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# If x is an integer, what is the value of x^5 + 3^5 ?

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If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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Updated on: 10 Nov 2018, 06:26
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Difficulty:

75% (hard)

Question Stats:

35% (01:07) correct 65% (01:13) wrong based on 104 sessions

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Weekly Quant Quiz Question -4

If x is an integer, what is the value of $$x^5 + 3^5$$ ?

(1) $$\sqrt[n]{x^n}$$ $$= 3$$

(2) $$x^3 +8$$ $$= 35$$

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Originally posted by gmatbusters on 29 Sep 2018, 10:15.
Last edited by Bunuel on 10 Nov 2018, 06:26, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 22:41
1

Official Solution:

Most important learning from this question :
$$\sqrt[n]{x^n}$$ = x , only if n is odd
$$\sqrt[n]{x^n}$$ = |x|, if n is even.

Statement 1, $$\sqrt[n]{x^n}$$ $$= 3$$,
here x can be 3 , if n is odd
but if n is even, x can be +3 or -3
hence it is NOT SUFFICIENT

Statement 2: x ^3 = 35-8 = 27 , hence x = 3
hence, SUFFICIENT.

gmatbusters wrote:

Weekly Quant Quiz Question -4

If x is an integer, what is the value of $$x^5 + 3^5$$ ?
a)$$\sqrt[n]{x^n}$$ $$= 3$$
b) $$x^3 +8$$ $$= 35$$

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:20
1
IMO Option (D) should be correct. Please find my solution in attached image.

Attachments

Q4_sep29.jpeg [ 129.04 KiB | Viewed 1186 times ]

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:20
From 1) x=3
its suffiecient

From 2) x^3+8=35
gives two values
not sufficient

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:21
D -

a) can be written as x^n (1/n) = 3
x^1 = 3 - sufficient
b) x3+8x3+8 =35=35
X^3 = 27
because its odd power it retains the number sign therefore x = 3 - sufficient
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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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Updated on: 29 Sep 2018, 10:22
1) x^(n/n)=3
x=3 sufficient
2) x^3+8=35
x^3=27
x=3, sufficient
D

Originally posted by Manvi_nagpal on 29 Sep 2018, 10:21.
Last edited by Manvi_nagpal on 29 Sep 2018, 10:22, edited 1 time in total.
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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:22
a) Suff Implies x=3 .... hence the req value can be determined.
b) Suff Implies x=3 .... hence the req value can be determined........Ans D
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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:22
(1) we know that the n root of x raised to the n = 3. Then n's cancel each other out so we know that x =3

Sufficient

(2) $$x^3$$ = 35 - 8

so x^3 = 27

x=3

Sufficient

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:24
Answer is D as both statements individually are sufficient
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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:24
Consider A, if n=0, A doesn't hold. so x^5 + 3^5 can't be determined. For n>0 the question can be determined a fixed value. A is not sufficient,

Consider B, x^3 = 35-8 = 27. x = 3-> x^5 + 3^5 = 486. B is sufficient.

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 10:35
1) Says (x)^(n/n)=3
Therefore x=3
Sufficient
2) X=either +3 or -3, -3 ruled out as the sum is positive
x=3
sufficient.
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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 11:59
1) (x) to the power of n*1/n = 3

Thus,x = 3

Sufficient

2) (x) to the power of 3 = 35 -8 = 27

Thus, x = 3 (as 27 is positive and x is raised to an odd power)

Thus, sufficient

Ans. D

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 12:36
IMO Option (D) should be correct. Please find my solution in attached image.

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 12:37
What if the value of n in first statement is 2 then there will be 2 values of x??

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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29 Sep 2018, 14:57
Just by looking at A and B I could say that X is 3.

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Re: If x is an integer, what is the value of x^5 + 3^5 ?  [#permalink]

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Updated on: 29 Sep 2018, 22:46
Statement I:

$$x^n = 3^n$$.
Here, x = -3,3 for n =2,4,6... etc.

Statement II:

$$x^3 = 27$$
x = 3.

Hence, B.
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Originally posted by rahul16singh28 on 29 Sep 2018, 22:31.
Last edited by rahul16singh28 on 29 Sep 2018, 22:46, edited 1 time in total.
Re: If x is an integer, what is the value of x^5 + 3^5 ?   [#permalink] 29 Sep 2018, 22:31
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