Statements 1 & 2
Notice that statement 1 leads us to conclude that X must equal 1 of 4 different values (13, 22, 31 or 40). Great.
Statement 2 further limits the possible values to just 13 and 31.
Since we still cannot be sure what the value of X is, the statements combined are NOT SUFFICIENT, so the answer is E

Cheers,
Brent
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by neelgandham » Sun Apr 22, 2012 10:07 am
What is the value of the two-digit number X?
1) The Sum of the two digits is 4
Possible values of X - 40,13,31,22. We have four different answers to the question. So, statement I isn't sufficient to answer the question.
2) The diff. between the two digits is 2
Possible values of X - 97,79,86,68,75,57,64,46,53,35,42,24,31,13,20. We, now, have 15 different answers to the question. So, statement II isn't sufficient to answer the question.
From I and II
Possible value of X - 13,31. We have two different answers to the question. So,answer is E
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