X is negative

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akinade: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Jul 14, 2010 9:45 pm

by akinade » Sun Sep 26, 2010 9:13 am

if x is negative, is x < -3 ?

(1) x^2 > 9

(2) x^3 < -9

source: OG 12, DS #97

I just do not understand OG explanation, I would appreciate if someone can break it down for me.

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Source: Beat The GMAT — Problem Solving | Sun Sep 26, 2010 9:13 am

fsutanto: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sun May 30, 2010 2:34 am

by fsutanto » Sun Sep 26, 2010 9:53 am

I would approach this by plugging values... Since it is stated that x is negative, we can easily narrow down our test values...

Test for (1):
if x = -2 , (1) not true
if x = -4 , (1) stands when X < -3.
Therefore (1) is sufficient

Test for (2):
If x = -2 , (2) -8 is NOT less than -9, therefore not true
If x = -4 , (2) -64 IS less than -9, therefore (2) stands when x < -3.
Therefore (2) is sufficient

If we go back to the earlier question, is x < -3? Both statement (1) & (2) leads to X being LESS than -3, so the answer should be (D).

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abhimanyu.tanwar: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Wed Sep 22, 2010 9:09 am; Location: Pune, India; Thanked: 1 times

by abhimanyu.tanwar » Sun Sep 26, 2010 10:12 am

(1) for x^2 = 9, x has to be 3
for x^2 > 9, x > 3 or x < -3, as it is already given in the question that x is negative, x^2 can only be greater than 9 when x < -3
SUFFICIENT

(2) it is nowhere given that x is an integer, even for x = -2.5 will give us a value -15.625 which is less than -9.
hence this is not sufficient.

Regards
Abhimanyu

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akinade: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Jul 14, 2010 9:45 pm

by akinade » Sun Sep 26, 2010 10:33 am

fsutanto,
thanks for your response, by picking numbers -it became clear to me. However, the OA is A and here is an explanation:

for statement 2: x^3 < -9

assume x = -4
statement 2: -64 < -9 YES
now going back to original question, is -4 < -3? YES

assume x = -3
statement 2: -27 < -9 YES
now going back to original question, is -3 < -3? NO

So therefore, statement 2 is NOT sufficient but statement 1 is SUFFICIENT.

Answer is A

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