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# Is p > q? (i) p^2 > q (ii) p^3 > q

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Senior RC Moderator
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 2260
Location: Pakistan
GPA: 3.39
Is p > q? (i) p^2 > q (ii) p^3 > q  [#permalink]

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15 Oct 2018, 09:25
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:24) correct 39% (01:03) wrong based on 44 sessions

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Is p > q?

(i) p^2 > q

(ii) p^3 > q

EG

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Is p > q? (i) p^2 > q (ii) p^3 > q  [#permalink]

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15 Oct 2018, 09:37
1
1st statement:
$$p^2$$>q
p=2 q=2
p=3 q=2
Not Suff.

2nd statement
$$p^3$$>q
p=2 q=2
p=3 q=2
Not Suff

with both statements we cant arrive at unique answer

IMO
Ans: E
CEO
Joined: 11 Sep 2015
Posts: 3447
Re: Is p > q? (i) p^2 > q (ii) p^3 > q  [#permalink]

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15 Oct 2018, 09:38
1
Top Contributor
Is p > q?

(i) p² > q

(ii) p³ > q

EG

Target question: Is p greater than q?

Statement 1: p² > q
This statement doesn't feel sufficient, so I'll TEST some values
There are several values of p and q that satisfy statement 1. Here are two:
Case a: p = 1 and q = 0. In this case, the answer to the target question is YES, p IS greater than q
Case b: p = -0.5 and q = -0.5. In this case, the answer to the target question is NO, p is NOT greater than q
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: p³ > q
Let's test some values.
IMPORTANT: If you want to test values for statement 2, AND you've already tested values in statement 1, check to see whether you can RE-USE the same values you used in statement 1.
It turns out we CAN re-use them:
Case a: p = 1 and q = 0. In this case, the answer to the target question is YES, p IS greater than q
Case b: p = -0.5 and q = -0.5. In this case, the answer to the target question is NO, p is NOT greater than q
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: p = 1 and q = 0. In this case, the answer to the target question is YES, p IS greater than q
Case b: p = -0.5 and q = -0.5. In this case, the answer to the target question is NO, p is NOT greater than q
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: Is p > q? (i) p^2 > q (ii) p^3 > q   [#permalink] 15 Oct 2018, 09:38
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