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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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New post 03 Sep 2019, 23:01
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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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New post Updated on: 05 Sep 2019, 01:03
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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New post 03 Sep 2019, 23:34
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

AD/BCE

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.

AD/BCE

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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New post 03 Sep 2019, 23:52
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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New post Updated on: 04 Sep 2019, 23:07
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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New post 04 Sep 2019, 00:10
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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New post 04 Sep 2019, 03:36
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.

Answer (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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New post 04 Sep 2019, 06:15
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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What is the value of x^5? (1) x^2 = 9 (2) x^3 >9  [#permalink]

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New post Updated on: 08 Sep 2019, 01:11
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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New post 04 Sep 2019, 08:46
(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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New post 04 Sep 2019, 10:01
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 \(x = 3\)

 \(x^5 = 3^5 = 243\)

Answer (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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New post 04 Sep 2019, 10:22
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!
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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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