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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]

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14 Apr 2011, 04:04
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83% (01:06) correct 18% (01:40) wrong based on 136 sessions

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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

[Reveal] Spoiler:
D

I dont have the OA.
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14 Apr 2011, 04:36
1
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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

[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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14 Apr 2011, 04:56
-----------P-------Q-------S--------T------------
(-1) (2)

PQ = 2QS

QS = ST

So Q = 1

TS = QS, So T = 3

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15 Apr 2011, 20:43
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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16 Apr 2011, 16:05
q+1 = 2(2-q) => q = 1

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

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17 Apr 2011, 15:12
need to draw the number line
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30 Apr 2011, 20:37
p ------------q -------s-------t
2x x x
-1 1 2 3

Hence D.
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13 Dec 2012, 01:14
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

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Re: On the real number line, there are four points P, Q, S, and [#permalink]

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14 Jul 2016, 11:24
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

[Reveal] Spoiler:
D

I dont have the OA.

No fancy mathematics is need here just make a big line and divide it into 4 parts (like we do in a number line)

Now since the ascending order is p,q,s,t ; name the parts p,q,s and finally t in the same order
p=-1 q= unknown, s=2, t= unknown
This is the halfway down the question

Then the question tells us P to Q=2 Q to S
It means p=-1 q=1,s=2 {p to q= 1-(-1)=2; and since s we know is 2 then q to us is 2-1 =1}
S is the average of q and t
$$therefore 2=1+\frac{t}{2}$$

t+1 =4
t=3

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

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14 Jul 2016, 11:26
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

[Reveal] Spoiler:
D

I dont have the OA.

No fancy mathematics is need here just make a big line and divide it into 4 parts (like we do in a number line)

Now since the ascending order is p,q,s,t ; name the parts p,q,s and finally t in the same order
p=-1 q= unknown, s=2, t= unknown
This is the halfway down the question

Then the question tells us distance from (P to Q)=twice the distance from (Q to S)
It means p=-1 q=1,s=2 {p to q= 1-(-1)=2; and since s we know is 2 then q to us is 2-1 =1}
S is the average of q and t
therefore $$S=\frac{q+t}{2}$$

therefore $$2=\frac{1+t}{2}$$

t+1 =4
t=3

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 367 [0], given: 36

On the real number line, there are four points P, Q, S, and   [#permalink] 14 Jul 2016, 11:26
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