f(x) = x^2 - x. For which of the following values of a is

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Apr 14, 2019 10:10 am

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f(x) = x^2 - x. For which of the following values of "a" is f(a) ≥ f(8)?

I. a = -7
II. a = -8
III. a = -9

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Sun Apr 14, 2019 10:10 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 14, 2019 3:39 pm

VJesus12 wrote:f(x) = x² - x. For which of the following values of "a" is f(a) ≥ f(8)?

I. a = -7
II. a = -8
III. a = -9

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

GIVEN: f(x) = x² - x
So, f(8) = 8² - 8 = 56

I. a = -7
So, f(-7) = (-7)² - (-7) = 56
This means f(a) ≥ f(8)
Check the answer choices. . . ELIMINATE B and C

II. a = -8
So, f(-8) = (-8)² - (-8) = 72
This means f(a) ≥ f(8)
Check the answer choices. . . ELIMINATE A

II. a = -9
So, f(-9) = (-9)² - (-9) = 90
This means f(a) ≥ f(8)
Check the answer choices. . . ELIMINATE D

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Apr 26, 2019 2:36 pm

VJesus12 wrote:f(x) = x^2 - x. For which of the following values of "a" is f(a) ≥ f(8)?

I. a = -7
II. a = -8
III. a = -9

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

f(8) = 8^2 - 8 = 64 - 8 = 56

Let’s analyze each Roman numeral:

I. a = -7

f(-7) = (-7)^2 - (-7) = 49 + 7 = 56. Yes, f(-7) ≥ f(8) because 56 ≥ 56.

II. a = - 8

f(-8) = (-8)^2 - (-8) = 64 + 8 = 72. Yes, f(-8) ≥ f(8) because 72 ≥ 56.

III. a = -9

f(-9) = (-9)^2 - (-9) = 81 + 9 = 90. Yes, f(-9) ≥ f(8) because 90 ≥ 56.

Answer: E

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