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BeatTheGmatPrep Math Question

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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BeatTheGmatPrep Math Question

by OptinumGmat » Fri May 27, 2016 9:16 am
Hi,

I'm having trouble with this question:

In a certain dormitory, 1/3 of the students are jets fan, 1/6 are bears fan and 1/12 are raiders fan. If the renaming 30 students are Dolphins fan, how many students are in the dormitory?

To first solve this question. You need to add up all the fractions, so 1/3 + 1/6 + 1/12 = 7/12. In the video you are able to translate 30 students into 5/12 and I'm wondering how did you do that? How did you know 30 would translate into 5/12?
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by [email protected] » Fri May 27, 2016 6:11 pm
Hi OptinumGMAT,

To start, when posting GMAT questions, you should make sure to post the ENTIRE question (along with the answer choices). This question can be solved rather easily by TESTing THE ANSWERS, but since you have not included them, you're forcing everyone to approach this question algebraically.

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by Brent@GMATPrepNow » Sat May 28, 2016 6:40 am
Here's the question, Rich:
Image

Here's the video solution:
https://www.gmatprepnow.com/module/gmat ... video/1072

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by OptinumGmat » Sat May 28, 2016 7:53 am
Brent@GMATPrepNow wrote:Here's the question, Rich:
Image

Here's the video solution:
https://www.gmatprepnow.com/module/gmat ... video/1072

Cheers,
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Hi Brent,

How did you get 5/12?
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by [email protected] » Sun May 29, 2016 10:49 am
Hi OptinumGMAT,

This question is essentially a 'lift' of an OG question:

OG13/GMAT2015 pg. 154, #15
GMAT2016 pg. 154, #19

Both the OG question and this question can be solved by TESTing THE ANSWERS. Here's how:

Since we're adding two considerably smaller fractions to 1/3, you don't actually have to add those fractions up to know that the total fraction can't be much more than about a half. With that deduction, the remaining 30 students represent approximately half of the total students. Since the question asks for the total number of students, the correct answer is likely either A or B. Under typical circumstances, we would start by TESTing either Answer B or D first, so I'll start with B.

Answer B: 72 students

IF....there were 72 students....
(1/3)(72) = 24 are Jets fans
(1/6)(72) = 12 are Bears fans
(1/12)(72) = 6 are Raiders fans

24+12+6 = 42 fans accounted for. That leaves...

72 - 42 = 30 fans left. 30 is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer: B

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by Brent@GMATPrepNow » Sun May 29, 2016 12:16 pm
[email protected] wrote: This question is essentially a 'lift' of an OG question:
If you're suggesting that word problems featuring information about fractions of a population and additional information about the remaining members of that population are solely the domain of the GMAT, you might want to take a look at any elementary math textbook on the planet.
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by Matt@VeritasPrep » Tue Jun 07, 2016 10:12 pm
You could think of the total as being t, so you have

(1/3)t = Jets fans
(1/6)t = Bears fans
(1/12)t = Raiders fans
t = fans of everybody (including the Dolphins)

if we add up all the teams individually, we get

(1/3)t + (1/6)t + (1/12)t + 30

this is the same as if we took them all together, so that = t, and we have

(1/3)t + (1/6)t + (1/12)t + 30 = t

30 = t - (1/3)t - (1/6)t - (1/12)t

30 = (5/12)t
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