If is n is multiple of 5, and n=p^2*q where p and q are prim : GMAT Problem Solving (PS)
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# If is n is multiple of 5, and n=p^2*q where p and q are prim

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If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink]

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05 Feb 2010, 11:51
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If is n is multiple of 5, and n=p^2*q where p and q are prime, which of the following must be a multiple of 25?

A. p^2
B. q^2
C. pq
D. p^2*q^2
E. p^3*q
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Re: GMAT Prep - Prime Number [#permalink]

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05 Feb 2010, 12:11
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If $$n$$ is multiple of $$5$$, and $$n = p^2q$$ where $$p$$ and $$q$$ are prime, which of the following must be a multiple of $$25$$?

A $$p^2$$
B. $$q^2$$
C. $$pq$$
D. $$p^2q^2$$
E. $$p^3q$$

$$n=5k$$ and $$n=p^2p$$, ($$p$$ and $$q$$ are primes).
Q: $$25m=?$$

Well obviously either $$p$$ or $$q$$ is $$5$$. As we are asked to determine which choice MUST be multiple of $$25$$, right answer choice must have BOTH, $$p$$ and $$q$$ in power of 2 or higher to guarantee the divisibility by $$25$$. Only D offers this.

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Re: GMAT Prep - Prime Number [#permalink]

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12 Mar 2010, 05:35
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If n is a multiple of 5 and n = p^2*q, where p and q are prime numbers which of the following must be a multiple of 25

n is a multiple of 5 and p and q are prime numbers.
the only prime number which multiple of 5 i s5 itself
so either p or q is 5
This is why we can surely say that p^2*q^2 is the multiple of 25 since one of thme is 5 and 5^2 = 25
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06 Apr 2010, 21:55
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n is a multiple of 5
n = pq^2 and p and q are primes numbers... so either p or q is 5 or both are 5

A. p^2 -- q could be 5, so this might not be a multiple of 25
B. q^2 -- p could be 5, so this might not be a multiple of 25
C. pq -- p could be 5 and q some other prime number,so this might not be a multiple of 25
D. p^2q^2 -- bingo, either p or q has to be 5, and this one sure will be a multiple of 25
E.p^3q - q could be 5, so this might not be a multiple of 25

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18 Apr 2010, 12:43
MMMs wrote:
Sorry (in advance) if I'm not posting this in the right place. Not sure I quite figured what to post where...
Could someone help me with this question? TIA!

If n is a multiple of 5 and $$n=p^2q$$, where p and q are prime numbers, which of the following must be a multiple of 25?
a) $$p^2$$
b) $$q^2$$
c) $$pq$$
d) $$p^2q^2$$
e) $$p^3q$$

IMHO D

if n is a multiple of 5, it means [/m]p^2q[/m]is multiple of 5. Now both p and q are prime, so atleast one of them should be 5.

let say if p=5, then and q=3, (n=75) ,then option b is out. >>> [/m]3^2[/m] is not a multiple of 25.
let say if p=3, then and q=5, (n=45) ,then option a is out. >>> [/m]3^2[/m] is not a multiple of 25.
let say if p=3, then and q=5, (n=45) ,then option c is out. >>> 3 * 5 is not a multiple of 25.
let say if p=3, then and q=5, (n=135) ,then option e is out. >>>[/m]3^3 * 5[/m] is not a multiple of 25.

Let see option D.

Both p or q can be 5, and if any one of them is squared, the result will be divisible by 5...!!
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19 Dec 2011, 14:43
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For this question, it's best to look at the equation and the conditions together. Here's what we know:
1. n must be a multiple of 5
2. n=p^2*q
3. p and q are prime numbers.

For n to be a multiple of 5, either p or q has to be 5. They can't be 10, 15, 25, etc. since they have to be prime numbers. As long as one of the two is 5, the other can be any prime number. Knowing this, take a look at the answer choices:

A. p^2
B. q^2
C. pq
D.p^2*q^2
E.p^3*q

A and B should be eliminated, because the question asks "which of the following MUST be a multiple of 25", which means for whatever values we put in that fulfill the conditions in the stem, the correct answer choice should be 25. A and B are both at risk of either p or q being the "other" prime number (p=5 and q=3, p=3 and q=5) in which case 9 won't be divisible by 25.

C is also out-- we can finagle p and q into both being 5 to make this true, but it will not be true for every case, since p or q can just as easily be 3, and 15 won't be divisible by 25.

