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Intriguing Integers

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Intriguing Integers

by gmat_pallavi » Mon Oct 26, 2009 8:17 am
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? :x

Even statement 2 is not sufficient as -
x = 1/2 x = 2
2x = 2 2x = 4
Again we do not get a definite answer.

According to me the answer should be E.

Could you please help and tell me if I am going wrong somewhere or am missing out on something?
Pallavi Mittra
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Re: Intriguing Integers

by xcusemeplz2009 » Mon Oct 26, 2009 8:56 am
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.

Not able to understand what u are trying to do here

So just with the aid of Statement 1 how can we say for sure whether x is an integer or not? :x

Even statement 2 is not sufficient as -
x = 1/2 x = 2
2x = 2 2x = 4
Again we do not get a definite answer.

According to me the answer should be E.

Could you please help and tell me if I am going wrong somewhere or am missing out on something?
statment1) if x/2 is an int then x is an int...take any no...for eg: x/2=3;x=6
x/2=-2;x=-4

we can not take x=1/2 bcoz then x/2 will not be a int....we need to chose a no. which satisfy the given condition

so statement 1) is suff.

statment 2)2x is int; suppose x=1/2 then 2x is int x is not
and x=1 then bth 2x and x is int...

hence two possibilties
therefore not suff....

A is correct
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Re: Intriguing Integers

by Stuart@KaplanGMAT » Mon Oct 26, 2009 2:25 pm
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? :x
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).
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Thanks

by gmat_pallavi » Tue Oct 27, 2009 5:40 am
Excusemeplz2009 : I get the point now. was actually missing out on a very obvious and simple thing.
Thanks for the help.

Stuart : Thanks a lot for that amazing funda. Its of great help.
Pallavi Mittra
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