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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]  06 Dec 2012, 06:46
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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.
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  06 Dec 2012, 06:50
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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.

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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  18 Dec 2012, 05:35
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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.

Hi,

St1 and st 2 alone are not sufficient so combining we get

IS

(d2+30)/(r2+30) > d2/r2

The asnwer to this Question will depend upon the ratio of d2/r2.

If d2/r2 is <1, then on adding the same + ve qty to Num & Den will increase the ratio value
if d2/r2 is > 1 ,then on adding the same qty will decrease the ratio

Hence ans E
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Distance and Speed - Question 90 from OG13 [#permalink]  31 Jan 2013, 09:20
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.

Now, when I solved this question, I was surprised to see that the solution was (E), i.e, none of the statements provide sufficient information.

I recall, however, that when you add the same number to both the numerator and denominator of a fraction, the resulting fraction is always closer to 1. Using that logic, statements (1) and (2) TOGETHER provide sufficient information. Am I approaching this wrong here?

EDIT:
[Reveal] Spoiler:
Okay, figured it out. The information regarding which number is bigger (the speed or the distance) is not provided. Which means that the new fraction (r2 and d2) could actually be approaching 1 from either 0 or from infinity. Clever.
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Re: Distance and Speed - Question 90 from OG13 [#permalink]  31 Jan 2013, 09:44
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Hi Absar,

As with all DS: translating the given information is critical

So the real question is: D1/R1 > D2/R2?

(1) D1 = D2 + 30 You can substitute one of the variables. BUT R1 and R2 could be anything so you could answer yes by making R1 very tiny number and R2 a huge number or you could do the opposite and the answer would be no. Insufficient.

(2) R2 = R2 + 30 The same logic as a above for this statement

(1) + (2) If you put the statements together the question becomes: D2+30/R2+30 > D2/R2

You should test very big values and very small values to see what happens. If R2 is a very tiny value and D2 is a massive value then the left side will be smaller than the right side because R2 will be increased by a much greater factor than will D2.

D2 = 1000 --------> 1030/31 > 1000/1 NO
R2 = 1

And vice-versa, if DS is a tiny value and R2 is a massive value than the left side will be greater because D2 will have a greater percentage increase than R2.

D2 = 1 ---------> 31/1030 > 1/1000 YES
R2 = 1000

So, you are able to say Yes and No to the original question so there the answer is E

Let me know if you have any questions on this!

HG.
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Re: Distance and Speed - Question 90 from OG13 [#permalink]  31 Jan 2013, 13:25
Expert's post
AbsarShah 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.

Now, when I solved this question, I was surprised to see that the solution was (E), i.e, none of the statements provide sufficient information.

I recall, however, that when you add the same number to both the numerator and denominator of a fraction, the resulting fraction is always closer to 1. Using that logic, statements (1) and (2) TOGETHER provide sufficient information. Am I approaching this wrong here?

EDIT:
[Reveal] Spoiler:
Okay, figured it out. The information regarding which number is bigger (the speed or the distance) is not provided. Which means that the new fraction (r2 and d2) could actually be approaching 1 from either 0 or from infinity. Clever.

Merging similar topics. Please refer to the solutions above and ask if anything remains unclear.
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Is the number of seconds required to travel d1 feet at r1 feet p [#permalink]  15 May 2013, 22:41
kapilnegi 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.

questions is t1 > t2?
or (d1/r1) > (d2 / r2)?
=> (d2 + 30)/(r2 + 30) > (d2/r2)?
=> [[(d2+30)-(r2+30)]/(r2 + 30)] > (d2-r2)/r2 -- subtract 1 on both sides
=> [(d2-r2)/(r2+30)]>(d2-r2)/r2
=> 1/(r2+30) > 1/(r2)
=> (r2+30) < r2
=> 30 < 0 ?
This questions IMO is not answerable but justified in OG . Any thoughts? Am I wrong?
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  16 May 2013, 00:29
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kapilnegi 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.

This problem depends on the following concept.

If a,b are two positive numbers. and k is any positive number

a. if a/b is greater than 1 then a+k/b+k is less than a/b
b. if a/b is less than 1 then a+k/b+k is greater than a/b

Now consider the Above question

we have d1/r1 and d2/r2.

but d1 = d2 + 30
r1 = r2 + 30

so we have d2+30/r2 + 30 and d2/r2

but we don't know whether d2 is greater than r2. So together these statements are not sufficient
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Re: Is the number of seconds required to travel d1 feet at r1 fe [#permalink]  16 May 2013, 03:49
Expert's post
kiranck007 wrote:
kapilnegi 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.

questions is t1 > t2?
or (d1/r1) > (d2 / r2)?
=> (d2 + 30)/(r2 + 30) > (d2/r2)?
=> [[(d2+30)-(r2+30)]/(r2 + 30)] > (d2-r2)/r2 -- subtract 1 on both sides
=> [(d2-r2)/(r2+30)]>(d2-r2)/r2
=> 1/(r2+30) > 1/(r2)
=> (r2+30) < r2
=> 30 < 0 ?
This questions IMO is not answerable but justified in OG . Any thoughts? Am I wrong?

