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Rate/Work DS - Really bugging me!

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Rate/Work DS - Really bugging me!

by wayofjungle » Sat May 14, 2011 9:52 am
Is the number of seconds required to travel D feet at R feet per second greater than the number of seconds to travel T feet at F feet per second?

1. D is 30 greater than T
2. R is 30 greater than F

[spoiler]This is Q87 from OG12, OA is E, but I am convinced the answer is C. When both statements are combined the question becomes is (T+30)/(F+30) > T/F right? In that case the answer should be 'yes'. OG gives no explanation, so please enlighten me if you understand. Thanks[/spoiler]
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by manpsingh87 » Sat May 14, 2011 10:03 am
wayofjungle wrote:Is the number of seconds required to travel D feet at R feet per second greater than the number of seconds to travel T feet at F feet per second?

1. D is 30 greater than T
2. R is 30 greater than F

[spoiler]This is Q87 from OG12, OA is E, but I am convinced the answer is C. When both statements are combined the question becomes is (T+30)/(F+30) > T/F right? In that case the answer should be 'yes'. OG gives no explanation, so please enlighten me if you understand. Thanks[/spoiler]
1) D=30+T; since we don't have information about R and F hence 1 alone is not sufficient to answer the question.

2) R=30+F; since we don't have information about D and T hence 2 alone is not sufficient to answer the question.

combining 1 and 2 we have;

D=30+T and R=30+F;

therefore time taken in traveling D feet= 30+T/30+F;
and time taken in traveling T feet = T/F;

if T=F=2; we have time taken in traveling D and T feet=1 seconds;
if T=4 and F=2; time taken in traveling D distance would be; 34/32=17/16~1.06; while T/F=4/2=2;

as different results are possible depending upon different values of T and F hence answer should be E
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by smackmartine » Sat May 14, 2011 10:10 am
IMO E

R(S1) = D & T(S2) = F , where S1 and S2 are respective times(in sec)
Asked : S1-S2 is -ve or positive

1) D=T+30 , NO info about relation between Rates --> Insufficient
2) R=F+30 , NO info about relation between distance--> Insufficient

Combining 1 and 2

S1-S2 = (D/R) - (F/T) = (T+30)/R - (R-30)/T ----> There is no way we can solve this expression using two unknown variables , So Insufficient
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by wayofjungle » Sat May 14, 2011 11:21 am
Yikes. I was stuck on the concept as discussed on page 28 of the 2nd MGMAT Guide (Fractions, Decimals...) which states:

"Adding the same number to BOTH the numerator and denominator brings the fraction CLOSER TO 1, regardless of the fraction's value"

In this problem I neglected to consider the case where T/F is not truly a fraction but instead simply a division operation of two variables where T > F, or a mixed number.

Thanks for helping me get smarter!
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by GMATGuruNY » Sun May 15, 2011 1:48 am
wayofjungle wrote:Is the number of seconds required to travel D feet at R feet per second greater than the number of seconds to travel T feet at F feet per second?

1. D is 30 greater than T
2. R is 30 greater than F

[spoiler]This is Q87 from OG12, OA is E, but I am convinced the answer is C. When both statements are combined the question becomes is (T+30)/(F+30) > T/F right? In that case the answer should be 'yes'. OG gives no explanation, so please enlighten me if you understand. Thanks[/spoiler]
Question: Is D/R > T/F?

Since the question is restricted to positive integers, we can cross-multiply and rephrase the question:

Is DF > RT?

Statement 1: D is 30 greater than T.
No information about F or R.
Insufficient.

Statement 2: R is 30 greater than F.
No information about D or T.
Insufficient.

Statements 1 and 2 combined:
D is 30 greater than T and R is 30 greater than F.
Is DF > RT?
Let T=1, D=31, F=1, R=31.
Is 31*1 > 31*1? No.
Let T=1, D=31, F=2, R=32.
Is 31*2 > 32*1? Yes.
Since the answer can be both No and Yes, insufficient.

The correct answer is E.
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by bblast » Sun May 15, 2011 5:37 am
this tests a fundamental concept of ratios.

"if the same number is added to the numerator and denominator a fraction:

1> if the fraction is proper the value of fraction increases
example
1/3 - add 1 to both num and denominator- fraction increases to 2/4


2> if the fraction is improper the value of fraction decreases"
example
3/2 - add 1 to both num and denominator- fraction decreases to 4/3


Hence in this solution we cannot say which of the fractions is larger.

(T+30)/(F+30)
OR
T/F



Mitch, please Correct me if I am wrong
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