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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, 18:12
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25% (medium)

Question Stats:

76% (02:05) correct 24% (02:14) wrong based on 427 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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05 Jun 2012, 23:56
4
4
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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Re: The positive integer q is divisible by 15. If the product of  [#permalink]

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06 Mar 2013, 12:34
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.
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Re: The positive integer q is divisible by 15. If the product of  [#permalink]

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06 Mar 2013, 14:22
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: 52902
Re: The positive integer q is divisible by 15. If the product of  [#permalink]

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07 Mar 2013, 00:58
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.
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12 May 2014, 07:47
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: 16 May 2014
Posts: 39

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19 May 2014, 04:37
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!!!

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Joined: 16 Oct 2010
Posts: 8882
Location: Pune, India

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19 May 2014, 19:59
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.
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Posts: 529
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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, 20:14
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, 21:43
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, 03:45
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, 07:19
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, 12:06
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, 12:09
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, 13:05
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, 13:05
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