Ratio and Proportion : GMAT Quantitative Section
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# Ratio and Proportion

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16 Jul 2012, 08:23
Hi Guys,

Need help in understanding a simple concept in Ratio & Proportion. Here it goes:

If a:b = 2/3 ; b:c=3/4 ; c:d=8/9 and d:e = 27/12, then what is the ratio of a:b:c:d:e ??

Thanks a lot.

Cheers
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16 Jul 2012, 09:52
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Hi,

a:b = 2/3 ; b:c=3/4 ; c:d=8/9 and d:e = 27/12

take d:e = 27/12 => d= 27*e/12 = 9e/4 ...(1)

c:d = 8/9 => c = 8*d/9 = 8 *(9e/4)/9 (substituting value of d from (1) )
=> c = 2e ....(2)

b:c = 3/4 => b =3c/4 => 3*2e/4 (substituting value of c from (2) )

=> b = 3e/2 ....(3)

a/b = 2/3 => a=2b/3 => a = 2(3e/2) / 3 (substituting value of b from (3) )

=> a = e ....(4)

From (1) , (2) , (3) and (4) we have

a:b:c:d:e = e:(3e/2):2e:(9e/4):e = 1:3/2:2:9/4:1 = 4:6:8:9:4

hope this helps!
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16 Jul 2012, 10:44
gmat102012 wrote:
Hi Guys,

Need help in understanding a simple concept in Ratio & Proportion. Here it goes:

If a:b = 2/3 ; b:c=3/4 ; c:d=8/9 and d:e = 27/12, then what is the ratio of a:b:c:d:e ??

Thanks a lot.

Cheers

d/e=27/12 = 9/4
Now your task is to make alternate numerator and denominator same, so that they cancel out on multiplication.

1. d/e =9/4
2. c/d=8/9
3. b/c=3/4=6/8
4. a/b=2/3=4/6

Mark - this has made the value of my variables same in all the ratios:
a=4 (from 4)
b=6 (from 4 and 3)
c=8 (from 3 and 2)
d=9 (from 2 and 1)
e=4 (from 1)
=> a:b:c:d:e = 4:6:8:9:4

Alternatively, quick way to find is:

a/e = (a/b) x (b/c) x (c/d) x (d/e) X (e/e)
= (2/3) X (3/4) x (8/9) x (27/12) X (1/1)
= (12/18) x (18/24) x (24/27) x (27/12) x (12/12) -> starting from the biggest make the adjacent non-paired numbers ( not within braces) equal, while maintaining the ratio
Take the numerators
12:18:24:27:12
Cancel common factors
4:6:8:9:4
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17 Jul 2012, 21:26
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Expert's post
gmat102012 wrote:
Hi Guys,

Need help in understanding a simple concept in Ratio & Proportion. Here it goes:

If a:b = 2/3 ; b:c=3/4 ; c:d=8/9 and d:e = 27/12, then what is the ratio of a:b:c:d:e ??

Thanks a lot.

Cheers

Given:
a:b = 2:3 and b:c = 3:4
What does the ratio a:b = 2:3 imply? It means "if a is 2, b is 3"
What does the ratio b:c = 3:4 imply? It means "if b is 3, c is 4"

What do we get from this? "if a is 2, b is 3 and c is 4"
If a:b:c = 2:3:4 and c:d = 8:9
c is not the same in both the ratios but can we make it same? Multiply the first ratio by 2. (ratio doesn't change if you multiply/divide each term by the same number)
a:b:c = 4:6:8 and c:d = 8:9
So, a:b:c:d = 4:6:8:9 and d:e = 27:12 = 9:4 (we divide the ratio by 3. It still stays the same.)
So a:b:c:d:e = 4:6:8:9:4

For more on ratios, check: http://www.veritasprep.com/blog/2011/03 ... of-ratios/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 13484 Followers: 576 Kudos [?]: 163 [0], given: 0 Re: Ratio and Proportion [#permalink] ### Show Tags 04 Dec 2013, 11:56 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 13484 Followers: 576 Kudos [?]: 163 [0], given: 0 Re: Ratio and Proportion [#permalink] ### Show Tags 23 Mar 2015, 11:51 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8306 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 381 Kudos [?]: 2466 [0], given: 163 Re: Ratio and Proportion [#permalink] ### Show Tags 23 Mar 2015, 16:53 Hi All, When dealing with a prompt that includes multiple ratios, it's often helpful to start with the variable that has the "weirdest" ratios attached to it. In this example, none of the ratios is that "weird", so I'd look at the variable with the "biggest" numbers attached and start there.... We're given: A:B 2:3 B:C 3:4 C:D 8:9 D:E 27:12 D has to be a multiple of 9 and 27, so let's "lock in" that value at 27.... D = 27 so..... E = 12 C:D 8:9 Since we "tripled" the D, we have to "triple" the C......C = 8(3) = 24 With the value of C, we can work back to figure out the B and the A C = 24 B:C 3:4 Since we had to multiply the C by 6, we have to multiply the B by 6.... B = 3(6) = 18 A:B 2:3 Finally, we had to multiply the B by 6, so we have to multiply the A by 6.... A = 2(6) = 12 The final ratio of A:B:C:D:E is.... 12:18:24:27:12 Since all of these numbers are divisible by 3, we can reduce this ratio to.... 4:6:8:9:4 GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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01 Apr 2015, 23:32
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This rule is useful in Ratio & Proportion topic.

Rule of Three
The method of finding the 4th term of the proportion when the other three are known is known as the Rule of Three / Simple Proportion. Let’s understand it with an example.

Example 2: If in a particular interval of time 12 girls make 111 dolls, then how many girls should be employed for making 148 dolls?
Solution:
Rule I - ____ : ____ = ____ : Number of Girls
Rule II- ____ : ____ = 12 : X
Rule III- 111 : 148 = 12 : X
According to Rule of Three,
X = (Multiplication of Means)/ (First Term)
So, Number of girls = X = (12*148)/111 = 16

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17 Aug 2016, 04:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Ratio and Proportion   [#permalink] 17 Aug 2016, 04:19
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