If p, q, x, y And z Are Different Positive Integers, Which Of The Five GMAT Data Sufficiency

Question:
If p, q, x, y, and z are different positive integers, which of the five integers is the median?

(1) p + x < q
(2) y < z

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.

Solutions and Explanation
Approach Solution : 1

Statement - 1 : p + x < q
We understand that q is greater than both p and x because p and x are both positive. Q will be the median if it is less than both y and z. The median will be one of the quantities other than q, though, if it is not.
Therefore this statement is not sufficient.
Statement - 2 : y < z
With this, we have no idea about p, q, and x.
Therefore this statement is not sufficient
We still lack enough details to calculate the median, even when the two statements are taken together. For instance, q is the median if p + x < q < y < z. The median will, however, be a different quantity than q if y < z < q.
Therefore combining them will also not be sufficient.

Correct Answer: (E)

Approach Solution : 2

Statement - 1 : p + x < q
It can either be p x q or x p q if we arrange in increasing order. Since we are unsure of the y and z values, we are unable to arrange them and, as a result, cannot calculate the median of the data points.
Therefore this statement is not sufficient.
Statement - 2 : y < z
In this case, other values are unknown.
Therefore this statement is not sufficient
By putting the two sentences together, the following four combinations can be obtained by arranging the positive integers in ascending order.
p x q y z
x p q y z
y z x p q
y z p x q

Therefore this is also not sufficient as the middle term changes.

Correct Answer: (E)

“If p, q, x, y and z are different positive integers, which of the five” - is a topic of the GMAT Quantitative reasoning section of GMAT. 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.

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