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# M04-26

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:23
4
10
00:00

Difficulty:

55% (hard)

Question Stats:

51% (00:48) correct 49% (00:38) wrong based on 241 sessions

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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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16 Sep 2014, 00:23
1
1
Official Solution:

$$\frac{7^7}{7^x} = 7^{7-x}$$, so as long as $$x$$ is an integer and $$x \le 7$$, the expression is an integer.

Statement (1) by itself is insufficient. S1 says that $$x$$ can be between 0 and 7, so it can be an integer or any fraction.

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

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26 Nov 2014, 13:20
1
Bunuel wrote:
Official Solution:

$$\frac{7^7}{7^x} = 7^{7-x}$$, so as long as $$x$$ is an integer and $$x \le 7$$, the expression is an integer.

Statement (1) by itself is insufficient. S1 says that $$x$$ can be between 0 and 7, so it can be an integer or any fraction.

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

Hi Bunnel,
S2 is found by substituting values or by any other way ? Any other way available other than substituting ??

Thanks,
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27 Nov 2014, 06:49
1
prashd wrote:
Bunuel wrote:
Official Solution:

$$\frac{7^7}{7^x} = 7^{7-x}$$, so as long as $$x$$ is an integer and $$x \le 7$$, the expression is an integer.

Statement (1) by itself is insufficient. S1 says that $$x$$ can be between 0 and 7, so it can be an integer or any fraction.

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

Hi Bunnel,
S2 is found by substituting values or by any other way ? Any other way available other than substituting ??

Thanks,

You can solve it algebraically:

Square |x| = x^2;

x^2 = x^4;

x^2(x^2 - 1) = 0

x^2(x - 1)(x + 1) = 0;

x = 0, 1, or -1.

Hope it's clear.
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28 Nov 2014, 07:31
2
1
need to be careful..........
x is not integer, x can be 1.2, 3.5 5.6 anything. Any decimal in (0,7).....
CAREFUL!!!!!!!!!!!!!!!!!!!!!!!!!!
hence using 1st option it can be fraction!!!! Grrr.....
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15 Jan 2015, 16:27
Oh, yes ~ In the heat of battle, it is so easy to bypass the hidden constraint with Statement 1.. Great question, indeed!
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06 Sep 2015, 04:13
I think this is a high-quality question and I don't agree with the explanation. I think the answer should be D.
Reason:
For the expression to be an integer, we need to show that x<=7 and condition in statement A gives us that value. Please explain if i am wrong
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06 Sep 2015, 05:09
I think this is a high-quality question and I don't agree with the explanation. I think the answer should be D.
Reason:
For the expression to be an integer, we need to show that x<=7 and condition in statement A gives us that value. Please explain if i am wrong

Have you read the solution? What if x = 1/2?
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02 Jun 2016, 15:43
I think this is a poor-quality question and I agree with explanation. I believe GMAT does give explanation of every variable they use - whether X is a number or integer was not presented in this question. Do we see that in actual GMAT? If we dont, this is confusing the test taker as we would have to make an assumption for x - is it integer or number??? Not Good!
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02 Jun 2016, 16:12
sa2222 wrote:
I think this is a poor-quality question and I agree with explanation. I believe GMAT does give explanation of every variable they use - whether X is a number or integer was not presented in this question. Do we see that in actual GMAT? If we dont, this is confusing the test taker as we would have to make an assumption for x - is it integer or number??? Not Good!

x is a number what else it can be? Not every question will specify that a variable is an integer. In this case it can be an integer, or non-integer, basically any real number.
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02 Jun 2016, 17:52
Bunuel wrote:
sa2222 wrote:
I think this is a poor-quality question and I agree with explanation. I believe GMAT does give explanation of every variable they use - whether X is a number or integer was not presented in this question. Do we see that in actual GMAT? If we dont, this is confusing the test taker as we would have to make an assumption for x - is it integer or number??? Not Good!

x is a number what else it can be? Not every question will specify that a variable is an integer. In this case it can be an integer, or non-integer, basically any real number.

