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

[BTGModeratorVI]

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

[RaghavKhanna]

4 < 7 - 2x < 12

=> Subtract 7 from both sides

=> -3 < -2x < 5

=> Multiply by -1

=> 3 > 2x > -5
=> 1.5 > x > -2.5

=> Possible integral values of x = -2,-1,0,1
=> 4 values.

Answer: B

[Brent@GMATPrepNow]

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

Cheers,
Brent

[Scott@TargetTestPrep]

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

Solution:

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