# Solutions

Get detailed explanations to advanced GMAT questions.

### Question

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

I. The coordinate of M is 1.5

II. The coordinate of S is 6

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

### Difficulty Level

Hard### Solution

Option D is the correct answer.

### Option Analysis

Let PS = 6x, implying that PR = (1/3)(6x) = 2x and PM = (1/2)(6x) = 3x.

The following number line is yielded:

P<–2x–>R=0<–x–>M<——-3x——->S

In the number line above, P = 0-2x.

Thus, to determine the value of P, we must know the value of x.

Question stem, rephrased: What is the value of x?

Statement I is sufficient: The coordinate of M is 1.5

According to the number line above,

M = 0+x.

Since M=1.5, we get:

1.5 = 0+x

x = 1.5. Sufficient.

Statement II is sufficient: The coordinate of S is 6

According to the number line above,

S = 0 + x + 3x

Since S=6, we get:

6 = 0 + x + 3x

6 = 0 + 4x

x = 1.5. Sufficient

### Related Questions

- To raise funds, a racing team sold T-shirts imprinted with the team’s logo. The team paid their supplier a…

- A certain group of car dealerships agreed to donate x dollars to a Red Cross Chapter for each car…

- If r is an integer, what is the value of 3^(2r)/ 27^(r-1)?

- At a certain committee meeting only associate professors and assistant professors are present…

- If T is a list of consecutive integers in increasing order, what is the sum of integers in T?