Last visit was: 12 Aug 2024, 23:36 It is currently 12 Aug 2024, 23:36
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 02 Dec 2012
Posts: 172
Own Kudos [?]: 24700 [214]
Given Kudos: 29
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649126 [75]
Given Kudos: 86922
Tutor
Joined: 27 Jan 2013
Posts: 257
Own Kudos [?]: 629 [12]
Given Kudos: 38
GMAT 1: 760 Q47 V48
GMAT 2: 770 Q49 V47
GMAT 3: 780 Q49 V51
General Discussion
Director
Joined: 25 Apr 2012
Posts: 529
Own Kudos [?]: 2335 [11]
Given Kudos: 740
Location: India
GPA: 3.21
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
8
Kudos
3
Bookmarks
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
Intern
Joined: 20 Jan 2013
Posts: 27
Own Kudos [?]: 7 [1]
Given Kudos: 3
Location: United Arab Emirates
GMAT 1: 680 Q46 V38
WE:Engineering (Consulting)
Distance and Speed - Question 90 from OG13 [#permalink]
1
Kudos
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:
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.
Intern
Joined: 14 Jan 2013
Posts: 19
Own Kudos [?]: 94 [0]
Given Kudos: 43
Location: India
Is the number of seconds required to travel d1 feet at r1 feet p [#permalink]
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?
Intern
Joined: 05 Mar 2013
Posts: 33
Own Kudos [?]: 145 [4]
Given Kudos: 14
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06-05-2013
GPA: 3.2
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
4
Kudos
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
Senior Manager
Joined: 13 May 2013
Posts: 311
Own Kudos [?]: 574 [0]
Given Kudos: 134
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
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)
Manager
Joined: 01 Nov 2013
Posts: 245
Own Kudos [?]: 972 [0]
Given Kudos: 410
GMAT 1: 690 Q45 V39
WE:General Management (Energy and Utilities)
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
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?
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11528
Own Kudos [?]: 35118 [1]
Given Kudos: 333
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
1
Kudos
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..
Intern
Joined: 23 Jul 2013
Posts: 10
Own Kudos [?]: 2 [0]
Given Kudos: 29
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
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?
Current Student
Joined: 10 Mar 2013
Posts: 355
Own Kudos [?]: 2751 [1]
Given Kudos: 200
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.7
WE:Marketing (Telecommunications)
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
1
Kudos
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)
Manager
Joined: 17 Nov 2013
Posts: 65
Own Kudos [?]: 248 [0]
Given Kudos: 19
Is the number of seconds required to travel d1 feet at r1 [#permalink]
R1T1 =D1 AND R2T2 =D2 => THE QUESTION ASKS IF THE TIME FOR 1 IS FASTER THAN FOR 2. SO FORMULA ALONE YOU CAN SAY $$T1 = \frac{D1}{R1}$$, $$T2 = \frac{D2}{R2}$$

STMT1 SAYS THAT D1> D2 AND IF I PUT THAT INTO THE FORMULA I AM NOT SURE WHAT THE Rs ARE FOR ME TO CONFIRM WHICH ONE IF GREATER. INSUFFICIENT.

STMT2 SAYS THAT R1>R2 AND SIMILAR TO STMT1 I DONT HAVE ENOUGH INFORMATION TO CONFIRM.

COMBINING TOGETHER WE KNOW THAT D1>D2 AND R1>R2, AND OUR FORMULA OF $$\frac{D1}{R1} > \frac{D2}{R2}$$ BUT WHAT WE KNOW ABOUT THESE VALUES DOES NOT HELP BECAUSE D1>D2 HELPS THE LEFT SIDE OF OUR EQUATION TO BE BIGGER WHILE R1>R2 HELPS THE RIGHT SIDE OF THE EQUATION TO BE BIGGER. WITHOUT KNOWING MORE NUMBERS I CANNOT SUFFICIENTLY. ANSWER E.
Intern
Joined: 11 Nov 2014
Posts: 26
Own Kudos [?]: 92 [1]
Given Kudos: 106
Concentration: Marketing, Finance
WE:Programming (Computer Software)
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
1
Kudos
time to travel d1 at r1 speed = d1/r1
time to travel d2 at r2 speed = d2/r2

is d1/r1 > d2/r2 ??

from (1)
d1 = d2+30
not sufficient
from (2)
r1 = r2+30
not sufficient

now from (1) + (2)
is (d2+ 30)/(r2+30) > d2/r2

first lets take d2 = 1 and r2 = 2
31/32 > 1/2 holds true
but if d2 = 2 and r2 = 1
32/31 < 2/1 does nt hold true.

so correct option is E .
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6691 [6]
Given Kudos: 1646
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
5
Kudos
1
Bookmarks
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.

