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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: 4710
GPA: 3.82
What is the value of (p-q)(p+q)? [#permalink]

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26 Dec 2017, 00:51
00:00

Difficulty:

35% (medium)

Question Stats:

73% (00:49) correct 27% (00:57) wrong based on 48 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
[Reveal] Spoiler: OA

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Joined: 18 Aug 2016
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GMAT 1: 630 Q47 V29
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Re: What is the value of (p-q)(p+q)? [#permalink]

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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
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Luckisnoexcuse

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Posts: 5539
Re: What is the value of (p-q)(p+q)? [#permalink]

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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
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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Math Revolution GMAT Instructor
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Re: What is the value of (p-q)(p+q)? [#permalink]

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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.

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Re: What is the value of (p-q)(p+q)?   [#permalink] 27 Dec 2017, 23:29
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