It is currently 21 Jan 2018, 20:26

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x^2 is divisible by 160, what is the minimum possible value of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43347
If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

### Show Tags

07 Dec 2017, 20:23
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

80% (00:45) correct 20% (00:35) wrong based on 74 sessions

### HideShow timer Statistics

If x^2 is divisible by 160, what is the minimum possible value of integer x?

A. 10
B. 20
C. 40
D. 80
E. 160
[Reveal] Spoiler: OA

_________________
Intern
Joined: 02 Jul 2017
Posts: 5
Re: If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

### Show Tags

07 Dec 2017, 20:41
X is an integer greater than 0 and X^2 is divisible by 160 .. we can write X^2 as X^2=160*K k is an integer

let us solve this X^2-160K=0 which leads to X=4*Sq.root(10*k)

For x to be integer 10*K must be a perfect square for that to happen minimum possible value of k has to be 10 leading sq.root (10*k) =10

so answer is 4*10=40 i.e C
VP
Joined: 22 May 2016
Posts: 1259
Re: If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

### Show Tags

10 Dec 2017, 00:41
Bunuel wrote:
If x^2 is divisible by 160, what is the minimum possible value of integer x?

A. 10
B. 20
C. 40
D. 80
E. 160

These problems make me feel as if I am trying (unsuccessfully) to think in reverse. I used answer choices.

$$x^2$$ is divisible by 160.
We need a number, x, that, when squared, is divisible by 160. And we need the smallest x for which that is true. Minimum possible value of $$x$$?

A.10
$$x = 10$$
$$x^2 = 10^2 = 100$$
100 is not divisible by 160. REJECT

B. 20
$$x = 20$$. $$x^2 = 20^2 = 400$$
400 is not divisible by 160. REJECT

C. 40
$$x = 40$$. $$x^2 = 40^2 = 1,600$$
1,600 IS divisible by 160
$$x = 40$$ works.

And $$x = 40$$ is smaller than the next two answers' numbers (D = 80 and E = 160), so REJECT Answers D and E.

From these answer choices, the minimum possible integer that x could be is 40.

Posted from my mobile device
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Math Expert
Joined: 02 Aug 2009
Posts: 5537
Re: If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

### Show Tags

10 Dec 2017, 00:51
Bunuel wrote:
If x^2 is divisible by 160, what is the minimum possible value of integer x?

A. 10
B. 20
C. 40
D. 80
E. 160

Get 160 into prime factor with each factor squared if possible as x^2 is being used and x should then be product of these prime factors..
160=$$2^2*2^2*2*5$$..
So x=2*2*2*5=40

Other simpler way would be make use of choices..
10^2=100, not div by 160
20^2=400, again no
40^2=1600, YES

C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Re: If x^2 is divisible by 160, what is the minimum possible value of   [#permalink] 10 Dec 2017, 00:51
Display posts from previous: Sort by