Solution:

We need to determine whether the number of seconds required to travel d_1 feet at r_1 feet per second is greater than the number of seconds required to travel d_2 feet at r_2 feet per second. We can set this question up in the form of an inequality. Remember that:

time = distance/rate

Is d_1/r_1 > d_2/r_2 ?

When we cross multiply we obtain:

Is (d_1)(r_2) > (d_2)(r_1) ?

Statement One Alone:

d_1 is 30 greater than d_2.

From statement one, we can create the following equation:

d_1 = 30 + d_2

Since d_1 = 30 + d_2, we can substitute 30 + d_2 in for d_1 in the inequality (d_1)(r_2) > (d_2)(r_1):

Is (30 + d_2)(r_2) > (d_2)(r_1) ?

We see that we still cannot answer the question. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

r_1 is 30 greater than r_2.

From statement two we can create the following equation:

r_1 = 30 + r_2

Since r_1 = 30 + r_2, we can substitute 30 + r_2 for r_1 in the inequality (d_1)(r_2) > (d_2)(r_1):

Is (d_1)(r_2) > (d_2)(30 + r_2) ?

We see that we still cannot answer the question. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two we have the following equations:

1) d_1 = 30 + d_2

2) r_1 = 30 + r_2

Since d_1 = 30 + d_2 and since r_1 = 30 + r_2, we can substitute 30 + d_2 for d_1 and 30 + r_2 for r_1 in the inequality (d_1)(r_2) > (d_2)(r_1):

Is (30 + d_2)(r_2) > (d_2)(30 + r_2) ?

Is (30)(r_2) + (d_2)(r_2) > (30)(d_2) + (d_2)(r_2) ?

Is (30)(r_2) > (30)(d_2) ?

Is r_2 > d_2 ?

Since we cannot determine whether r_2 is greater than d_2, statements one and two together are not sufficient to answer the question.

Manager
Joined: 12 Jun 2016
Posts: 145
Own Kudos [?]: 233 [0]
Given Kudos: 151
Location: India
WE:Sales (Telecommunications)
Is the number of seconds required to travel d1 feet at r1 [#permalink]
Clearly S1 and S2 are insufficient by themselves. The Key thing here is to make the right judgement on S1+S2. What this question is really testing is our understanding of - what happens when the Numerator and denominator of a fraction is increased by a fixed number?

To really hammer this concept and others related to it, do not forget to read this excellent post by Bunuel/MIKE McGARRY - https://gmatclub.com/forum/gmat-shortcu ... l#p1856037

I hope you find the above link useful
Manager
Joined: 27 Dec 2016
Posts: 194
Own Kudos [?]: 186 [0]
Given Kudos: 285
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE:Marketing (Education)
Is the number of seconds required to travel d1 feet at r1 [#permalink]
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.

Bunuel,

Since d2 and r2 both are positive integers, we can multiply the latest inequality : $$\frac{(30+d2)}{(30+r2)} > \frac{d2}{r2}$$ --> $$30*r2 + d2*r2 > 30*d2 + d2*r2$$. Thus we can eliminate $$d2*r2$$ on the both side, we get : $$30r2>30d2$$ --> $$r2>d2$$. With this inequality, your first test case : r2=d2 should not apply and this bring me to the C answer.

What is wrong with my approach?
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649126 [0]
Given Kudos: 86922
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
septwibowo wrote:
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.

Bunuel,

Since d2 and r2 both are positive integers, we can multiply the latest inequality : $$\frac{(30+d2)}{(30+r2)} > \frac{d2}{r2}$$ --> $$30*r2 + d2*r2 > 30*d2 + d2*r2$$. Thus we can eliminate $$d2*r2$$ on the both side, we get : $$30r2>30d2$$ --> $$r2>d2$$. With this inequality, your first test case : r2=d2 should not apply and this bring me to the C answer.

What is wrong with my approach?

The question becomes whether $$\frac{d_2+30}{r_2+30}>\frac{d_2}{r_2}$$ or whether $$r_2>d_2$$.

If $$d_2=r_2$$, the answer would be NO
If $$d_2=1$$ and $$r_2=2$$, the answer would be YES.
Intern
Joined: 06 Oct 2015
Posts: 4
Own Kudos [?]: 1 [0]
Given Kudos: 12
Is the number of seconds required to travel d1 feet at r1 [#permalink]
Why are we not considering negative rates in this problem? Bunuel
Senior Manager
Joined: 05 Feb 2018
Posts: 308
Own Kudos [?]: 835 [0]
Given Kudos: 325
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
Nothing says d2 can't be 0.

Say d2=0 and r2=2, thus the time2 is 0
d1=30,r1=32, thus the time1 is about .9, YES

Now say d2=10 and r2=2, time2 is 5
d1=40,r1=32, time1 is 1.25, NO

Statements are still insufficient together.
Re: Is the number of seconds required to travel d1 feet at r1 [#permalink]
1   2
Moderator:
Math Expert
94906 posts