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# The positive integer q is divisible by 15. If the product of

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The positive integer q is divisible by 15. If the product of [#permalink]

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05 Jun 2012, 19:12
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Question Stats:

77% (01:25) correct 23% (01:37) wrong based on 390 sessions

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The positive integer q is divisible by 15. If the product of q and the positive integer x is divisible by 20, which of the following must be a factor of $$x^2*q$$?

A. 25
B. 60
C. 75
D. 150
E. 300

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06 Jun 2012, 00:56
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alchemist009 wrote:
The positive integer q is divisible by 15. If the product of q and
the positive integer x is divisible by 20, which of the following
must be a factor of x^2q ?
(A) 25
(B) 60
(C) 75
(D) 150
(E) 300

how do i solve this questions. what would be the cheatcode?

q = 3*5*n (n is some integer)
x*q = 4*5*m (m is some integer)
Since q has 3 as a factor, x*q must have 3 as a factor too.
x*q = 3*4*5*a = 60*a (a is some integer)
Hence 60 must be a factor of x*q.

What about $$x^2*q$$? It must have x*x*q = x*60*a
So, 60 must be a factor of $$x^2*q$$.

Notice that all the other options have 25 as a factor. We do not know whether 5 is a factor of x or not. Hence the opther options COULD be factors of $$x^2*q$$, but it is not essential that they have to be. Only 60 MUST be a factor of $$x^2*q$$.

The cheat code of every GMAT question is the same: Have a strong conceptual understanding!
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1370 GMAT 1: 780 Q51 V48 GRE 1: 1540 Q800 V740 Re: The positive integer q is divisible by 15. If the product of [#permalink] ### Show Tags 06 Mar 2013, 13:34 1 1 q is divisible by 15 and the product of q and x is divisible by 20 => x is a multiple of 4 Therefore x^2(q) will have two fours and a 15 in its product, i.e. it will have 60, 16, 15, and 240 as factors. Of the given options, only B fits into these possibilities. B is therefore the answer. _________________ GyanOne | Top MBA Rankings and MBA Admissions Blog Top MBA Admissions Consulting | Top MiM Admissions Consulting Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738 Intern Joined: 28 Nov 2012 Posts: 37 Re: The positive integer q is divisible by 15. If the product of [#permalink] ### Show Tags 06 Mar 2013, 15:22 Is this right, I feel like I got it by scrambling and plugging in numbers. q/15 and qx/20 for the equations to fit I plugged in 30 for q (satisfying the first equation) and 2 for x in the second 60 (2*30)/20 so x=2 and q=30 (2^2)*30 = 120......60 is the only one that goes into it. Is this right with my logic? Thank you. Math Expert Joined: 02 Sep 2009 Posts: 46333 Re: The positive integer q is divisible by 15. If the product of [#permalink] ### Show Tags 07 Mar 2013, 01:58 skiingforthewknds wrote: Is this right, I feel like I got it by scrambling and plugging in numbers. q/15 and qx/20 for the equations to fit I plugged in 30 for q (satisfying the first equation) and 2 for x in the second 60 (2*30)/20 so x=2 and q=30 (2^2)*30 = 120......60 is the only one that goes into it. Is this right with my logic? Thank you. q could be 30 and x could be 2. In this case options A, C, D and E are not the factors of x^2q, thus these options are NOT ALWAYS true. Thus, by POE (process of elimination) the answer must be B. Hope it's clear. _________________ Intern Joined: 26 Jan 2013 Posts: 9 Concentration: Marketing, Strategy GMAT Date: 10-11-2014 Re: help needed [#permalink] ### Show Tags 12 May 2014, 08:47 VeritasPrepKarishma wrote: alchemist009 wrote: The positive integer q is divisible by 15. If the product of q and the positive integer x is divisible by 20, which of the following must be a factor of x^2q ? (A) 25 (B) 60 (C) 75 (D) 150 (E) 300 how do i solve this questions. what would be the cheatcode? q = 3*5*n (n is some integer) x*q = 4*5*m (m is some integer) Since q has 3 as a factor, x*q must have 3 as a factor too. x*q = 3*4*5*a = 60*a (a is some integer) Hence 60 must be a factor of x*q. What about $$x^2*q$$? It must have x*x*q = x*60*a So, 60 must be a factor of $$x^2*q$$. Notice that all the other options have 25 as a factor. We do not know whether 5 is a factor of x or not. Hence the opther options COULD be factors of $$x^2*q$$, but it is not essential that they have to be. Only 60 MUST be a factor of $$x^2*q$$. The cheat code of every GMAT question is the same: Have a strong conceptual understanding! Hello, Please explain this in a simple manner. did not get the solution Intern Joined: 17 May 2014 Posts: 40 Re: help needed [#permalink] ### Show Tags 19 May 2014, 05:37 1 msharmita wrote: VeritasPrepKarishma wrote: alchemist009 wrote: The positive integer q is divisible by 15. If the product of q and the positive integer x is divisible by 20, which of the following must be a factor of x^2q ? (A) 25 (B) 60 (C) 75 (D) 150 (E) 300 how do i solve this questions. what would be the cheatcode? q = 3*5*n (n is some integer) x*q = 4*5*m (m is some integer) Since q has 3 as a factor, x*q must have 3 as a factor too. x*q = 3*4*5*a = 60*a (a is some integer) Hence 60 must be a factor of x*q. What about $$x^2*q$$? It must have x*x*q = x*60*a So, 60 must be a factor of $$x^2*q$$. Notice that all the other options have 25 as a factor. We do not know whether 5 is a factor of x or not. Hence the opther options COULD be factors of $$x^2*q$$, but it is not essential that they have to be. Only 60 MUST be a factor of $$x^2*q$$. The cheat code of every GMAT question is the same: Have a strong conceptual understanding! Hello, Please explain this in a simple manner. did not get the solution Given: q is divisible by 15, and x*q is divisible by 20 q = 15 k (minimum value of q = 15) When x*q is divide 20, we get a 5 from q. We need a 4 to make it divisible by 20. Therefore, minimum values of x =4 or x= 4n x^2 * q = 16 n^2 * 15 K = 240 r This is divisible by 60 among the options given. Also note that we have only one 5 coming from 15 which we can be sure of. All other options are factors of 25 which can't divide some number containing single 5. Hope you get it!!! Please press kudos if you like!!! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8105 Location: Pune, India Re: help needed [#permalink] ### Show Tags 19 May 2014, 20:59 1 msharmita wrote: VeritasPrepKarishma wrote: alchemist009 wrote: The positive integer q is divisible by 15. If the product of q and the positive integer x is divisible by 20, which of the following must be a factor of x^2q ? (A) 25 (B) 60 (C) 75 (D) 150 (E) 300 how do i solve this questions. what would be the cheatcode? q = 3*5*n (n is some integer) x*q = 4*5*m (m is some integer) Since q has 3 as a factor, x*q must have 3 as a factor too. x*q = 3*4*5*a = 60*a (a is some integer) Hence 60 must be a factor of x*q. What about $$x^2*q$$? It must have x*x*q = x*60*a So, 60 must be a factor of $$x^2*q$$. Notice that all the other options have 25 as a factor. We do not know whether 5 is a factor of x or not. Hence the opther options COULD be factors of $$x^2*q$$, but it is not essential that they have to be. Only 60 MUST be a factor of $$x^2*q$$. The cheat code of every GMAT question is the same: Have a strong conceptual understanding! Hello, Please explain this in a simple manner. did not get the solution I think you need to go through the basics of factors. Check out my post: http://www.veritasprep.com/blog/2014/02 ... r-factors/ Then come back to the solution. It might make more sense. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: The positive integer q is divisible by 15. If the product of q and the [#permalink]

