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DS: Inequality criteria for fractions.

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DS: Inequality criteria for fractions.

by simplyjat » Wed Jan 16, 2008 11:16 pm
AFAIK, (x+a)/(y+a) is always greater than x/y; i.e. if you add same number to numerator and denominator, the value of fraction increases.

Yesterday I came across a DS problem that basically boiled down to comparison between (x+a)/(y+a) & x/y. And the OA was E (both insufficient) but my opinion was of C (both sufficient together)

Is my memory wrong in claiming (x+a)/(y+a) is always greater than x/y or it is just that OA is wrong...
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by simplyjat » Wed Jan 16, 2008 11:51 pm
Just of everyone's reference; here is the question

Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?
(1) d1 is 30 greater than d2.
(2) r1 is 30 greater than r2.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.
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by StarDust845 » Thu Jan 17, 2008 6:22 am
the question boils down to Is 30/30 > d2/r2? where 30 > d2 and 30 > r2? In other words is d2 > r2? We have INSUFF info to answer this question. Hence E.

I don't know where you got x+a from.

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by Stuart@KaplanGMAT » Thu Jan 17, 2008 6:34 am
simplyjat wrote:Just of everyone's reference; here is the question

Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?
(1) d1 is 30 greater than d2.
(2) r1 is 30 greater than r2.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.
From the original, we get the two equations:

t1 = d1/r1 and t2 = d2/r2

The question is asking: is t1 > t2?

(1) d1 = d2 +30

Nothing about r1 or r2, insufficient.

(2) r1 = r2 + 30

Nothing about d1 or d2, insufficient.

If we combine them, we can rewrite the original question as:

Is (d2 +30)/(r2+30) > d2/r2 ?

Let's pick numbers to see if we can get both a yes and a no.

If d2 = 20 and r2 = 10, then we get the question:

Is 50/40 > 20/10? Is 5/4 > 2? No.

If d2 = 10 and r2 = 20, then we get the question:

Is 40/50 > 10/20? Is 4/5 > 1/2? Yes.

Since we can get both a yes and a no, we still don't have enough information to answer the question: choose (E)!
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by StarDust845 » Thu Jan 17, 2008 9:04 am
Thanks Stuart. I should read the question more carefully.
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by simplyjat » Thu Jan 17, 2008 9:56 pm
Thanks for the explanation "Stuart"

I forgot the concept of proper fraction,
(x+a)/(y+a) is greater than x/y only when x/y is a proper fraction, i.e. x < y
This does no hold true for improper fractions.
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