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# If P=2^(x^2+10x+72) and Q=2^(x^2+16x+54), where x is a positive

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If P=2^(x^2+10x+72) and Q=2^(x^2+16x+54), where x is a positive  [#permalink]

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14 Mar 2018, 08:26
1
00:00

Difficulty:

45% (medium)

Question Stats:

60% (02:05) correct 40% (02:40) wrong based on 26 sessions

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If $$P=2^{(x^2+10x+72)}$$ and $$Q=2^{(x^2+16x+54)}$$, where x is a positive integer, such that the LCM of P and Q is P, the number of values that x can take is
A) 1
B) 2
C) 3
D) 4
E) 5

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Re: If P=2^(x^2+10x+72) and Q=2^(x^2+16x+54), where x is a positive  [#permalink]

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14 Mar 2018, 08:58
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1
souvonik2k wrote:
If $$P=2^{(x^2+10x+72)}$$ and $$Q=2^{(x^2+16x+54)}$$, where x is a positive integer, such that the LCM of P and Q is P, the number of values that x can take is
A) 1
B) 2
C) 3
D) 4
E) 5

If LCM of p and q is p, then p will not be less than Q, but equal to or greater than q..
So $$x^2+10x+72>=x^2+16x+54.....6x<=18.....x<=3$$

Since x is positive integer, it can take value of 1,2 or 3..
Ans 3

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If P=2^(x^2+10x+72) and Q=2^(x^2+16x+54), where x is a positive &nbs [#permalink] 14 Mar 2018, 08:58
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