Find the range of values of $x$ that satisfy the

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AAPL: Moderator; Posts: 2640; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Fri Mar 22, 2019 5:44 am

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e-GMAT

Find the range of values of $x$ that satisfy the inequality $(x+1)(x-2)>4$.

A. $x > -2$
B. $x < -2$
C. $x > 3$
D. $x < 3$
E. $x > 3$ or $x < -2$

OA E

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Source: Beat The GMAT — Problem Solving | Fri Mar 22, 2019 5:44 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Fri Mar 22, 2019 11:37 am

(x+1)(x-2) > 4
x^2 - x - 2 > 4
x^2 - x - 6 > 0
(x-3)(x+2) > 0

So either x-3 and x+2 are both positive, which will be true when x > 3, or both x-3 and x+2 are negative, which will be true when x < -2.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Mar 22, 2019 11:50 am

Hi All,

We're asked for the range of values of X that satisfy the inequality (X+1)(X-2) > 4. This question can be approached in a couple of different ways, including by TESTing VALUES.

IF... X=10, then (11)(8) = 88 which is greater than 4. Thus, X=10 is a possible solution.
Eliminate Answers B and D.

IF... X= - 10, then (-9)(-12) = 108 which is also greater than 4. Thus, X = -10 is also a possible solution.
Eliminate Answers A and C.
..
There's only one answer remaining.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8149; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Mar 24, 2019 5:15 pm

AAPL wrote:e-GMAT

Find the range of values of $x$ that satisfy the inequality $(x+1)(x-2)>4$.

A. $x > -2$
B. $x < -2$
C. $x > 3$
D. $x < 3$
E. $x > 3$ or $x < -2$

OA E

(x + 1)(x - 2) > 4

x^2 - x - 2 > 4

x^2 - x - 6 > 0

(x - 3)(x + 2) > 0

To have (x - 3)(x + 2) > 0, EITHER x - 3 > 0 and x + 2 > 0 OR x - 3 < 0 and x + 2 < 0. In the former case, we have x > 3 and x > - 2, which really means x > 3. In the latter case, we have x < 3 and x < -2, which really means x < -2. So the correct answer is x > 3 or x < -2.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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