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

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Is the number of seconds required to travel d1 feet at r1 [#permalink]  21 Nov 2010, 00:57
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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.

Statements 1 and 2 ALONE are surely not sufficient to answer the question.

However i think BOTH statements TOGETHER are sufficient

From Statement 1:

(d2 + 30)/r1

From Statement 2:

d1 / (r2 + 30)

From Statement 1 and 2:

(d2 + 30) / (r2 + 30)

Now if anyone has done Manhattan, refer Page 28 FDP which says, ''increasing BOTH the numerator and the denominator by THE SAME VALUE brings the fraction closer to 1."

It means it increases the original value, right.

So if i have to decide which is greater, (1) (d2 + 30) / (r2 + 30) or (2) d2 / r2, obviously it has to be (1).

OG explaination says Statement (1) and (2) TOGETHER are not sufficient.

What's yours view guys??
[Reveal] Spoiler: OA
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Re: OG 12 DS Q 87 - Can someone validate my logic? [#permalink]  21 Nov 2010, 01:45
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chiragatara 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.

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.

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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Re: OG 12 DS Q 87 - Can someone validate my logic? [#permalink]  21 Nov 2010, 12:22
excellent explanation by bunuel
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  02 Feb 2012, 09:05
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.
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  02 Feb 2012, 10:04
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thuydo246 wrote:
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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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  02 Feb 2012, 11:52
Oh thank you. I just created a brand new problem. Thanks for pointing this out.
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Re: OG 12 DS Q 87 - Can someone validate my logic? [#permalink]  10 Mar 2012, 00:24
Bunuel wrote:
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

This is the key property to remember. Thank you Bunuel! +1
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  24 Jun 2013, 02:17
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  25 Jun 2013, 07:28
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  04 Oct 2014, 09:53
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Re: Is the number of seconds required to travel d1 feet at r1   [#permalink] 04 Oct 2014, 09:53
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