D is the correct answer because regardless of what p or q may be individually, the fact is that one of them will always have to be 5 and thus the result of p^2*q^2 will always be divisible by 25, which is what we're looking for in the correct answer.

E is incorrect because it's actually very similar to C, where we can potentially make it divisible by 25, but it won't be true for every case.

I hope that helps, feel free to let me know if you have any other questions!
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19 Dec 2011, 21:54
with the given conditions: either p or q has be 5. now picking number for each answer: only D satisfies.
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20 Dec 2011, 03:16
fro me its D P^2*q^2
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05 Jan 2012, 03:40
Clear D. As already discussed above, others may not always be divisible by 25.
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Re: If is n is multiple of 5, and n=p^2*q where p and q are [#permalink]

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15 Jan 2012, 15:45
Tip - whenever given like n = 5k, and n = pq, always check the possibility of both p and Q as 5. I did only for 1 variable and got the answer wrong then later Bunnel post helped.
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Re: If is n is multiple of 5, and n=p^2*q where p and q are [#permalink]

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18 Apr 2012, 18:56
either p or q can be the prime 5 so squaring both numbers shows the term must be divisible by 25
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Re: If n is a multiple of 5 and n=(p^2)q, where p and q are prim [#permalink]

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19 Jan 2013, 02:17
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kiyo0610 wrote:
If n is a multiple of 5 and n=(p^2)q, where p and q are prime numbers, which of the following must be a multiple of 25 ?

(a)p^2
(b)q^2
(c)pq
(d)(p^2)(q^2)
(e)(p^3)q

either p = 5 or q = 5
Simply go to options
a) p = 2 say and q = 5
b) q =2 and p = 5
c) p =2 and q =5
d) either of p or q is 5 so this will be multiple of 25
e) p = 2 and q =5

So only D stands
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Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink]

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21 Jan 2013, 06:51
In order to be a multiple of 25 we must have 5*5 derived somewhere from the equation. Also for n to be a factor of 5 the number 5 must be either p or q.

The only answer that MUST have 25 as an outcome of either p or q is D.
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Re: if n is a multiple of 5 ... [#permalink]

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24 Jul 2013, 17:26
if n is a multiple of 5 and n=P^2q,where p and g are prime numbers, which of the following must be a multiple of 25?
a. p^2 - q can be a multiple of 25

b. q^2 - - P can be a multiple of 25

c. pq - PQ is definitely a multiple of 5 but it not necessarily a multiple of 25

d. (P^2)(q^2) - Correct

e. (P^3)(q) - Assuming the worst case scenario (P is some other prime number except 5), Q is definitely a multiple of 5 but it not necessarily a multiple of 25
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Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink]

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27 Aug 2014, 03:39
My question is that what if n in the following question stem is equal to p^(2q), instead of (p^2)(q). how would the answer change.... My reasoning goes like this:

Since p raised to some integer power means p.p.p.p..... up to 2q. (1) and since (1) is divisible by 5, p must be divisible by 5. Hence, p^2 must be divisible by 25. Is this reasoning correct?
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Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink]

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27 Aug 2014, 04:12
megatron13 wrote:
If $$n$$ is multiple of $$5$$, and $$n = p^2q$$ where $$p$$ and $$q$$ are prime, which of the following must be a multiple of $$25$$?

A $$p^2$$
B. $$q^2$$
C. $$pq$$
D. $$p^2q^2$$
E. $$p^3q$$

My question is that what if n in the following question stem is equal to p^(2q), instead of (p^2)(q). how would the answer change.... My reasoning goes like this:

Since p raised to some integer power means p.p.p.p..... up to 2q. (1) and since (1) is divisible by 5, p must be divisible by 5. Hence, p^2 must be divisible by 25. Is this reasoning correct?

Yes, if we were told that p^(2q) is a multiple of 5 where p and q are primes, then p must be 5, which will guarantee divisibility by 25 of each option but B (q^2) and C (pq).
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If is n is multiple of 5, and n=p^2*q where p and q are prime, w [#permalink]

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20 Dec 2014, 09:49
Lets say p^2 * q = 5
Then only q^2 and p^2 *q^2 can be 25 -> All other options are eliminated.
Lets say p^2 * q = 25
then q^2 is eliminated.
Hence D)
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Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink]

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Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink]

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22 Dec 2016, 02:49
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Re: If is n is multiple of 5, and n=p^2*q where p and q are prim   [#permalink] 22 Dec 2016, 02:49
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