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Senior Manager  S
Status: No dream is too large, no dreamer is too small
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On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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4 00:00

Difficulty:   5% (low)

Question Stats: 86% (01:38) correct 14% (01:49) wrong based on 238 sessions

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On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s – t)/(t – r) =

(A) 1/4
(B) 1/3
(C) 4/3
(D) 3
(E) 4

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Originally posted by Baten80 on 17 Feb 2011, 07:54.
Last edited by Bunuel on 05 May 2019, 20:23, edited 2 times in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 64949
Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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1
1
Baten80 wrote:
On the number line, if r<S, if p is the halfway between r and s, and if t is the halfway between p and r, then s-t/t-r=

1/4
1/3
4/3
3
4

Also what do you mean by "What i will the s-t either s minus t or s to t"?

Original question is:

On the number line, if r<s, if p is halfway between r and s, and if t is halfway between p and r then (s-t)/(t-r)=
A. 1/4
B. 1/3
C. 4/3
D. 3
E. 4

Let r=0 and s=4 --> p is halfway between r and s: p=2;
t is halfway between p=2 and r=0: t=1;

(s-t)/(t-r)=(4-1)/(1-0)=3.

P.S. On the GMAT we can often see such statement: $$k$$ is halfway between $$m$$ and $$n$$ on the number line. Remember this statement can ALWAYS be expressed algebraically as: $$\frac{m+n}{2}=k$$.
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Senior Manager  S
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Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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Math Expert V
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Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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Baten80 wrote:

Question is: $$\frac{s-t}{t-r}=?$$.
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Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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Bunuel wrote:
On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s – t)/(t – r) =

(A) 1/4
(B) 1/3
(C) 4/3
(D) 3
(E) 4

We can solve it using integers..i would like to take negative integers first

r.......t.......p.................s.......0
-5....-4......-3................-1

on solving (-1+4)/(-4+5) = 3

Just to check with positive integers

0.......r.......t.......p.................s
0.......2......3........4................6

on solving (6-3)/(3-2) = 3

Hence D
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Joined: 22 May 2016
Posts: 3938
Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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Bunuel wrote:
On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s – t)/(t – r) =

(A) 1/4
(B) 1/3
(C) 4/3
(D) 3
(E) 4

Find endpoints.

Sketch r < s. From info and logic, neither p nor t can be an endpoint; both are midpoints.

r < s, p is halfway between:

R_____________P_____________S
|------------------|------------------|

t is halfway between p and r:

R______T______P____________S
|----x---|----x---|------2x------|

Track on distance as above. Then use smallest length to define. Let RT = x. Then TP = x, and PS = 2x.

Assign integer value to x; 1 is easy. Assign cardinal values in keeping with the ratios.

Let r = 1. Then t = 2, p = 3, and s, which is 2x = (2)(1) away from p, = 5.

A. (s - t) => (5 - 2) = 3
B. (t - r) => (2 - 1) = 1

$$\frac{A}{B}$$ = $$\frac{3}{1}$$ = 3

I tested it with x=2 as well, and started with r = 3. The ratio holds.

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Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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Bunuel wrote:
Baten80 wrote:
On the number line, if r<S, if p is the halfway between r and s, and if t is the halfway between p and r, then s-t/t-r=

1/4
1/3
4/3
3
4

Also what do you mean by "What i will the s-t either s minus t or s to t"?

Original question is:

On the number line, if r<s, if p is halfway between r and s, and if t is halfway between p and r then (s-t)/(t-r)=
A. 1/4
B. 1/3
C. 4/3
D. 3
E. 4

Let r=0 and s=4 --> p is halfway between r and s: p=2;
t is halfway between p=2 and r=0: t=1;

(s-t)/(t-r)=(4-1)/(1-0)=3.

P.S. On the GMAT we can often see such statement: $$k$$ is halfway between $$m$$ and $$n$$ on the number line. Remember this statement can ALWAYS be expressed algebraically as: $$\frac{m+n}{2}=k$$.

niks18 hi there i took following numbers R=2, S=5, T=3, P =4 whats wrong with my reasoning ? im free to choose any numbers as long as p is the halfway between r and s, and if t is the halfway between p and r. No ?  thanks & have a great weekend Retired Moderator D
Joined: 25 Feb 2013
Posts: 1123
Location: India
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Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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1
dave13 wrote:
Bunuel wrote:
Baten80 wrote:
On the number line, if r<S, if p is the halfway between r and s, and if t is the halfway between p and r, then s-t/t-r=

1/4
1/3
4/3
3
4

Also what do you mean by "What i will the s-t either s minus t or s to t"?

Original question is:

On the number line, if r<s, if p is halfway between r and s, and if t is halfway between p and r then (s-t)/(t-r)=
A. 1/4
B. 1/3
C. 4/3
D. 3
E. 4

Let r=0 and s=4 --> p is halfway between r and s: p=2;
t is halfway between p=2 and r=0: t=1;

(s-t)/(t-r)=(4-1)/(1-0)=3.

P.S. On the GMAT we can often see such statement: $$k$$ is halfway between $$m$$ and $$n$$ on the number line. Remember this statement can ALWAYS be expressed algebraically as: $$\frac{m+n}{2}=k$$.

niks18 hi there i took following numbers R=2, S=5, T=3, P =4 whats wrong with my reasoning ? im free to choose any numbers as long as p is the halfway between r and s, and if t is the halfway between p and r. No ?  thanks & have a great weekend Hi dave13

Before I answer your question, what according to you is "halfway"? how do you define "halfway" and as per that definition what will be the "halfway" of 2 & 5
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Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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dave13 wrote:
i took following numbers R=2, S=5, T=3, P =4 whats wrong with my reasoning ? im free to choose any numbers as long as p is the halfway between r and s, and if t is the halfway between p and r. No ?  thanks & have a great weekend Hey dave13 ,

Halfway means middle of the two numbers.

So, If the distance between you and I is 1000 Kms, then the halfway between us will be 500 Kms away from both of us.

Does that make sense?
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Re: On the number line, if r < s, if p is halfway between r and s, and if  [#permalink]

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_________________ Re: On the number line, if r < s, if p is halfway between r and s, and if   [#permalink] 17 Apr 2020, 05:53

# On the number line, if r < s, if p is halfway between r and s, and if  