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# If x is a negative integer, which of the following must be a negative

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Joined: 02 Sep 2009
Posts: 50000
If x is a negative integer, which of the following must be a negative  [#permalink]

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12 Apr 2016, 02:30
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If x is a negative integer, which of the following must be a negative integer?

A. x + 1
B. x/2+3
C. x^4
D. x – y
E. x^11

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If x is a negative integer, which of the following must be a negative  [#permalink]

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Updated on: 21 Apr 2016, 22:59
1
Bunuel wrote:
If x is a negative integer, which of the following must be a negative integer?

A. x + 1
B. x/2+3
C. x^4
D. x – y
E. x^11

We need to check each option here:

A. x + 1
This will depend on the value of x. Nothing can be said
B. x/2+3
This will depend on the value of x. Nothing can be said
C. x^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. x – y
This will depend on the value of x and y. Nothing can be said
E. x^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative

Correct Option: E

Originally posted by OptimusPrepJanielle on 12 Apr 2016, 03:27.
Last edited by OptimusPrepJanielle on 21 Apr 2016, 22:59, edited 1 time in total.
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Re: If x is a negative integer, which of the following must be a negative  [#permalink]

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21 Apr 2016, 12:23
OptimusPrepJanielle wrote:
Bunuel wrote:
If x is a negative integer, which of the following must be a negative integer?

A. x + 1
B. x/2+3
C. x^4
D. x – y
E. x^11

We need to check each option here:

A. x + 1
This will depend on the value of x. Nothing can be said
B. x/2+3
This will depend on the value of x. Nothing can be said
C. x^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. x – y
This will depend on the value of x. Nothing can be said
E. x^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative

Correct Option: E

What does "This will depend on the value of x" in the 4 option mean?
is it a typo?
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If x is a negative integer, which of the following must be a negative  [#permalink]

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21 Apr 2016, 12:36
1
Bunuel wrote:
If x is a negative integer, which of the following must be a negative integer?

A. x + 1
B. x/2+3
C. x^4
D. x – y
E. x^11

1. -ve $${number }^{odd}$$ = -ve $$number$$

2. -ve $${number }^{even}$$ = +ve $$number$$

A. x + 1

If x = -1 result will be 0, so this can be a non negative number.

B. x/2+3

Result depends on the value of x , if x is a negative even < -6 then only result will be -ve

C. x^4

Follows rule 1, result will always be +ve

D. x – y

y is an unknown number we can not comment.

E. x^11

Follows rule 2.

-ve $${number }^{even}$$ = +ve $$number$$

Hence this answer is option (E)

stonecold wrote:
What does "This will depend on the value ofx" ( I feel this will be y ) in the 4 option mean?
is it a typo?

Me too with you.
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Re: If x is a negative integer, which of the following must be a negative  [#permalink]

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21 Apr 2016, 22:57
stonecold wrote:

What does "This will depend on the value of x" in the 4 option mean?
is it a typo?

Hi stonecold,
Sorry for the typo, the value of x – y will depend on the value of x and y.
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If x is a negative integer, which of the following must be a negative  [#permalink]

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22 Apr 2016, 04:24
1
Bunuel wrote:
If x is a negative integer, which of the following must be a negative integer?

A. x + 1
B. x/2+3
C. x^4
D. x – y
E. x^11

Checking Options :

A. x + 1 If x is -0.5 then this option will be positive Hence, INCORRECT
B. x/2+3 If x is -2 then this option will be positive Hence, INCORRECT
C. x^4 If x is any negative value then this option will be positive Hence, INCORRECT
D. x – y If x is -1 and y is +2 then this option will be positive Hence, INCORRECT
E. x^11 Since $$(-ve)^{anyODDvalue}=(-ve)$$, Hence, CORRECT
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Re: If x is a negative integer, which of the following must be a negative  [#permalink]

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18 Apr 2017, 04:19
Bunuel wrote:
If x is a negative integer, which of the following must be a negative integer?

A. x + 1
B. x/2+3
C. x^4
D. x – y
E. x^11

When it says must and there is always one option to choose then only odd power qualifies
Choice:E
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Re: If x is a negative integer, which of the following must be a negative  [#permalink]

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24 Apr 2017, 16:57
1
Bunuel wrote:
If x is a negative integer, which of the following must be a negative integer?

A. x + 1
B. x/2+3
C. x^4
D. x – y
E. x^11

We should recall the rule that when a number is raised to an odd-powered exponent, the result will retain the sign of the original base. Thus, since x is negative, x^11 will also be negative.

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Re: If x is a negative integer, which of the following must be a negative &nbs [#permalink] 24 Apr 2017, 16:57
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