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# If p = (n)(5^x)(3^k), is p divisible by 10?

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Math Expert
Joined: 02 Sep 2009
Posts: 47092
If p = (n)(5^x)(3^k), is p divisible by 10? [#permalink]

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04 Feb 2015, 08:42
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65% (hard)

Question Stats:

50% (00:49) correct 50% (00:58) wrong based on 135 sessions

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If $$p = (n)(5^x)(3^k)$$, is p divisible by 10?

(1) n, x, and k are even.

(2) $$x > n > k > 0$$.

Kudos for a correct solution.

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Re: If p = (n)(5^x)(3^k), is p divisible by 10? [#permalink]

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04 Feb 2015, 10:43
1
Bunuel wrote:
If p = (n)(5^x)(3^k), is p divisible by 10?

(1) n, x, and k are even.
(2) x > n > k > 0.

Kudos for a correct solution.

ans C..
1) it does not tell us anything . not even if p is an integer as -ive values of x and k will give us a fraction.. insufficient
2) it tells us all of them are +ive, still p may not be an integer if they are fractions ..

combined it does tell us that p is a multiple of atleast 100.. sufficient
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If p = (n)(5^x)(3^k), is p divisible by 10? [#permalink]

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04 Feb 2015, 11:10
1
Bunuel wrote:
If p = (n)(5^x)(3^k), is p divisible by 10?

(1) n, x, and k are even.
(2) x > n > k > 0.

Kudos for a correct solution.

we want n=2^z where z>0 and z = integer; x > 0 and x = integer; k = integer and k>=0

1) assume n=2, x=0, k=0 --> p/10 is not an integer. Assume n=2, x=1, k=0 --> p/10 = int.
Not sufficient

2) x>n>k>0. we don't know whether k, n, and x are integers. Assume k=0,1; n=0,2; x=0,3. Not sufficient.

1+2) variables are integers and are all greater than zero. Sufficient.
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Re: If p = (n)(5^x)(3^k), is p divisible by 10? [#permalink]

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04 Feb 2015, 18:57
Bunuel wrote:
If p = (n)(5^x)(3^k), is p divisible by 10?

(1) n, x, and k are even.
(2) x > n > k > 0.

Kudos for a correct solution.

Statement 1: n, x, k are even integers
n=2
x=0
k=0
p = 2 , which is not divisible by 10

n=2
x=2
k=2
p = 450 , which is divisible by 10

Insufficient

Statement 2:
0 < k < n < x
could be 0 < 1/2 < 1 < 2 (p not divisible) or 0 < 2 < 4 < 6 (p is divisible)
Insufficient

Combined, n, x, k is even and 0 < k < n < x
must be 0 < 2 < 4 < 6 or some combination of increasing even integers. so p is always divisible
Sufficient

Math Expert
Joined: 02 Sep 2009
Posts: 47092
Re: If p = (n)(5^x)(3^k), is p divisible by 10? [#permalink]

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09 Feb 2015, 05:09
Bunuel wrote:
If p = (n)(5^x)(3^k), is p divisible by 10?

(1) n, x, and k are even.
(2) x > n > k > 0.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Solution: (C)

Watch out! It’s tempting to think that if n is even and has a factor of 2, the product p will automatically be a multiple of 10. (A number will be divisible by 10 whenever it has factors of 2 and 5.) But this is not the case. Choosing negative values for the exponents here easily shows that the product of these three terms may not be a multiple of 10, even when n is even. So Statement (1) alone is insufficient, and the answer is either (B), (C), or (E). Statement (2) alone doesn’t tell us much more than that the variables take on positive values, and choosing non-integer values will show that this statement is also not sufficient. Combining the two statements, we can conclude that n, x, and k are positive even integers, and in that case the product will indeed always be a multiple of 10, because it will always have at least one factor of 5 and at least one factor of 2. So the correct answer is (C).
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Re: If p = (n)(5^x)(3^k), is p divisible by 10? [#permalink]

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10 Oct 2017, 13:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If p = (n)(5^x)(3^k), is p divisible by 10?   [#permalink] 10 Oct 2017, 13:17
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