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M04 q26

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31 Mar 2009, 12:05
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Is $$\frac{7^7}{7^x}$$ an integer?

(1) $$0 \le x \le 7$$
(2) $$|x|=x^2$$

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31 Mar 2009, 17:15
Is 7^7 / 7^x an integer ?

=> Is 7^ (7-x) an integer ?

The moment x is 7-x < 0 the equation does not result in an integer. Option A satisfies this condition.

So A is sufficient.

|x| = x^2

which means x = x^2 or -x=x^2 which implies x = 1 or x=-1

1 = 1^2 -(-1) = (-1)^2

So if x=1 7 ^ (7-1) is an integer
if x=-1 7^(7-(-1)) is also an integer

Hence option B is sufficient.

The answer has to be D - are you sure it's B ? If so I might be missing something as well.

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01 Apr 2009, 02:42
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That's what it says:
Statement (1) by itself is insufficient. S1 says that can be between 0 and 7, so it can be an integer or any fraction.

Statement (1) by itself is sufficient. S2 implies that is one of (-1, 0, 1). .

Anyway, it is probably just a bug. I wanted to make sure that I am not the only person who thinks that the indicated answer is wrong.

Thanks

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01 Apr 2009, 07:59
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Nowhere does S1 say that $$x$$ is an INTEGER. If $$x$$ is $$\frac{3}{2}$$, the expression from the question stem might look like this:
$$\frac{7^7}{7^x} = \frac{7^7}{7^{\frac{3}{2}}} = \frac{7^7}{\sqrt{7^3}}$$

Obviously, this is not an integer.

Hope this helps.

kotofei4 wrote:
That's what it says:
Statement (1) by itself is insufficient. S1 says that can be between 0 and 7, so it can be an integer or any fraction.

Statement (1) by itself is sufficient. S2 implies that is one of (-1, 0, 1). .

Anyway, it is probably just a bug. I wanted to make sure that I am not the only person who thinks that the indicated answer is wrong.

Thanks

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01 Apr 2009, 09:09
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dzyubam wrote:
Nowhere does S1 say that $$x$$ is an INTEGER. If $$x$$ is $$\frac{3}{2}$$, the expression from the question stem might look like this:
$$\frac{7^7}{7^x} = \frac{7^7}{7^{\frac{3}{2}}} = \frac{7^7}{\sqrt{7^3}}$$

Obviously, this is not an integer.

Hope this helps.

kotofei4 wrote:
That's what it says:
Statement (1) by itself is insufficient. S1 says that can be between 0 and 7, so it can be an integer or any fraction.

Statement (1) by itself is sufficient. S2 implies that is one of (-1, 0, 1). .

Anyway, it is probably just a bug. I wanted to make sure that I am not the only person who thinks that the indicated answer is wrong.

Thanks

Dang !!!! I ALWAYS miss out on fractions ... Thanks so much dzyubam. +1
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15 Feb 2010, 19:05
This is a wonderfully written question and put in to your head - always check the question to make sure whether the value is integer /fraction
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19 Oct 2010, 05:34
Nice explanation..dzyubam...
I think whenever answering the questions relating to integers (number systems, in general), and where variables can assume a range of values, I try to imagine the diagram of a number line, with 0, +ve and -ve numbers...tht helps me tide over these questions.

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19 Oct 2010, 10:08
we tend to assume any number as an integer..

but in GMAT, i have practiced many problems where i hv fell into this trap... beware....do not assume is one lesson i hv learnt...

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20 Oct 2010, 04:01
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Statement 1 Insufficient because:
When x = 2, The result is integer
When x = 2.1, the result is non-integer

Statement 2 is sufficient because: The only values that satisfy the given condition are: { -1, 0, 1}. All these 3 inputs for x give the Integer result.

Hence, B

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21 Oct 2011, 05:48
kotofei4 wrote:
Is $$\frac{7^7}{7^x}$$ an integer?

1. $$0 \le x \le 7$$
2. $$|x|=x^2$$

[Reveal] Spoiler: OA
B

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the indicated answer is B while I was sure it was D.

I don't understand how 1 is not sufficient - IMHO it must be an integer.

Thanks.

we have $$\frac{7^7}{7^x}$$ or 7^(7-x)
lets start-
stmt1-$$0 \le x \le 7$$ -not suff, since we do not know whether x is integer or not. x could be 0 or 1/2 etc

stmt 2- $$|x|=x^2$$ it means that x could be -1,0,1 . applying any of these numbers we get an integer.
so, stmt 2 is suff
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21 Oct 2011, 07:27
Great question to highlight the trap that GMAT sets when working with integers and fractions. I too have fallen into it more than once and now always read the question carefully for words like "Integer", "Positive Integer" etc.

If none of these words are mentioned, I always assume that all numbers are valid. Here with the integer in the question, one can easily be thrown off assuming that x is also an integer, when clearly, it doesn't have to be.

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24 Oct 2011, 00:40
+1 for B too.

This question is a classic example of ZIP(Zero, Integer, Positive/Negative) trap.

BR
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01 Nov 2011, 01:37
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IMO B.
S1 if x= 3 then answer is an integer if 3/2 then answer is not an integer. hence insufficient
s2 x can be 1 0 or -1 hence sufficient
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29 Nov 2011, 14:22
B. Since in Statement 1 X can not be an integer so it cant be B. Statement 2 forces X to not only be an integer but to be equal to 0 or 1.

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23 Oct 2012, 05:13
For every data sufficiency question, Always apply the FOIN checks
Can the variable in question assume any of the following types of values :

Fraction
0Zero
Integer or Irrational
Negative
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21 Oct 2013, 18:10
why does statement 2 imply only integers?

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21 Oct 2013, 22:19
naik8797 wrote:
why does statement 2 imply only integers?

|x| = x^2 --> x=-1, x=0 or x=1. All three are integers.
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22 Oct 2013, 01:42
Nice question. I eliminated A and D due to the possibility that X could be a fraction. However, I did something weird and didn't realize that |x| had to be -1, 0, 1. I selected C.

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26 Nov 2013, 07:32
1+ for B.

Statement 1 is a kind of common trap. It does not state that x must be integer. Our minds automatically goes for integers and the trap got us badly! If x does not be an integer the answer would be a non-integer. So A and D are out.

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25 Dec 2013, 00:20
Is (7^7)/(7^x) an Integer?

(1) 0≤x≤7

(2) |x|=(x^2)

Can Someone help me understand this?

My understanding:

Statement 1: Sufficient
Because, x can be any value in the range (0, 1, 2, 3, 4, 5, 6, 7)

rewriting the given expression: 7^(7-x) and considering x values, we get integer for any given 'x';

Statement 2: Sufficient
Because, same as Statement 1 explanation.

But the explanation says something different.
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