On the number line, if r<s, if p is halfway between rand 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
[spoiler](OA) D[/spoiler]
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GMATGuruNY
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Let r=1 and p=3.AkiB wrote:On the number line, if r<s, if p is halfway between rand 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
Since t is halfway between r=1 and p=3, t=2.
Since p=3 is halfway between r=1 and s, s=5.
Thus, (s-t)/(t-r) = (5-2)/(2-1) = 3.
The correct answer is D.
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Mathsbuddy
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First put the letters in order to see what it looks like:
SMALLEST... r t p q s (where q is a space holder half-way between p and s) ...BIGGEST
Now use simple numbers, such as r = 0, t = 1, p = 2, s = 4:
(s-t)/(t-r) = (4-1)/(1-0) = 3.
SMALLEST... r t p q s (where q is a space holder half-way between p and s) ...BIGGEST
Now use simple numbers, such as r = 0, t = 1, p = 2, s = 4:
(s-t)/(t-r) = (4-1)/(1-0) = 3.
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ceilidh.erickson
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I agree with other posters that picking numbers is by far the easiest approach to this question. If you insist upon doing it algebraically, though, here is the solution:
p is halfway between rand s
We can infer that s - p = p - r
t is halfway between p and r
p - t = t - r
Solve for s in the first equation:
s - p = p - r
s = 2p - r
Solve for p in the 2nd equation:
p - t = t - r
p = 2t - r
Plug in for p in the 1st:
s = 2(2t - r) - r
s = 4t - 3r
Plug this value of s into the expression (s - t)/(t - r):
(4t - 3r - t)/(t - r)
(3t - 3r)/(t - r)
Factor a 3 out of the numerator, and the (t - r) terms will cancel. We're left with 3.
p is halfway between rand s
We can infer that s - p = p - r
t is halfway between p and r
p - t = t - r
Solve for s in the first equation:
s - p = p - r
s = 2p - r
Solve for p in the 2nd equation:
p - t = t - r
p = 2t - r
Plug in for p in the 1st:
s = 2(2t - r) - r
s = 4t - 3r
Plug this value of s into the expression (s - t)/(t - r):
(4t - 3r - t)/(t - r)
(3t - 3r)/(t - r)
Factor a 3 out of the numerator, and the (t - r) terms will cancel. We're left with 3.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
