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# On the real number line, there are four points P, Q, S, and

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On the real number line, there are four points P, Q, S, and [#permalink]  14 Apr 2011, 03:04
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71% (01:45) correct 29% (00:57) wrong based on 61 sessions
On the real number line, there are four points P, Q, S, and T, with coordinates p, q, s, and t, respectively. Suppose p < q < s < t, p = -1, s = 2. If the distance between P and Q is twice the distance between Q and S, and S is the midpoint of Q and T, then T has coordinate

A) 0
B) 1
C) 2
D) 3
E) 4

My answer is
[Reveal] Spoiler:
D

I dont have the OA.
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Kudos [?]: 1128 [1] , given: 376

Re: Number line PS [#permalink]  14 Apr 2011, 03:36
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gmatpapa wrote:
On the real number line, there are four points P, Q, S, and T, with coordinates p, q, s, and t, respectively. Suppose p < q < s < t, p = -1, s = 2. If the distance between P and Q is twice the distance between Q and S, and S is the midpoint of Q and T, then T has coordinate

A) 0
B) 1
C) 2
D) 3
E) 4

My answer is
[Reveal] Spoiler:
D

I dont have the OA.

------------P(p=-1)-----0-----Q(q=1)-----S(s=2)-----T(t=3)------------------

p < q < s < t
$$PQ+QS=s-p=2-(-1)=3$$

distance between P and Q is twice the distance between Q and S
$$2QS+QS=3$$
$$3QS=3$$
$$QS=1$$
$$s-q=1$$
$$2-q=1$$
$$q=1$$

S is the midpoint of Q and T
$$QS=ST$$
$$s-q=t-s$$
$$2-1=t-2$$
$$t=3$$

Ans: "D"
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Re: Number line PS [#permalink]  14 Apr 2011, 03:56
-----------P-------Q-------S--------T------------
(-1) (2)

PQ = 2QS

QS = ST

So Q = 1

TS = QS, So T = 3

Answer - D
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Kudos [?]: 25 [0], given: 4

Re: Number line PS [#permalink]  15 Apr 2011, 19:43
p < q < s < t
______________P_________Q_____S_____T_____

p = -1 and S=2
PQ/QS = 2/1
so Q=1
QS = ST, so T = 3

It is D.
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Director
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Kudos [?]: 71 [0], given: 42

Re: Number line PS [#permalink]  16 Apr 2011, 15:05
q+1 = 2(2-q) => q = 1

(1+t)/2 = 2 => t =3.

Answer is D.
Manager
Joined: 17 Jan 2011
Posts: 231
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Kudos [?]: 25 [0], given: 4

Re: Number line PS [#permalink]  17 Apr 2011, 14:12
need to draw the number line
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Re: Number line PS [#permalink]  30 Apr 2011, 19:37
p ------------q -------s-------t
2x x x
-1 1 2 3

Hence D.
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Re: Number line PS [#permalink]  13 Dec 2012, 00:14
Best way is to draw... <-----p------q-------s--------t----->

We know p=-1 and s=2... <---(-1)------q-------(2)--------t------>

The distance between P and Q is twice the distance of Q and S...

S-P = 3 = 3x Thus, x=1

S-Q=1
2-Q=1
Q=1 <---(p=-1)------(q=1)-------(s=2)--------t------>

S is the midpoint of q and t. Thus, t=3

Answer: D
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Re: Number line PS   [#permalink] 13 Dec 2012, 00:14
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# On the real number line, there are four points P, Q, S, and

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