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# What is the value of (p-q)(p+q)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6804
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the value of (p-q)(p+q)?  [#permalink]

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26 Dec 2017, 00:51
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Difficulty:

35% (medium)

Question Stats:

74% (01:15) correct 26% (01:07) wrong based on 61 sessions

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[GMAT math practice question]

What is the value of $$(p-q)(p+q)$$?

1) $$p-q=5$$
2) $$p$$ and $$q$$ are prime numbers

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Current Student Joined: 18 Aug 2016 Posts: 623 Concentration: Strategy, Technology GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: What is the value of (p-q)(p+q)? [#permalink] ### Show Tags 26 Dec 2017, 03:56 MathRevolution wrote: [GMAT math practice question] What is the value of $$(p-q)(p+q)$$? 1) $$p-q=5$$ 2) $$p$$ and $$q$$ are prime numbers 1) p, q can be 5,0 ; 6, 1; 7, 2.....p^2 - q^2 will have diff answers NS 2) p,q can be 2,3; 2,5; 3, 7; 2, 7;........p^2 - q^2 will have diff answers NS on combining q can only be a odd no. as p is even and their difference is 7 (7,2) C _________________ We must try to achieve the best within us Thanks Luckisnoexcuse Math Expert Joined: 02 Aug 2009 Posts: 7200 Re: What is the value of (p-q)(p+q)? [#permalink] ### Show Tags 26 Dec 2017, 06:58 MathRevolution wrote: [GMAT math practice question] What is the value of $$(p-q)(p+q)$$? 1) $$p-q=5$$ 2) $$p$$ and $$q$$ are prime numbers 1) $$p-q=5$$ p+q can take various values.. Insuff 2) $$p$$ and $$q$$ are prime numbers again P and Q can be any of the prime numbers... 3 and 2... 5 5 and 3....16 insuff combined.. Difference of TWO prime will be ODD only when one is 2, so q is 2 ODD-EVEN = odd p-2=5...p=7 so ans (7-2)(7+2) = 5*9=45 suff C _________________ 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 GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6804 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of (p-q)(p+q)? [#permalink] ### Show Tags 27 Dec 2017, 23:29 => 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 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) and 2) together first. Conditions 1) and 2) Since $$p$$ and $$q$$ are prime numbers satisfying $$p – q = 5$$, one of them is an odd prime and the other is an even prime. The unique even prime is $$2$$. Therefore, $$q = 2$$ and $$p = 7$$, and $$(p-q)(p+q) = (7-2)(7+2) = 5*9 = 45.$$ Both conditions 1) and 2) together are sufficient. Normally, in problems which require 2 equations such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E. 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$149 for 3 month Online Course"
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Re: What is the value of (p-q)(p+q)? &nbs [#permalink] 27 Dec 2017, 23:29
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