Algebra

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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

by phoenix9801 » Sun Jun 27, 2010 12:01 am

Hi, can someone please help to explain the step-by-step instructions (in detail) in the most simplest way and clear to understand.

1-
A rainstorm increased the amount of water stored in state J reservoirs from 124 billion gallons to 138 billions gallons. If the Storm increased the amount of water in the reservoirs to 82 percent of total capacity, appropriately how many billion gallons of water the reservoirs short of total capacity prior to the storm?

2-
At least 2/3 pf the 40 members of a committee must vote in favor of a resolution for it to pass. What is the greatest number of members who could vote could vote against the resolution and still have it pass?

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Source: Beat The GMAT — Problem Solving | Sun Jun 27, 2010 12:01 am

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Sun Jun 27, 2010 12:39 am

Question 1:

124 to 138 is the increase, which means the increase is of 14 billion gallons. This increased volume to 82% of max.

That means 138 billion gallons = 82% of maximum volume

MAx volume = 138 / 82% = 138 * 100 / 82 = 168.3

Therefore volume that the reservoir was short of the full capacity before storm is 168.3 - initial value = 124

So 44.3 billion gallons or approx 44.

Question 2:

Atleast 2/3 must vote FOR. That means amount who vote against cannot be 1/3 or more. 1/3 is 13.33 so this means maximum number of people who can vote against it 13. If 14 vote, then this becomes 14/40 = 7/ 20 which is greater than 1/3 and hence means the resolution will fail.

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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

by phoenix9801 » Sun Jun 27, 2010 2:00 am

albatross86 wrote:Question 1:

124 to 138 is the increase, which means the increase is of 14 billion gallons. This increased volume to 82% of max.

That means 138 billion gallons = 82% of maximum volume

MAx volume = 138 / 82% = 138 * 100 / 82 = 168.3

Therefore volume that the reservoir was short of the full capacity before storm is 168.3 - initial value = 124

So 44.3 billion gallons or approx 44.

Question 2:

Atleast 2/3 must vote FOR. That means amount who vote against cannot be 1/3 or more. 1/3 is 13.33 so this means maximum number of people who can vote against it 13. If 14 vote, then this becomes 14/40 = 7/ 20 which is greater than 1/3 and hence means the resolution will fail.

Thanks for the clarification and help. But on

Question 1: can you please explain why you multiplied by 100?

Question 2: Can you please explain how did you know right aways 1/3 voted against (is there mathematical why of doing it)?

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Sun Jun 27, 2010 2:09 am

Thanks for the clarification and help. But on

Question 1: can you please explain why you multiplied by 100?

Question 2: Can you please explain how did you know right aways 1/3 voted against (is there mathematical why of doing it)?

Sure.

In Question 1 we are trying to find the max volume.

We realised that 138 = 82% of max volume say C

=> 138 = 82/100 * C

So C = 138 * 100 / 82

Hope that makes sense.

In question 2, this is purely based on wording.

The question says, atleast 2/3 MUST vote. 2/3 of 40 is approx 26.67
But, a number of members must be an integer, right? Can it be 26? No - because that is LESS than 2/3 and we need aTLEAST 2/3. Thus the minimum possible value is 27.

This means the maximum possible value of the number of members who can vote against is (40 - 27) = 13

This is because if 14 voted against, then that means only 26 voted For, so this fails the criteria of ATLEAST 2/3.

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Sun Jun 27, 2010 5:49 am

138 - 82
? - 100

?=(100*138)/82
=168.29

shortage before storm=168-124=44

-------------

for 2/3*40= 26.66
against 1/3*40=13.33

so maximum vote against can be 13

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