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# Does p^2 = q if p is a prime number?

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
Does p^2 = q if p is a prime number?  [#permalink]

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09 Nov 2015, 22:05
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:20) correct 41% (01:16) wrong based on 140 sessions

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Does p^2 = q if p is a prime number?

(1) q^2 – p^2 =0
(2) p^2 = 49

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Re: Does p^2 = q if p is a prime number?  [#permalink]

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09 Nov 2015, 23:44
(1) $$q^{2}$$ – $$p^{2 }$$=0
=> $$q^{2}$$ = $$p^{2}$$

If $$p^{2}$$= q is true then
q= $$q^{2}$$
=>q(q-1)=0
=>q= 0 or 1

Now , p can take values -1 , 0 and 1-- none of which is a prime number .
Sufficient.

(2)$$p^{2}$$ = 49

Not sufficient.
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Re: Does p^2 = q if p is a prime number?  [#permalink]

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10 Nov 2015, 00:47
Statement 1:

(q-p)(q+p)=0

(q-p)=0 so q=p

OR

(q+p)=0 so q=-p

This means that p^2=q^2

Statement one is sufficient

Statement 2:

Statement two is insufficient

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Re: Does p^2 = q if p is a prime number?  [#permalink]

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15 Nov 2015, 00:50
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Does p^2 = q if p is a prime number?

(1) q^2 – p^2 =0
(2) p^2 = 49

There are 2 variables (p,q) and 1 equation (p^2=q) in the original condition, 2 equations in the given conditions. This makes (D) our likely answer.
For condition 1, q^2-p^2=q^2-q=0, or q(q-1)=0, or q=0,1 --< p=0,1. They are all not prime numbers, so 'no' and is sufficient.
For condition 2, this answers the question 'yes' for p=7, but 'no' for p=-7, so this is insufficient.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Does p^2 = q if p is a prime number?  [#permalink]

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24 Dec 2018, 04:13
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Re: Does p^2 = q if p is a prime number? &nbs [#permalink] 24 Dec 2018, 04:13
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