I appreciate your reply. And, I do agree that it is a number. BUT, I believe GMAT specifies any variables they give in their questions. Since, these are GMAT related problems, I am expecting the same rules. That's the only point I am trying to make. The answer to this question does change based on the assumption we make, x - number (current answer), x - integer (which is again a number) (answer would be D).
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03 Jun 2016, 01:31
sa2222 wrote:
Bunuel wrote:
sa2222 wrote:
I think this is a poor-quality question and I agree with explanation. I believe GMAT does give explanation of every variable they use - whether X is a number or integer was not presented in this question. Do we see that in actual GMAT? If we dont, this is confusing the test taker as we would have to make an assumption for x - is it integer or number??? Not Good!

x is a number what else it can be? Not every question will specify that a variable is an integer. In this case it can be an integer, or non-integer, basically any real number.

I appreciate your reply. And, I do agree that it is a number. BUT, I believe GMAT specifies any variables they give in their questions. Since, these are GMAT related problems, I am expecting the same rules. That's the only point I am trying to make. The answer to this question does change based on the assumption we make, x - number (current answer), x - integer (which is again a number) (answer would be D).

No, your assumptions are wrong. All numbers by default are real numbers on the GMAT. Sometimes a question specifies that a variable is an integer, or a positive integer, ... but not always. Please check the questions in PS or DS forums. Also, when you say "x = number", what does it mean? It does not make sense. Do you mean a fraction?
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16 Jul 2016, 23:01
I think this is a high-quality question and I agree with explanation.
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24 Jul 2016, 07:47
Just a small doubt
st 2) three values of x are derived... -1 , 0 ,1
so three different values... and stiff st sufficient?
thanks
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24 Jul 2016, 08:24
Celestial09 wrote:
Just a small doubt
st 2) three values of x are derived... -1 , 0 ,1
so three different values... and stiff st sufficient?
thanks

The question asks whether 7^7/7^x is an integer. For each of those values 7^7/7^x IS an integer. So, we have an YES answer.
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25 Jul 2016, 19:25
Celestial09 wrote:
Just a small doubt
st 2) three values of x are derived... -1 , 0 ,1
so three different values... and stiff st sufficient?
thanks

If the question is about determining the Exact VALUE, so B would be insufficient. However, the question is YES/NO question, so there is not matter how many values satisfy the condition as long as we get same answer. So in question above, we have 3 values have same answer Yes so B is sufficient.
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07 Oct 2016, 17:21
Bunuel wrote:
prashd wrote:
Bunuel wrote:
Official Solution:

$$\frac{7^7}{7^x} = 7^{7-x}$$, so as long as $$x$$ is an integer and $$x \le 7$$, the expression is an integer.

Statement (1) by itself is insufficient. S1 says that $$x$$ can be between 0 and 7, so it can be an integer or any fraction.

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

Hi Bunnel,
S2 is found by substituting values or by any other way ? Any other way available other than substituting ??

Thanks,

You can solve it algebraically:

Square |x| = x^2;

x^2 = x^4;

x^2(x^2 - 1) = 0

x^2(x - 1)(x + 1) = 0;

x = 0, 1, or -1.

Hope it's clear.

I think aswer should be E

This is how I see S2:
x is equivalent to its absolute value which is given as x^2

7^7/7^x2

and thats all we get using S2 alone. From s1, we then plug in the values of x. when we reach value 7, 7 square is 49 hence 7^7 / 7^49 is NOT an integer

now obviously i know im wrong since this is not the correct answer but i wanted to show my understanding of the question. can anyone please clarify? thanks
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08 Oct 2016, 03:07
jonmarrow wrote:

I think aswer should be E

This is how I see S2:
x is equivalent to its absolute value which is given as x^2

7^7/7^x2

and thats all we get using S2 alone. From s1, we then plug in the values of x. when we reach value 7, 7 square is 49 hence 7^7 / 7^49 is NOT an integer

now obviously i know im wrong since this is not the correct answer but i wanted to show my understanding of the question. can anyone please clarify? thanks

As shown there only 3 values of x satisfy |x| = x^2: 0, 1 and -1. The question asks whether 7^7/7^x is an integer. For each of those values 7^7/7^x IS an integer. So, we have an YES answer.
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12 Nov 2016, 05:09
is there a typo in the explanation in the second line?
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12 Nov 2016, 05:13
warriorguy wrote:
is there a typo in the explanation in the second line?

Can you please tell me what typo there is?
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Re: M04-26 &nbs [#permalink] 12 Nov 2016, 05:13

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# M04-26

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