• Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Ratio and Proportion OG 12ed #66

This topic has 3 expert replies and 2 member replies

Ratio and Proportion OG 12ed #66

Post Sun Sep 22, 2013 12:50 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the number of first graders to the number of third graders?

a) 16 to 15
b) 9 to 5
c) 5 to 16
d) 5 to 4
e) 4 to 5

Is there a better explanation than the one provided in the OG?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Sun Sep 22, 2013 3:26 pm
Quote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. if the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?

A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
A very fast approach:

1st/3rd = 1st/2nd * 2nd/4th * 4th/3rd.

In the equation above, all of the values in red cancel out.
Thus:
1st/3rd = 3/4 * 8/5 * 2/3 = 4/5.

The correct answer is E.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
ganeshrkamath Master | Next Rank: 500 Posts
Joined
23 Jun 2013
Posted:
283 messages
Followed by:
25 members
Upvotes:
97
Test Date:
August 12, 2013
GMAT Score:
750
Post Tue Sep 24, 2013 1:05 am
juliet.foster@gmail.com wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the number of first graders to the number of third graders?

a) 16 to 15
b) 9 to 5
c) 5 to 16
d) 5 to 4
e) 4 to 5

Is there a better explanation than the one provided in the OG?
Number of first graders = A
Number of second graders = B
Number of third graders = C
Number of fourth graders = D

B/D = 8/5
A/B = 3/4
C/D = 3/2
A/C = ?
We need to find A in terms of C
A = (3/4)B
A = (3/4)(8/5)D
A = (3/4)(8/5)(2/3)C
A = (4/5)C
A/C = 4/5
Choose e

Cheers

_________________
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attempt-750-in-2-months-t268332.html#688494

  • +1 Upvote Post
  • Quote
  • Flag
Mathsbuddy Master | Next Rank: 500 Posts Default Avatar
Joined
08 Nov 2013
Posted:
447 messages
Followed by:
1 members
Upvotes:
25
Post Fri Nov 08, 2013 12:21 pm
Originally I tried working out lowest common multiples, so that the fractions would all disappear, but the excess of arithmetic seemed redundant.

List given ratios in order (this just makes the question easier to read)
1st:2nd = 3:4
2nd:4th = 8:5
3rd:4th = 3:2

Work out the required "ratio journey"
[1st -> third] = [1st -> 2nd -> 4th -> 3rd]
= 3:4 -> 8:5 -> 2:3 (in the form x:y)

The product of x values, X = 3 x 8 x 2 = 48
The product of y values, Y = 4 x 5 x 3 = 60

So the overall ratio (X,Y) = 48:60 = 4:5

No different to the 2 previous solutions really, except for the presentation of the algorithm.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Fri Nov 08, 2013 3:36 pm
Hi juliet.foster,

In these types of ratio questions, you can TEST VALUES; you just have to make sure that you test numbers that match the given information.

We have 1st, 2nd, 3rd and 4th graders. Based on the given ratios, we know the that the number of 4th graders has to be a multiple of 2 AND a multiple of 5.

Let's pick:
4th graders = 10

Based on the given ratios, we'd have….
3rd graders = 15
2nd graders = 16
1st graders = 12

The ratio of 1st to 3rd graders is:
12:15

This reduces to:
4:5

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Post Tue Jun 30, 2015 11:49 am
juliet.foster@gmail.com wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the number of first graders to the number of third graders?

a) 16 to 15
b) 9 to 5
c) 5 to 16
d) 5 to 4
e) 4 to 5

Is there a better explanation than the one provided in the OG?
Solution:

Background: Ratios show the relationship between members of two or more categories. As an example, if the ratio of horses to ponies is 7:4 and the ratio of ponies to goats is 4:2, then we can directly express the ratio of horses to goats as 7:2 because the original ratios had matching values for ponies. A more complicated pair of ratios would be horses to ponies is 7:4 and ponies to goats is 2:1. We must make the ponies numbers equal in both ratios before being able to directly express the ratio of horses to goats. We would thus multiply the second ratio (ponies to goats) by 2 to get the equivalent ratio of 4:2. Now that the ponies numbers match, we can directly express the ratio of horses to goats as 7:2.

We are given the following:

1) The ratio of the number of second graders to the number of fourth graders is 8 to 5.

2) The ratio of the number of first graders to the number of second graders is 3 to 4.

3) The ratio of the number of third graders to the number of fourth graders is 3 to 2.

That is:

1) 2nd : 4th = 8 : 5

2) 1st : 2nd = 3 : 4

3) 3rd : 4th = 3 : 2

From the first and second ratios, we see that they both contain 2nd graders, so let’s make 2nd graders the same number. We see that the number for 2nd graders in the first ratio is 8 and that for the 2nd graders in the second ratio is 4. We multiply the second ratio by 2, obtaining 6 : 8, and now both ratios have a matching 8 for 2nd graders.

1) 2nd : 4th = 8 : 5

2) 1st : 2nd = 6 : 8

Now we see that the ratio of 4th graders to 1st graders must be 5 to 6. That is:

4th : 1st = 5 : 6

We will now compare this with the third ratio we set up originally:

3rd : 4th = 3 : 2

We see that both ratios contain 4th graders, so let’s make 4th graders the same number. We must change both ratios. We multiply the ratio 5 : 6 by 2, to get an equivalent ratio of 10 : 12. Then we multiply the ratio 3 : 2 by 5, to get an equivalent ratio of 15 : 10. That is:

4th : 1st = 10 : 12

3rd : 4th = 15 : 10

Now that 4th graders have a matching 10 in each ratio, we can express the ratio of 1st graders to 3rd graders as 12 : 15. That is:

1st : 3rd = 12 : 15

We can reduce this ratio by dividing both 12 and 15 by 3:

1st : 3rd = 4 : 5

Answer: E

_________________
Jeffrey Miller Head of GMAT Instruction

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 GMATGuruNY 89 first replies
2 Brent@GMATPrepNow 65 first replies
3 Rich.C@EMPOWERgma... 35 first replies
4 Jay@ManhattanReview 22 first replies
5 Sionainn@Princeto... 17 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

139 posts
2 image description GMATGuruNY

The Princeton Review Teacher

133 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

118 posts
4 image description Scott@TargetTestPrep

Target Test Prep

111 posts
5 image description Max@Math Revolution

Math Revolution

82 posts
See More Top Beat The GMAT Experts