Data Sufficiency

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?

(1) The coordinate of M is 1.5
(2) The coordinate of S is 6

From the GMAT Question pack 1

GMATGuruNY wrote:

late4thing wrote:


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?

(1) The coordinate of M is 1.5
(2) The coordinate of S is 6

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 1: 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 2: 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.

The correct answer is D.

Hi Mitch

I believe from statement 1 we can deduce 1 more possibility.

If we take P = 0.6(say) , R = 0 , M = 1.5 ,we can get S = 2.4

clearly here, PR = 0.6 , PM = 0.9 and PS = 1.8.

this satisfies the following conditions : PR = 1/3PS as well as PM = 1/2PS

Hence Statement 1 is INSUFFICIENT.

Please confirm.Thanks!!

[email protected] wrote: I believe from statement 1 we can deduce 1 more possibility.

If we take P = 0.6(say) , R = 0 , M = 1.5 ,we can get S = 2.4

clearly here, PR = 0.6 , PM = 0.9 and PS = 1.8.

this satisfies the following conditions : PR = 1/3PS as well as PM = 1/2PS

Hence Statement 1 is INSUFFICIENT.

Please confirm.Thanks!!

When the prompt gives a picture of a number line, the points are IN THE ORDER SHOWN.
The given number line indicates that P is to the LEFT of R=0.
Thus, P=0.6 is not valid.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


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?

(1) The coordinate of M is 1.5
(2) The coordinate of S is 6

If we get PR=d from the original condition, RS=2d, and RM=.05d. There is only one variable, and 2 equations, which makes (D) our likely answer.
From condition 1, 0.5d=1.5, d=3; this is a sufficient condition.
From condition 2, 2d=6, d=3, which is also a sufficient condition. The answer is therefore (D)

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According to the number line above, M = 0+x.

Hi GMATGuru ,

I understood everything , but can you please advise how come M=0+x.

Also can you please share the link of these type of questions.

Many thanks in advance.

SJ.