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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 RaghavKhanna » Thu Jun 11, 2020 8:48 pm
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
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Re: If 4 < 7 - 2x < 12, how many integer values of x are there?

by Brent@GMATPrepNow » Fri Jun 12, 2020 6:14 am
BTGModeratorVI wrote: ↑
Thu Jun 11, 2020 8:33 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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Brent
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Re: If 4 < 7 - 2x < 12, how many integer values of x are there?

by Scott@TargetTestPrep » Wed Jun 17, 2020 3:21 am
BTGModeratorVI wrote: ↑
Thu Jun 11, 2020 8:33 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
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

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