GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Aug 2019, 13:59 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # M04-26

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 57025
M04-26  [#permalink]

### Show Tags

4
18 00:00

Difficulty:   55% (hard)

Question Stats: 53% (01:14) correct 47% (01:09) wrong based on 169 sessions

### HideShow timer Statistics

Is $$\frac{7^7}{7^x}$$ an integer?

(1) $$0 \le x \le 7$$

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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re M04-26  [#permalink]

### Show Tags

2
1
Official Solution:

Is $$\frac{7^7}{7^x}$$ an integer?

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

(1) $$0 \le x \le 7$$. If $$x$$ is an integer from this range, then $$\frac{7^7}{7^x}$$ will be an integer but if $$x$$ is a fraction from this range, then $$\frac{7^7}{7^x}$$ will NOT be an integer.

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

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. For each of those values $$\frac{7^7}{7^x}$$ IS an integer. So, we have an YES answer.

Answer: B
_________________
Intern  Joined: 22 Jul 2014
Posts: 21
GMAT 1: 450 Q38 V12 WE: Information Technology (Computer Software)
Re: M04-26  [#permalink]

### Show Tags

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).

Answer: B

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

Thanks,
_________________
Failures are stepping stones to success !!!
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: M04-26  [#permalink]

### Show Tags

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).

Answer: B

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.
_________________
Intern  Status: Brushing up rusted Verbal....
Joined: 30 Oct 2013
Posts: 11
Location: India
Schools: AGSM '16
GMAT Date: 11-30-2014
GPA: 3.96
WE: Information Technology (Computer Software)
Re: M04-26  [#permalink]

### Show Tags

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.....
Retired Moderator B
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 232
Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE: Asset Management (Investment Banking)
Re: M04-26  [#permalink]

### Show Tags

Just a small doubt
st 2) three values of x are derived... -1 , 0 ,1
so three different values... and stiff st sufficient?
thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: M04-26  [#permalink]

### Show Tags

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.
_________________
Intern  Joined: 22 Jun 2016
Posts: 47
Re: M04-26  [#permalink]

### Show Tags

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).

Answer: B

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.

im sorry how was this even calculated?

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
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: M04-26  [#permalink]

### Show Tags

jonmarrow wrote:
im sorry how was this even calculated?

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.
_________________
Intern  B
Joined: 05 Jun 2015
Posts: 3
Re: M04-26  [#permalink]

### Show Tags

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Can you please elaborate on how " S2 implies that xx is one of (-1, 0, 1)."?
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: M04-26  [#permalink]

### Show Tags

rakshithv22 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Can you please elaborate on how " S2 implies that xx is one of (-1, 0, 1)."?

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

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. For each of those values $$\frac{7^7}{7^x}$$ IS an integer. So, we have an YES answer.
_________________
Intern  B
Joined: 03 Oct 2018
Posts: 1
Re: M04-26  [#permalink]

### Show Tags

I have a question about the approach, why to answer option 2 we have to square? is that a kind of technique?
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: M04-26  [#permalink]

### Show Tags

davidmch1989 wrote:
I have a question about the approach, why to answer option 2 we have to square? is that a kind of technique?

Yes, it's one of the advanced techniques when solving hard modulus questions. Squaring helps to get rid of the absolute values.

10. Absolute Value

For more check Ultimate GMAT Quantitative Megathread

_________________
Intern  B
Joined: 22 Sep 2018
Posts: 1
Re M04-26  [#permalink]

### Show Tags

I think this is a high-quality question and I don't agree with the explanation. In (1) x is already given as less than equal to 0 or less then equal to 7, so x should be either 0 or 7 and in both cases we get integer as the answer.So, 1 should be sufficient to answer the question
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: M04-26  [#permalink]

### Show Tags

aartisaboo wrote:
I think this is a high-quality question and I don't agree with the explanation. In (1) x is already given as less than equal to 0 or less then equal to 7, so x should be either 0 or 7 and in both cases we get integer as the answer.So, 1 should be sufficient to answer the question

What if x is NOT an integer? The answer is correct!
_________________
Intern  Joined: 03 Aug 2019
Posts: 1
Re M04-26  [#permalink]

### Show Tags

I think this is a high-quality question and I don't agree with the explanation. option 1 is stating clearly its between 0 and 7
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: M04-26  [#permalink]

### Show Tags

piyushpawa9h wrote:
I think this is a high-quality question and I don't agree with the explanation. option 1 is stating clearly its between 0 and 7

Please re-read the question, solution and the discussion above more carefully. Hoe it helps.
_________________ Re: M04-26   [#permalink] 03 Aug 2019, 11:25
Display posts from previous: Sort by

# M04-26

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  