If x,y and z are Positive Numbers, is z between x and y? GMAT Data Sufficiency

Question: If x,y and z are positive numbers, is z between x and y?

1. x < 2z < y
2. 2x < z < 2y

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If x,y and z are positive numbers, is z between x and y?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution (1):

(1) x < 2z < y

If x = 1, y = 10 and z = 1 --- Answer No
If x = 1, y = 10 and z = 2 --- Answer Yes

Not Sufficient

(2) 2x < z < 2y

If x = 1, y = 2 and z = 3 --- Answer No
If x = 1, y = 10 and z = 3 --- Answer Yes

Not Sufficient

(1) + (2) Add the inequalities: 3x < 3z < 3y --- divide by 3: x < z < y.

Sufficient

Correct Answer: C

Approach Solution (2):

(!) x < 2z < y

Since 2z < y (and all positive) we can infer that z < y. but we do not know whether x < z

Insufficient

(2) 2x < z < 2y

Since 2x < z, we can infer x < z, but we can’t say if z< y

Insufficient

Combine both (1) and (2), x < z < y

Sufficient

Correct Answer: C

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