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12 Apr 2015, 21:14
1
Pretz wrote:
The positive integer q is divisible by 15. If the product of q and
the positive integer x is divisible by 20, which of the following
must be a factor of x^2 q ?

(A) 25
(B) 60
(C) 75
(D) 150
(E) 300

Q=3*5*k
xq divisible by 20 so x must have atleast 4

X2q will have atleast 4×4×3×5 . Clearly 60 must be a factor of x2q
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Re: The positive integer q is divisible by 15. If the product of q and the [#permalink]

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12 Apr 2015, 22:43
Hi Pretz,

This question can be solved by TESTing VALUES. Since the prompt asks which of the following MUST be a factor, we have to TEST the smallest values possible.

This prompt gives us a number of facts to work with:
1) Q is a positive integer divisible by 15
2) X is a positive integer
3) (Q)(X) is divisible by 20

IF....
Q = 15
X = 4
(Q)(X) = 60

We're asked which of the following must be a factor of (X^2)(Q)?

(X^2)(Q) = (4^2)(15) = (16)(15) = 240

The only answer that is a factor is 60.

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The positive integer q is divisible by 15. If the product of [#permalink]

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13 Oct 2016, 04:45
q=15k
q=15,30,45,60...
q*x=20p
Hence
q*x=20,40,60....
Let's say x=1(for convenience)
Then common value is 60
q=60
x^2*q= 60x^2
Hence 60 will always be a factor....

Focus on concept not on question

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The positive integer q is divisible by 15. If the product of [#permalink]

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13 Oct 2016, 08:19
alchemist009 wrote:
The positive integer q is divisible by 15. If the product of q and the positive integer x is divisible by 20, which of the following must be a factor of $$x^2*q$$?

A. 25
B. 60
C. 75
D. 150
E. 300

METHOD - I

PLUG IN SOME VALUES FOR q

CASE - I

q = 15 { Completely divisible by 15 }

x = 4

Quote:
If the product of q and the positive integer x is divisible by 20

qx = 60 { Completely divisible by 20}

CASE - II

q = 30 { Completely divisible by 15 }

x = 6

Quote:
If the product of q and the positive integer x is divisible by 20

qx = 180 { Completely divisible by 20}

So, In each case the number is divisible by 60....

METHOD - II

Quote:
q is divisible by 15...........

q/15 = Rem 0

Quote:
q and the positive integer x is divisible by 20

So, qx/15*20 = Rem 0

Check for the least possible number that will divide qx without any remainder using 15 & 20

qx = { 60, 120 , 180..........}

Hence answer will be (B) 60
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Re: The positive integer q is divisible by 15. If the product of [#permalink]

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05 Jan 2018, 13:06
What level question this must be?
Thanks

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Re: The positive integer q is divisible by 15. If the product of [#permalink]

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05 Jan 2018, 13:09
ra5867 wrote:
What level question this must be?
Thanks

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The positive integer q is divisible by 15. If the product of [#permalink]

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30 Jan 2018, 14:05
alchemist009 wrote:
The positive integer q is divisible by 15. If the product of q and the positive integer x is divisible by 20, which of the following must be a factor of $$x^2*q$$?

A. 25
B. 60
C. 75
D. 150
E. 300

I solved this problem with the LCM (Least Common Multiple of two numbers is the smallest number that is a multiple of both)

15= 5*3
20= 5*3*2*2
LCM= 5*3*2*2 = 60 (B)
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The positive integer q is divisible by 15. If the product of   [#permalink] 30 Jan 2018, 14:05
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