Merging similar topics.

The correct answer is E. Check here: is-the-number-of-seconds-required-to-travel-d1-feet-at-r1-143694.html#p1151497

Hope it helps.
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  30 Jul 2013, 14:50
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?

Time = distance/rate

t1>t2?

(1) d1 is 30 greater than d2

We know nothing about the rate for r1 and r2.
INSUFFICIENT

(2) r1 is 30 greater than r2.

We know nothing about the distance of 1 an 2. Even if r1 is greater, the distance for 2 may be proportionally less so that even at a slower speed, d2 is covered in less time than d1.
INSUFFICIENT

1+2)

Hypothetical A:

1: Distance = 31 feet and rate = 31 feet/second
2: Distance = 1 feet and rate = 1 foot/second

In this case the time it takes for both is the same.

Hypothetical B:

1: Distance = 330 feet and rate = 60 feet/second
Time = Distance / Rate
Time = 330 / 60
Time = 11/3 seconds

2: Distance = 300 feet and rate = 30 feet/second
Time = Distance/Rate
Time = 300 / 30
Time = 10 seconds

It's possible that the time to cover d1 is the same as d2. It also may be greater.
INSUFFICIENT

(E)
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  01 Aug 2014, 08:58
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  07 Mar 2015, 08:36
kiranck007 wrote:
kapilnegi 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.

questions is t1 > t2?
or (d1/r1) > (d2 / r2)?
=> (d2 + 30)/(r2 + 30) > (d2/r2)?
=> [[(d2+30)-(r2+30)]/(r2 + 30)] > (d2-r2)/r2 -- subtract 1 on both sides
=> [(d2-r2)/(r2+30)]>(d2-r2)/r2
=> 1/(r2+30) > 1/(r2)
=> (r2+30) < r2
=> 30 < 0 ?
This questions IMO is not answerable but justified in OG . Any thoughts? Am I wrong?

Can someone verify the above cited approach for this particular DS question?
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  07 Mar 2015, 09:17
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samichange wrote:
kiranck007 wrote:
kapilnegi 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.

questions is t1 > t2?
or (d1/r1) > (d2 / r2)?
=> (d2 + 30)/(r2 + 30) > (d2/r2)?
=> [[(d2+30)-(r2+30)]/(r2 + 30)] > (d2-r2)/r2 -- subtract 1 on both sides
=> [(d2-r2)/(r2+30)]>(d2-r2)/r2
=> 1/(r2+30) > 1/(r2)
=> (r2+30) < r2
=> 30 < 0 ?
This questions IMO is not answerable but justified in OG . Any thoughts? Am I wrong?

Can someone verify the above cited approach for this particular DS question?

hi samichange,
this kind of approach is not required, it will just complicate the matters .. take each statement separately and then combined to see if they satisfy the answer...
i think the approach was to show that the question is not justified as after simplifying it gives 30<0, which is not possible ...
however the person has gone wrong after the colored portion... u just cant cancel d2-r2 from each side..
you have to get the entire thing on one side and take d2-r2 as common term outside..
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  12 Jun 2015, 18:21
Bunuel 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?

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.

Hi Bunuel,

I got the correct answer. However, i just pondered over this and found the below. Can you help me find out where am i wrong over here?

D2 + 30 / r2 + 30 > d2/r2 ( combining the 2 statements)

Now, r2(d2 +30) > d2(r2 +30)
r2d2 + 30r2 > d2r2 + 30d2
r2 > d2

Then 2 st are sufficient together right?
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  28 Jul 2015, 09:52
what level question is this?
i know it says 700, but is it really?
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Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]  16 Nov 2015, 01:09
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.

I would rather simplify this expression further to derive at the answer:
$$\frac{d2+30}{r2+30} > \frac{d2}{r2}$$ --> $$r2*d2+30*r2 > d2*r2 + 30*d2$$, r2d2 cancel out and we have 30*r2 > 30*d2, if r2=d2 the answer is no, and if r2 > d2 the answer is yes, thus Answer (E)
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Re: Is the number of seconds required to travel d1 feet at r1   [#permalink] 16 Nov 2015, 01:09
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