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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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Math Expert
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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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29 Jul 2015, 14:54
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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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Kudos [?]: 139701 [0], given: 12794

Senior Manager
Joined: 15 Sep 2011
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Kudos [?]: 443 [1], given: 46

Location: United States
WE: Corporate Finance (Manufacturing)
Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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29 Jul 2015, 15:12
1
KUDOS
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

Kudos [?]: 443 [1], given: 46

Manager
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Posts: 104

Kudos [?]: 261 [1], given: 56

Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
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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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29 Jul 2015, 18:21
1
KUDOS
If a = -7, f(a) = 56
a=-8, f(a) = 72
a=-9, f(a) = 89

so E is the ans

Kudos [?]: 261 [1], given: 56

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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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29 Jul 2015, 22:07
1
KUDOS
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.

Kudos [?]: 80 [1], given: 36

Manager
Joined: 20 Jul 2011
Posts: 81

Kudos [?]: 18 [1], given: 17

GMAT 1: 660 Q49 V31
Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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29 Jul 2015, 23:51
1
KUDOS
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

Kudos [?]: 18 [1], given: 17

Intern
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Kudos [?]: 82 [1], given: 15

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

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30 Jul 2015, 02:21
1
KUDOS
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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Kudos [?]: 82 [1], given: 15

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139701 [0], given: 12794

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

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17 Aug 2015, 06:50
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.
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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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Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)? [#permalink]

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29 Sep 2017, 09:26
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

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.

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Jeffery Miller

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

Kudos [?]: 1051 [0], given: 5

Target Test Prep Representative
Affiliations: Target Test Prep
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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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29 Sep 2017, 09:29
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

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.

_________________

Jeffery Miller

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

Kudos [?]: 1051 [0], given: 5

Re: f(x) = x^2 - x. For which of the following values of a is f(a) ≥ f(8)?   [#permalink] 29 Sep 2017, 09:29
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