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Is \(\frac{7^7}{7^x}\) an integer? (1) \(0 \le x \le 7\) (2) \(x=x^2\) Source: GMAT Club Tests  hardest GMAT questions



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Re: M04 q26 [#permalink]
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31 Mar 2009, 17:15
Is 7^7 / 7^x an integer ? => Is 7^ (7x) an integer ? The moment x is 7x < 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 ^ (71) 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. pradeep
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Re: M04 q26 [#permalink]
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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). .
The correct answer is B.
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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Re: M04 q26 [#permalink]
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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). .
The correct answer is B.
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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Re: M04 q26 [#permalink]
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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). .
The correct answer is B.
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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Re: M04 q26 [#permalink]
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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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Re: M04 q26 [#permalink]
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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.
Cheers, R J



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Re: M04 q26 [#permalink]
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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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Re: M04 q26 [#permalink]
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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 noninteger 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 Cheers! Ravi
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Re: M04 q26 [#permalink]
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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. \(x=x^2\) Source: GMAT Club Tests  hardest GMAT questions 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^(7x) 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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Re: M04 q26 [#permalink]
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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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Re: M04 q26 [#permalink]
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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 Mandy



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Re: M04 q26 [#permalink]
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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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Re: M04 q26 [#permalink]
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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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Re: M04 q26 [#permalink]
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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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Re: M04 q26 [#permalink]
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21 Oct 2013, 18:10
why does statement 2 imply only integers?



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Re: M04 q26 [#permalink]
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21 Oct 2013, 22:19



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Re: M04 q26 [#permalink]
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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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Re: M04 q26 [#permalink]
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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 noninteger. So A and D are out.



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Is (7^7)/(7^x) an integer? [#permalink]
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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^(7x) 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. Please help.
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