GMAT Quantitative Reasoning Practice Test 6

Question : 5 of 100

Marks: +1, -0

What is the value of

x

?
(1)

22< 3 x+1< 28

(2)

x

is an integer.

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.
Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.
The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).
The problem can be solved using EITHER statement (1) only or statement (2) only.
The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

Validate

Solution:

Solve the compound inequality in statement (1):

22< 3 x+1< 28

. Subtract 1 from each part of the inequality:

22-1< 3 x+1-1< 28-1

.
Divide each part by

3: \;{21}/{3}< \;{3 x}/{3}< \;{27}/{3}

The result is that

x

is some number between 7 and 9; thus, statement (1) is not sufficient. Statement (2), together with statement (1), is sufficient, and the answer is conclusively one value - namely, 8 .

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