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What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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What is the value of x^5?

(1) x^2 = 9
(2) x^3 >9

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What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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What is the value of x^5?

(1) x^2 = 9
(2) x^3 >9

#1
x=+/-3 value of x^5 would vary insufficient
#2
x^3>9 ; x>2 so it can be 3,4,5,.... so x^5 value would vary insufficient
from 1 &2
we can determine that x =3..
IMO C

Originally posted by Archit3110 on 03 Sep 2019, 23:34.
Last edited by Archit3110 on 05 Sep 2019, 01:03, edited 1 time in total.
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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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1
What is the value of $$x^5$$?

(1)$$x^2$$ = 9
(2) $$x^3$$ >9

Statement 1: $$x^2$$ = 9

=> |x| = 3
=> x= 3 or x =-3. Therefore $$x^5$$ value will differ for x=3 and x = -3. Hence NOT SUFFICIENT

Statement 2: $$x^3$$ >9

From this statement, we can say that x = positive since $$x^3$$ must be an even number.
Also, x can be anything more than 2. i.e, x>2 . x can take any number, so Statement 2 is also NOT SUFFICIENT.

Statement 1 and Statement 2 together:

From statement 2 we know that x is positive and from statement 1, the only value x can take is x = 3.

Therefore we can find a unique value for $$x^5$$.

hence SUFFICIENT.

The answer is C
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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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1
We are to find x^5.
From statement 1, x^2=9 we get x=3 and x=-3
And this is insufficient because x^5 can be 243 or -243.

From statement 2, we know that x^3 > 9 and this is also insufficient because there are countless possible values of x which meet this criteria, hence a unique value cannot be gotten for x^5.

1+2 is sufficient because we are able narrow the value of x to be 3.
Hence x^5=243.
The answer is therefore C.

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What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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1
What is the value of x^5?

(1) x^2 = 9
x=+/-3
Two values
INSUFFICIENT!

(2) x^3 >9
x has to be +ve
x>2
x's value would differ. INSUFFICIENT!

(1)+(2)
x=3 SUFFICIENT!
Answer is option C
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Originally posted by EncounterGMAT on 03 Sep 2019, 23:53.
Last edited by EncounterGMAT on 04 Sep 2019, 23:07, edited 1 time in total.
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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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What is the value of x^5?

(1) x^2 = 9
x= 3 or -3
insufficient

(2) x^3 >9
x is a positive number greater than cuberoot of 9
clearly insufficient

together is sufficient, X equal 3 can satisfy both conditions.
it is enough to find what x^5 is
therefore, C
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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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Quote:
What is the value of x^5?

(1) x^2 = 9
(2) x^3 >9

(1) x^2 = 9: $$x^2 = 9…|x|=3…x={{3,-3}}$$ insufic.
(2) x^3 >9: $$x>0$$ insufic.

(1&2) $$x>0… |x|=3…x=3$$ sufic.

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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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IMO it's C.
From 1 we cannot be sure that x is -3 or +3.
From 2 we do not get the exact value.
Combining both we can say that x has to be +3.

What is the value of x^5?

(1) x^2 = 9
(2) x^3 >9
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GMAT 1: 780 Q51 V45 GRE 1: Q170 V167 What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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Analyzing the question:
Finding $$x^5$$ is the same as finding $$x$$ since it is an odd power. If we were to find $$x^6$$ instead we can simplify that to finding $$|x|$$.

Statement 1:
This tells us $$x = -3$$ or $$x = 3$$, two different answers for $$x$$ so insufficient.

Statement 2:
Although we cannot get the value of $$x$$, we can infer that $$x$$ must be positive since $$x^3$$ is positive. Insufficient.

Combined:
We take the positive root of (1), $$x = 3$$. Sufficient.

Note, a variation of this problem would be to find $$x^6$$ instead of $$x^5$$ and (1) would be sufficient in that case.
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Originally posted by TestPrepUnlimited on 04 Sep 2019, 08:26.
Last edited by TestPrepUnlimited on 08 Sep 2019, 01:11, edited 1 time in total.
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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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(c), Because with statement 1 you get : x^5=243 or -243
but with statement 2: you know that the sign of x^3 is positive so you need both
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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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What is the value of $$x^5$$?

(1) $$x^2 = 9$$
$$x = -3, 3$$

So, $$x^5 = -3^5 or 3^5$$

INSUFFICIENT.

(2) $$x^3 > 9$$

Since it is not given whether ‘x’ is an integer or non - integer.
So, $$x^3 = 10, 11, 12 …. 27$$…. and many. ‘x’ can have multiple values thus $$x^5$$ can have many values.

INSUFFICIENT.

Together 1) and 2)
Since $$x^3 > 9$$ i.e. $$x > 0$$ and $$x^2 = 9$$ gives $$x = 3$$

 $$x^5 = 3^5 = 243$$

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Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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What is the value of x^5?

(1) x^2 = 9
x = 3 or -3
$$x^5 = 3^5 or (-3)^5$$
x^5 can have two values , not sufficient

(2) x^3 >9
3^3 > 9
4^3 > 9
X can have many positive values, not sufficient

Combined stmt 1 & 2
from stmt 1, x can be 3 or -3
from stmt 2, only 3^3 > 9
so only one value satisfies and is sufficient

C is the answer! Re: What is the value of x^5? (1) x^2 = 9 (2) x^3 >9   [#permalink] 04 Sep 2019, 10:22
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