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A function f(x) is defined for all real numbers as f(x) = (x [#permalink]
Expert's post 00:00

Question Stats: 82% (00:37) correct 17% (00:17) wrong based on 29 sessions
A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4)

 Quantity A Quantity B f(2.5) f(3.5)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Joined: 13 May 2019
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Location: United States
GMAT 1: 770 Q51 V44
GRE 1: Q169 V168 WE: Education (Education)
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Re: A function f(x) is defined for all real numbers as f(x) = (x [#permalink]
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Expert's post
With GRE Quantitative Comparisons look for savvy methods for comparison to avoid unnecessary calculation. In this case note the number of negative values created in each quantity.

Quote:
A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4)

 Quantity A Quantity B f(2.5) f(3.5)

Now for Quantity A: x - 1 and x - 2 are each > 0 | x - 3 and x - 4 are each < 0 --> Positive x Positive x Negative x Negative will result in a product > 0
Now for Quantity B: x - 1 is the only value > 0 --> Positive x Negative x Negative x Negative will result in a product < 0

Therefore, Quantity A will always be greater and the correct choice is A.
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Stefan Maisnier

Manager Joined: 22 May 2019
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Kudos [?]: 25 , given: 194

Re: A function f(x) is defined for all real numbers as f(x) = (x [#permalink]
MyGuruStefan wrote:
With GRE Quantitative Comparisons look for savvy methods for comparison to avoid unnecessary calculation. In this case note the number of negative values created in each quantity.

Quote:
A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4)

 Quantity A Quantity B f(2.5) f(3.5)

Now for Quantity A: x - 1 and x - 2 are each > 0 | x - 3 and x - 4 are each < 0 --> Positive x Positive x Negative x Negative will result in a product > 0
Now for Quantity B: x - 1 is the only value > 0 --> Positive x Negative x Negative x Negative will result in a product < 0

Therefore, Quantity A will always be greater and the correct choice is A.

In quantity B, x-1, x-2 and x-3 all are positive, only x-4 is negative. GRE Instructor Joined: 10 Apr 2015
Posts: 3253
Followers: 124

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Re: A function f(x) is defined for all real numbers as f(x) = (x [#permalink]
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Expert's post
Carcass wrote:
A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4)

 Quantity A Quantity B f(2.5) f(3.5)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Quantity A: f(2.5) = (2.5 – 1)(2.5 – 2)(2.5 – 3)(2.5 – 4)
= (1.5)(0.5)(-0.5)(-1.5)
= (POSITIVE)(POSITIVE)(NEGATIVE)(NEGATIVE)
= (POSITIVE)(POSITIVE)(POSITIVE)
= POSITIVE

Quantity B: f(3.5) = (3.5 – 1)(3.5 – 2)(3.5 – 3)(3.5 – 4)
= (2.5)(1.5)(0.5)(-0.5)
= (POSITIVE)(POSITIVE)(POSITIVE)(NEGATIVE)
= (POSITIVE)(NEGATIVE)
= NEGATIVE

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Re: A function f(x) is defined for all real numbers as f(x) = (x   [#permalink] 03 Aug 2019, 06:29
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