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

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

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New post 29 Jul 2015, 15:54
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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


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Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 29 Jul 2015, 16:12
1
Bunuel 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


Kudos for a correct solution.


The problem asks which output is greater than or equal to the function with 8 input, or what's greater than or equal to \(8^{2}-8=56\)? Right off the bat, since \(|x|=|-x|\), any number with an ABS greater than or equal to ABS of 8, or \(|8|\), must be true, and therefore II and III is true. This eliminates A, B, C, D and only one answer choice is left, E. Prove answer choice is correct by calculating the figure for -7 and -8, both of which are greater than or equal to 56.

IMO E
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Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 29 Jul 2015, 19:21
1
If a = -7, f(a) = 56
a=-8, f(a) = 72
a=-9, f(a) = 89

so E is the ans
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Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 29 Jul 2015, 23:07
1
Bunuel 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


Kudos for a correct solution.


f(8) = 56

f(-7) = 49 +7 = 56.

Rest is > 56.

Answer E
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Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 30 Jul 2015, 00:51
1
Bunuel 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


Kudos for a correct solution.


f(x) = x^2 - x => x(x-1)

f(8) = 8*7 =56

1) f(-7) = -7*-8 = 56
2) f(-8) = -8*-9 = 72
3) f(-9) = -9*-10 = 90

Hence Option E
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Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 30 Jul 2015, 03:21
1
Bunuel 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


Kudos for a correct solution.


\(f(x) = x^2 - x\)
\(f(8) = 8^2 - 8 = 56\)

Test statement: f(a) >= 56

\(f(-7) = -7^2 - (-7) = 56 >= 56\) VALID
\(f(-8) = -8^2 - (-8) = 72 >= 56\) VALID
\(f(-9) = -9^2 - (-9) = 90 >= 56\) VALID

OA should be E
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Expert Post
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Joined: 02 Sep 2009
Posts: 46297
Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 17 Aug 2015, 07:50
Bunuel 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


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Beginning with the given f(8) function, you should see that \(f(8)=8^2-8=64-8=56\)

And then do the same for the three other possible values:

I. f(−7) means put -7 wherever you see the x: \((-7)^2-(-7)=49+7=56\), so f(-7) = f(8).

II. f(−8) means put -8 wherever you see the x: \((-8)^2-(-8)=64+8=72\), so f(-8) > f(8).

III. f(−9) means put -9 wherever you see the x: \((-9)^2-(-9)=81+9=90\), so f(-9) > f(8)

Since all three functions satisfy the question, the correct answer is E.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
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Status: Head GMAT Instructor
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Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 29 Sep 2017, 10:26
Bunuel 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


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

Let’s analyze each answer choice:

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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Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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New post 29 Sep 2017, 10:29
Bunuel 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


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

Let’s analyze each answer choice:

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
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)?   [#permalink] 29 Sep 2017, 10:29
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