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question 90 on OG 13th edition - please help

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question 90 on OG 13th edition - please help

by pcmdotcom » Fri Mar 22, 2013 7:57 am
the question goes like this
Is the number 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

I understand how 1 and 2 are insufficient but I dont understand how 1 and 2 combined (answer choice C) arent sufficient.

In my opinion the questions asks: Is d1/r1 > d2/r2?

If we combine the statements the equuation becomes

d1/r1 > d1 - 30/ r1 - 30 because d2 = d1- 30 and r2 = r1 - 30

For all possible values of d1 and r1 the left side will be greater than right side. Isn't my answer correct?

The answer listed in the solutions is E (both are insufficeint)
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by Anju@Gurome » Fri Mar 22, 2013 8:05 am
pcmdotcom wrote: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
We need to determine whether d1/r1 is greater than d2/r2 or not.

Consider the following cases,
  • ## d1 = 50, d2 = 20 and r1 = 40, r2 = 10
    d1/r1 = 50/40 = 5/4 = 1.25 and d2/r2 = 20/10 = 2
    Hence, d1/r1 < d2/r2
    ## d1 = 40, d2 = 10 and r1 = 50, r2 = 20
    d1/r1 = 40/50 = 4/5 = 0.8 and d2/r2 = 10/20 = 1/2 = 0.5
    Hence, d1/r1 > d2/r2
Both of the above examples satisfy both the statements but the answer is NO in the first case and YES in the second case.

The correct answer is E.
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by Anju@Gurome » Fri Mar 22, 2013 8:25 am
pcmdotcom wrote:In my opinion the questions asks: Is d1/r1 > d2/r2?

If we combine the statements the equuation becomes

d1/r1 > d1 - 30/ r1 - 30 because d2 = d1- 30 and r2 = r1 - 30

For all possible values of d1 and r1 the left side will be greater than right side. Isn't my answer correct?)
No. If you decrease both the numerator and denominator of a fraction by the same amount, there is no guarantee that the new fraction will be smaller than the original one. Even if you reduce the numerator more than the denominator, still we cannot say any such thing.

For example, 3/2 is not greater than (3 - 1)/(2 - 1) = 2

In this case, multiply both the denominator and numerator of my example with 30 : 90/60 is not greater than 60/30.

Hope that helps.
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by pcmdotcom » Fri Mar 22, 2013 8:48 am
Thank you. That was pretty helpful.
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by GMATGuruNY » Sat Mar 23, 2013 3:31 am
pcmdotcom wrote:the question goes like this
Is the number 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
Is d1/r1 > d2/r2?

Clearly, neither statement alone is sufficient.

Statements combined:
Since d1=d2+30 and r1=r2+30, the question stem can be rephrased as follows:
Is (d2 + 30)/(r2 + 30) > d2/r2?

Case 1: d2=1 and r2=1
(1+30)/(1+30) > 1/1
1 > 1.
NO.

Case 2: d2=1 and r2=2
(1+30)/(2+30) > 1/2
31/32 > 1/2.
YES.

Since in the first case the answer is NO, but in the second case the answer is YES, INSUFFICIENT.

The correct answer is E.
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