BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Scales problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Tue Jun 29, 2010 9:41 am
Thanked: 2 times

Scales problem

by taneja.niks » Sat Apr 16, 2011 5:43 am
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related
linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of
30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100
on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84

How to proceed this one???
Top
Source: — Problem Solving |
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Sat Apr 16, 2011 6:09 am
given: 6R=30S AND 24R=60S, find 100S on R-?
R(24-6)=S(60-30,) S=18R/30 AND S=3R/5, solving for R form (100-30)/(R-6) = 5/3
taneja.niks wrote:A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84

How to proceed this one???
Last edited by pemdas on Sat Apr 16, 2011 4:41 pm, edited 1 time in total.
Top
User avatar
Legendary Member
Posts: 582
Joined: Tue Mar 08, 2011 12:48 am
Thanked: 61 times
Followed by:6 members
GMAT Score:740

by force5 » Sat Apr 16, 2011 6:09 am
many ways to do it. i feel this is simpler

1 unit = 18/30
hence 40 =

18/30*40 = 24

hence 20+24 = 48
hence C
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Apr 16, 2011 6:13 am
taneja.niks wrote:A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related
linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of
30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100
on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84

How to proceed this one???
Since the relationship between R and S is linear, any pair of points (R,S) must yield the same slope.

Given points are (6,30), and (24,60).
Slope = (S₂ - S�)/(R₂ - R�) = (60-30)/(24-6) = 30/18 = 5/3.

(6,30) and (R,100) must yield the same slope.
(100-30)/(R-6) = 5/3.
70/(R-6) = 5/3.
Cross-mulitplying, we get:
5R-30 = 210.
R = 48.

The correct answer is C.
Last edited by GMATGuruNY on Sat Apr 16, 2011 6:16 am, edited 2 times in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Apr 16, 2011 6:13 am
taneja.niks wrote:A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related
linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of
30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100
on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84

How to proceed this one???
An easy way to proceed is to consider the R and S-scales as X and Y-axes respectively.
Then the coordinates are (6, 30), (24, 60), and (x, 100) all lie in the same line.
Then (60 - 30)/(24 - 6) = (100 - 30)/(x - 6)
3/18 = 7/(x - 6)
3(x - 6) = 126
x - 6 = 42 or x = 48

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sat Apr 16, 2011 9:18 am
taneja.niks wrote:A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related
linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of
30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100
on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84

How to proceed this one???
I'd like to make a brief comment regarding the phrase "related linearly."

Please know that you are not expected to know this specific term (and its implications). While you will find the phrase "linear equation" throughout the OG, you will find no reference to "linear relations" or "related linearly."

If this were an official GMAT question, you would be given additional information explaining that the relationship between the R-scale and S-scale could be represented as a line (or something to that extent).
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Sun Nov 18, 2012 7:09 am

by lazarogb » Sun Nov 18, 2012 7:27 am
Hello Brent,

This question is from the "extended package" you can buy for the Gmat Prep software.

I guess it is real GMAT material.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 18, 2012 8:19 am
That's good to know - thanks.
I guess the word "line" hiding in "linear" is enough of a tipoff :-)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Tue Jan 02, 2018 6:44 am
taneja.niks wrote:A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of
30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100
on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84
Since R and S are related linearly, it must be true that R = kS + l for some constants k and l.

We are given that when R = 6, S = 30; therefore, 6 = 30k + l.

We are also given that when R = 24, S = 60; therefore, 24 = 60k + l.

Let's subtract the first equation from the second:

18 = 30k

k = 3/5

Thus, R = (3/5)S + l. To find the value of l, we can substitute either R = 6 and S = 30 or R = 24 and S = 60 in the equation. Let's use the first pair:

6 = (3/5)(30) + l

6 = 18 + l

l = -12

Thus, R and S are related via R = (3/5)S - 12. When S = 100, we find that:

R = (3/5)(100) - 12 = 60 - 12 = 48

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1