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# m and n are positive integers. If p and q are

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6535
GMAT 1: 760 Q51 V42
GPA: 3.82
m and n are positive integers. If p and q are  [#permalink]

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04 Dec 2017, 00:35
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Difficulty:

65% (hard)

Question Stats:

22% (00:25) correct 78% (00:52) wrong based on 53 sessions

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[GMAT math practice question]

$$m$$ and $$n$$ are positive integers. If p and q are prime numbers, how many factors does $$p^mq^n$$ have?

1) $$m=2$$ and $$n=3$$
2) $$p=11$$ and $$q=13$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" DS Forum Moderator Joined: 21 Aug 2013 Posts: 1375 Location: India Re: m and n are positive integers. If p and q are [#permalink] ### Show Tags 04 Dec 2017, 01:21 MathRevolution wrote: [GMAT math practice question] $$m$$ and $$n$$ are positive integers. If p and q are prime numbers, how many factors does $$p^mq^n$$ have? 1) $$m=2$$ and $$n=3$$ 2) $$p=11$$ and $$q=13$$ We are not given whether p & q are Distinct prime numbers or not. They could be same too. (1) We have p^2 * q^3. Now if p and q are distinct, number of factors = 3*4 = 12. But if p and q are same we have p^5, thus number of factors = 6. Not Sufficient. (2) We have 11^m * 13^n. But we dont have values of m and n, so we cannot find number of factors. Not sufficient. Combining, we have all values of p, q, m , n. Question can be solved. Sufficient. Hence C answer Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6535 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: m and n are positive integers. If p and q are [#permalink] ### Show Tags 06 Dec 2017, 00:03 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 4 variables ($$p,q,m$$, and $$n$$) and 0 equations, the answer is most likely to be E. As E is the most likely answer, we should consider both conditions 1) and 2) together before considering each of them individually. If they are not sufficient when taken together, E is the answer. Conditions 1) & 2) The two conditions yield $$p^mq^n = 11^2x3^3$$. Since $$11$$ and $$13$$ are different prime numbers, the number of factors is $$(2+1)(3+1) = 12$$. Both conditions are sufficient, when taken together. Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A). Condition 1) This condition does not tell us whether $$p=q$$. Therefore, it is not sufficient. Condition 2) Since this condition does not tell us the values of the exponents, we can’t determine the number of factors. This condition is not sufficient Note: It is important to look out for the word, “different” in factor or prime factor questions. For example, suppose we are told that $$m$$ and $$n$$ are positive integers, and that $$p$$ and $$q$$ are different prime numbers. If we are then asked how many factors $$p^mq^n$$ has, and given the conditions 1) $$m=2$$ and $$n=3$$ 2) $$p=11$$ and $$q=13$$, the answer will be A. As we know that the number of factors of $$p^mq^n$$ is $$(m+1)(n+1)$$, the information provided by Condition 1) is sufficient (Condition 2) gives us no information about the exponents, and so is not sufficient). Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: m and n are positive integers. If p and q are &nbs [#permalink] 06 Dec 2017, 00:03
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