Data Sufficiency

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

They say answer is E. I think it is C. Here is the reasoning

d1 = d2 + 30;
r1 = r1 + 30

so d1/r1 = (d2+30)/(r2+30) and hence d1/r1 > dr/r2

for any two numbers a, b & c; a/b < (a+c)/(b+c)

Let me know if i am being crazy here.

With the DS questions I usually attempt to find just one scenario where both conditions together would fail. If d1 is a fraction then wouldn't the first rate be less than the second. For instance if d1= .5 and d2 = 30.5, wouldn't the d1 rate then be less than the d2 rate?

But they are asking to compare the seconds so we have to compare d/t

I can't explain the theory so I hope someone comes behind me and does that but if you have d1 =30 r1 = .5, and d2 =80 and r2 = 30.5 then the d2/r2 is faster, but if you use whole numbers with both then d1/r1 is faster

Thanks osirus0830
Tried a few more cases and was able to get the answer you were getting.

vinayakdl 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

They say answer is E. I think it is C. Here is the reasoning

d1 = d2 + 30;
r1 = r1 + 30

so d1/r1 = (d2+30)/(r2+30) and hence d1/r1 > dr/r2

for any two numbers a, b & c; a/b < (a+c)/(b+c)

Let me know if i am being crazy here.

Hi guys,
This is a nice little DS question.

This is my take on it:
vinayakdl, you're not being crazy but you have dropped your shield.

Your reasoning is almost there.

First, let's assume that the numbers involved are positive and they are.
Second, in order for a/b to be strictly less than (a+c)/(b+c), a must be strictly less than b (a < b).

I could prove this easily but take my word for it or try a few numbers yourself.

Now, we don't know whether d2<r2, so we won't know whether
d2/r2 < (d2 + 30)/(r2 + 30).
Hence, no way of knowing whether d1/r1 (which is the time required to travel distance d1 at rate r1) is greater than d2/r2 (which is the time required to travel distance d2 at rate r2).

You could have picked numbers as well but which numbers to pick here is another matter altogether.

(E) is the correct answer.

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This was today's GMAT math recipe from the GMAT Chef.