 It is currently 29 Nov 2020, 18:32 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # x^2 is divisible by both 40 and 75. If x has exactly three  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 13918
GRE 1: Q160 V160 Followers: 315

Kudos [?]: 3684 , given: 12942

x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
Expert's post 00:00

Question Stats: 31% (01:49) correct 68% (01:45) wrong based on 88 sessions Director Joined: 03 Sep 2017
Posts: 518
Followers: 2

Kudos [?]: 440  , given: 66

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
1
KUDOS
Probably there exist a faster way to solve this question. By the way, I used this one. In order to be a right answer, the square of X must be divisible for both 40 and 75 and X must have only three distinct prime factors.
Thus, I have checked for which of the numbers these two requirements are satisfied and they are for 60 and 240, thus answers B and D! VP Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1342  , given: 251

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
2
KUDOS
Carcass wrote:
$$x^2$$ is divisible by both 40 and 75. If x has exactly three distinct prime factors, which of the following could be the value of x?

Indicate all values that apply.

❑ 30

❑ 60

❑ 200

❑ 240

❑ 420

[Reveal] Spoiler: OA
B, D

The factors of 40 = 2*2*2*5 and factors of 75 = 3*5*5

since x^2 is divisible by both 40 and 75

so x must have = $$2^2*3*5$$ = 60. ( numerator should be the LCM of 40 and 75 ie $$2^3*3*5^2$$)

So check the option which is divisible by 60

Only option B and option D satisfy the condition.
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 9 , given: 100

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
IlCreatore wrote:
Probably there exist a faster way to solve this question. By the way, I used this one. In order to be a right answer, the square of X must be divisible for both 40 and 75 and X must have only three distinct prime factors.
Thus, I have checked for which of the numbers these two requirements are satisfied and they are for 60 and 240, thus answers B and D!

I saw that your method by using the calculator of GRE might take more than 1.5 minutes. However, the method in the second post takes less time.
Founder  Joined: 18 Apr 2015
Posts: 13918
GRE 1: Q160 V160 Followers: 315

Kudos [?]: 3684 , given: 12942

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
Expert's post Intern Joined: 09 Jul 2018
Posts: 10
Followers: 1

Kudos [?]: 18  , given: 0

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
6
KUDOS
Carcass wrote:
$$x^2$$ is divisible by both 40 and 75. If x has exactly three distinct prime factors, which of the following could be the value of x?

Indicate all values that apply.

❑ 30

❑ 60

❑ 200

❑ 240

❑ 420

[Reveal] Spoiler: OA
B, D

$$40 = 2*2*2*5$$ and $$75 = 3*5*5$$

For $$x^2$$ to be divisible by 40 and 75, its prime-factorization must include at least three 2's (since there are three 2's within 40), at least one 3 (since
there is one 3 within 75), and at least two 5's (since there are two 5's within 75):
$$2^3 * 3^1 * 5^2$$

However, since $$x^2$$ is a perfect square, its prime-factorization must have an EVEN NUMBER of every prime factor.
Since the prime-factorization of x must include $$2^3$$, $$3^1$$ and $$5^2$$ -- but $$x$$ must have an even number of each of these prime factors -- the least possible option for $$x^2$$ is as follows:
$$2^4 * 3^2 * 5^2$$
Since the least possible option for $$x^2 = 2^4 * 3^2 * 5^2$$, the least possible option for $$x = 2^2 * 3 * 5 = 60$$.

Implication:
$$x$$ must be a MULTIPLE OF 60.
In addtion, since $$x$$ must have exactly three distinct prime factors, it cannot be divisible by any prime number other than 2, 3 and 5.

Since 30 and 200 are not divisible by 60, eliminate A and C.
Since 420 is divisible by 7 -- a prime number other than 2, 3 and 5 -- eliminate E.

[Reveal] Spoiler:
B, D

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY at gmail
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

Intern Joined: 17 May 2020
Posts: 14
Followers: 0

Kudos [?]: 1 , given: 12

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
I thought E is correct 420/60=7
(420^2)/40 = 4410
(420^2)/75 = 2352 GRE Instructor Joined: 10 Apr 2015
Posts: 3909
Followers: 164

Kudos [?]: 4776  , given: 70

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
1
KUDOS
Expert's post
mageed wrote:
I thought E is correct 420/60=7
(420^2)/40 = 4410
(420^2)/75 = 2352

We're told that x has exactly three distinct prime factors
420 has FOUR distinct prime factors, since 420 = (2)(2)(3)(5)(7)
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: x^2 is divisible by both 40 and 75. If x has exactly three   [#permalink] 08 Jun 2020, 04:32
Display posts from previous: Sort by

# x^2 is divisible by both 40 and 75. If x has exactly three  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.