If $4 < 7 - 2x < 12$, how many integer values of \(x - The Beat The GMAT Forum

If $4 < 7 - 2x < 12$, how many integer values of \(x

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AAPL: Moderator; Posts: 2672; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Thu Nov 28, 2019 3:52 am

Economist GMAT

If $4 < 7 - 2x < 12$, how many integer values of $x$ are there?

A. 6
B. 4
C. 2
D. 1
E. 0

OA B

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Source: Beat The GMAT — Problem Solving | Thu Nov 28, 2019 3:52 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Nov 28, 2019 6:29 am

AAPL wrote:Economist GMAT

If $4 < 7 - 2x < 12$, how many integer values of $x$ are there?

A. 6
B. 4
C. 2
D. 1
E. 0

OA B

GIVEN: 4 < 7 - 2x < 12
Subtract 7 from all sides to get: -3 < -2x < 5
Divide all sides by -2 to get: 1.5 > x > -2.5 [ since I divided both sides of the inequality by a NEGATIVE value, I had to REVERSE the direction of the inequality symbols]

If x is an INTEGER that is BETWEEN -2.5 and 1.5, then x CAN equal -2, -1, 0 or 1 (4 options)

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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