Is the number of seconds required to travel d1 feet at r1

Is \(\frac{d_1}{r_1}>\frac{d_2}{r_2}\)?

Obviously each statement alone is not sufficient.

When taken together we'l have: is \(\frac{d_2+30}{r_2+30}>\frac{d_2}{r_2}\)? --> cross multiply (we can safely do that as in both fractions denominator and nominator are positive): \(d_2*r_2+30r_2>d_2*r_2+30d_2\) --> is \(r_2>d_2\)? so we have that \(\frac{d_2+30}{r_2+30}>\frac{d_2}{r_2}\) holds true when \(r_2>d_2\), but we don't know whether that's true so even taken together statements are not sufficient.

Answer: E.

Generally if \(a\), \(b\) and \(c\) are positive numbers and \(a>b\) then \(\frac{a}{b}>\frac{a+c}{b+c}\) (or as you mention \(\frac{a+c}{b+c}\) is closer to 1 then \(\frac{a}{b}\), but as \(\frac{a}{b}>1\) then \(\frac{a+c}{b+c}\) is getting less to be closer to 1). For example: \(\frac{3}{2}>\frac{3+30}{2+30}\);

But if \(a\), \(b\) and \(c\) are positive numbers and \(a<b\) then \(\frac{a}{b}<\frac{a+c}{b+c}\) (again \(\frac{a+c}{b+c}\) is closer to 1 then \(\frac{a}{b}\), but as \(\frac{a}{b}<1\) then \(\frac{a+c}{b+c}\) is getting bigger to be closer to 1). For example: \(\frac{4}{5}<\frac{4+30}{5+30}\).

Hope it's clear.
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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.

In the original condition, there are 4 variables(r1,d1,r2,d2), which should match with the number of equations. So you need 4 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. In 1) & 2), d1/r1>d2/r2? becomes (30+d2)/(30+r2)>d2/r2?, which also develops into (30+d2)r2>(30+r2)d2?. From 30r2+d2r2>30d2+r2d2?, delete r2d2 in the both equations and they become 30r2>30d2?. So, you cannot get the answer from r2>d2?, which is not sufficient. Therefore, the answer is E.


-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

excellent explanation by bunuel
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Hi

For this question, r1, r2 are positive
r1>r2+30
so 1/r1<1/r2
Thus, d1/r1>d2/r2.

I am not quite sure what I did wrong here. Help!
Thank you.

Your conclusion is not right. Also we have:

(1) \(d_1=d_2+30\);
(2) \(r_1=r_2+30\);

Not r1>r2+30 as you wrote.

Please, see my solution above (I've just merged the topics, so it's new there) and ask if anything remains unclear.

Hope it helps.
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Oh thank you. I just created a brand new problem. Thanks for pointing this out.

This is the key property to remember. Thank you Bunuel! +1

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


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Clearly either of the statements are not sufficient.

Lets look at (1) + (2) case

d1=30+d2
r1=r2+30
t1 = d1/r1 and t2=d2/r2
t1 = (30+d2)/(30+r1)

Lets consider two cases, lets take d2/r2 = 1/2 and 2/1

if t2=d2/r2 = 1/2

Then, t1 = 31/32 =0.9 something that is greater then 1/2 i.e. 0.5

if t2=d2/r2 = 2/1

Then, t1 = 32/31 =0.1 something that is less than 2/1 i.e. 2

Hence we cant say => Not sufficient

Ans: E

In this question I do have have a doubt could anyone help me and correct me if I'm wrong:
here Q: t1=d1/r1> t2=d2/r2

condtions : statement 1: d1=d2+30
statement 2: r1=r2+30

Individually insufficient, but why cant ans be C

plugging the values:

case1: d2=30 and r2=10==> d1=60 and r2=40==>t1=60/40=1.5 sec and t2=30/10=3sec==>1.5sec<3 sec SUFF

case 2: d2=20 and r2=5==> d1=50 and r2=35==>t1=20/5=4 sec and t2=50/35=1.4sec==>4 sec>1.4 sec SUFF

Because it gives ans yes/no

help

Responding to a pm:

The question is based on the concept discussed here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... round-one/

Question: Is \(\frac{d1}{r1} > \frac{d2}{r2}\)?

Each statement alone is not sufficient. Statement 1 doesn't give any data on rates and statement 2 doesn't give any data on distance.

Using both,
d1 = d2 + 30
r1 = r2 + 30

Question: Is \(\frac{d2+30}{r2+30} > \frac{d2}{r2}\)?

What is the number property related to adding same numbers to both numerator and denominator?

Say 3/4. Add 1 to both you get 4/5. Add 2 to both you get 5/6. It increases the fraction.

Say 5/4. Add 1 to both you get 6/5. Add 2 to both you get 7/6. It decreases the fraction.

So this depends on whether \(\frac{d2}{r2}\) is less than 1 or greater than 1.

Hence until and unless we know the value of d1/r1, we cannot answer this question.

Answer (E)
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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?

We need to find whether \(\frac{d_1}{r_1}>\frac{d_2}{r_2}\).

(1) d1 is 30 greater than d2 --> \(d_1=d_2+30\). Nothing about the rates. Not sufficient.
(2) r1 is 30 greater than r2 --> \(r_1=r_2+30\). Nothing about the distances. Not sufficient.

(1)+(2) The question becomes whether \(\frac{d_2+30}{r_2+30}>\frac{d_2}{r_2}\). Now, if \(d_2=r_2\), then \(\frac{d_2+30}{r_2+30}=\frac{d_2}{r_2}\), thus in this case the answer would be NO but if \(d_2=1\) and \(r_2=2\), then in this case \(\frac{d_2+30}{r_2+30}=\frac{31}{32}>\frac{1}{2}=\frac{d_2}{r_2}\), thus in this case the answer would be YES. Not sufficient.

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-the-number ... 43694.html
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