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The positive integer q is divisible by 15. If the product of
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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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Re: help needed
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06 Jun 2012, 00:56
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
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06 Mar 2013, 13:34
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
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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
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Re: help needed
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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
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19 May 2014, 05:37
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
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19 May 2014, 20:59
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 ... rfactors/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
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12 Apr 2015, 21:14
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
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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. Final Answer: GMAT assassins aren't born, they're made, Rich
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The positive integer q is divisible by 15. If the product of
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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....
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The positive integer q is divisible by 15. If the product of
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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  Iq = 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  IIq = 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  IIQuote: 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
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05 Jan 2018, 13:06
What level question this must be? Thanks Sent from my SMN910C using GMAT Club Forum mobile app



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