gmat_pallavi wrote:I came across this question in the GMAT CAT 1 Power Prep software from ETS but cannot derive the answer given in the software.Please help!
Is x an integer?
1. x/2 is an integer.
2. 2x is an integer.
The answer to the question (as given inthe Power Prep software) is A.
Now assuming x = 1/2 and x = 2.
x = 1/2 x = 2
x/2 = 2 x/2 = 1
In both the cases x/2 is an integer.
So just with the aid of Statement 1 how can we say for sure whether x is an integer or not?
xcuseme has diagnosed your problem, I just want to revisit the issue because it's one faced by a lot of test takers.
Here's a fundamental rule of data sufficiency:
the statements are immutable laws of the universe; when we pick numbers, the numbers we select must follow those laws.
So, when looking at the first statement:
1) x/2 is an integer
we are only allowed to consider values of x that go along with this statement.
You chose x = 1/2. However, when we plug x = 1/2 into statement (1), we get:
(1/2)/2 is an integer
(1/2)*(1/2) is an integer
1/4 is an integer
which is NOT true. Therefore, x cannot possibly be 1/2.
Note: this is not a "no" answer to the original question; we haven't even looked at the original question. All we've done is eliminate 1/2 as a possible value for x.
So, when we pick numbers in data sufficiency, there are two steps that we MUST follow:
1) pick numbers that go along with the statement (and with preliminary information in the question itself); then
2) plug those numbers back into the original question.
Since x=1/2 violates statement (1), we never get to the second step.
As an aside, here's a conceptual way of dealing with statements (1) and (2):
(1) x/2 is an integer can be translated into the equation:
x/2 = integer
Like any other equation, we can isolate for x. Multiply both sides by 2 to get:
x = 2*integer
Since an integer times an integer always yields an integer, x must be an integer... sufficient.
(2) 2x is an integer
2x = integer
x = integer/2
Well, if our integer is even, then integer/2 WILL be an integer; however, if our integer is odd, then integer/2 WILL NOT be an integer. Since (2) gives us a "sometimes yes and sometimes no" answer, it's insufficient.
(1) is sufficient, (2) is not: choose (A).
