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

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

by swerve » Thu Mar 19, 2020 11:05 am
BTGModeratorVI wrote: ↑
Thu Mar 19, 2020 5:35 am
 If 4 < 7 - 2x < 12, how many integer values of x are there?

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

Answer: B
Source: Economist GMAT
\(4 < 7 - 2x < 12\)

\(4-7 <- 2x < 12-7\)

\(-3 <- 2x < 5\)

\(3 > 2x > -5\)

\(3/2 > x > -5/2\)

\(x\) may be \(-2, -1, 0, 1\)

Hence, B
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Re: If 4 < 7 - 2x < 12, how many integer values of x are there?

by Brent@GMATPrepNow » Thu Mar 19, 2020 4:23 pm
BTGModeratorVI wrote: ↑
Thu Mar 19, 2020 5:35 am
 If 4 < 7 - 2x < 12, how many integer values of x are there?

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

Answer: B
Source: Economist GMAT
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

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

by Scott@TargetTestPrep » Sat Mar 21, 2020 3:07 pm
BTGModeratorVI wrote: ↑
Thu Mar 19, 2020 5:35 am
 If 4 < 7 - 2x < 12, how many integer values of x are there?

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

Answer: B
Source: Economist GMAT
4 < 7 - 2x < 12

-3 < -2x < 5

3/2 > x > -5/2

We see that, as an integer, x can be 1, 0, -1 or -2. Therefore, there are 4 possible integer values for x.

Answer: B

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