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

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21 Nov 2010, 00:57

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A

B

C

D

E

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62% (02:15) correct
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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.

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.

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: \(\frac{4}{5}<\frac{4+30}{5+30}\).

Re: OG 12 DS Q 87 - Can someone validate my logic? [#permalink]

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10 Mar 2012, 00:24

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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]

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04 Oct 2014, 09:53

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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]

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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.
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