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Which of the following must equal zero for all real numbers x

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Which of the following must equal zero for all real numbers x [#permalink]

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New post 23 Feb 2017, 07:10
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Which of the following must equal zero for all real numbers x ?

I. x^3 - x^2
II. x^0
III x^1

A. None.
B. I only
C. II only
D. I and II only
E. II and III only
[Reveal] Spoiler: OA
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Re: Which of the following must equal zero for all real numbers x [#permalink]

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New post 23 Feb 2017, 07:22
vikasp99 wrote:
Which of the following must equal zero for all real numbers x ?

I. x^3 - x^2
II. x^0
III x^1

A. None.
B. I only
C. II only
D. I and II only
E. II and III only


I. x^3 - x^2 = 0 ( Only when x = 1 ; for all other values of x the result in not zero )
II. x^0 = 1 ( For all values of x )
III. x^1 = x ( For all values of x )

Thus, None of the given options hold good, answer will be (A)
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Re: Which of the following must equal zero for all real numbers x [#permalink]

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vikasp99 wrote:
Which of the following must equal zero for all real numbers x ?

I. x^3 - x^2
II. x^0
III x^1

A. None.
B. I only
C. II only
D. I and II only
E. II and III only


This is a MUST question, which means if an expression can be shown to NOT EQUAL ZERO, we can eliminate it.

I. x^3 - x^2
Test a value.
For example, when x = 2, x^3 - x^2 = 2^3 - 2^2 = 8 - 4 = 4
Since x^3 - x^2 DOES NOT EQUAL ZERO we can eliminate statement I

II. x^0
Test a value.
For example, when x = 2, x^0 = 2^0 = 1
Since x^0 DOES NOT EQUAL ZERO we can eliminate statement II

III. x^1
Test a value.
For example, when x = 1, x^1 = 1^1 = 1
Since x^1 DOES NOT EQUAL ZERO we can eliminate statement III

Answer: A
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Re: Which of the following must equal zero for all real numbers x [#permalink]

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New post 27 Feb 2017, 10:44
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Quote:
Which of the following must equal zero for all real numbers x ?

I. x^3 - x^2
II. x^0
III x^1

A. None.
B. I only
C. II only
D. I and II only
E. II and III only


We need to determine which of the given expressions MUST equal zero for all real numbers.

Let’s test each Roman numeral.

I. x^3 - x^2

If x = 2, then x^3 - x^2 = 8 - 4 = 4, so x^3 - x^2 does not have to equal zero.

II. x^0

If x = 2, then x^0 = 2^0 = 1, so x^0 does not have to equal zero.

III. x^1

If x = 2, then x^1 = 2^1 = 2, so x^1 does not have to equal zero.

Answer: A
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Re: Which of the following must equal zero for all real numbers x   [#permalink] 27 Feb 2017, 10:44
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