Solutions

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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