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

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alchemist009
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The positive integer q is divisible by 15. If the product of [#permalink] New post   05 Jun 2012, 19:12
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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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B
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Re: help needed [#permalink] New post   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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Re: The positive integer q is divisible by 15. If the product of [#permalink] New post   06 Mar 2013, 13:34
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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] New post   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.
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Re: The positive integer q is divisible by 15. If the product of [#permalink] New post   07 Mar 2013, 01:58
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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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Re: help needed [#permalink] New post   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 :(
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Re: help needed [#permalink] New post   19 May 2014, 05:37
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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!!!
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Re: help needed [#permalink] New post   19 May 2014, 20:59
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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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/02 ... r-factors/

Then come back to the solution. It might make more sense.
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Re: The positive integer q is divisible by 15. If the product of q and the [#permalink] New post   12 Apr 2015, 21:14
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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] New post   12 Apr 2015, 22:43
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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.

Final Answer:
Show Spoiler
B


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The positive integer q is divisible by 15. If the product of [#permalink] New post   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] New post   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] New post   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] New post   05 Jan 2018, 13:09
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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] New post   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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Re: The positive integer q is divisible by 15. If the product of [#permalink] New post   01 May 2023, 22:37
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