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storm water reservoir

by BlueDragon2010 » Sat Jan 18, 2014 10:35 am

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A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

A) 9
B) 14
C) 25
D) 30
E) 44

Suggestions on how to set things up, and how to deal with the difficult arithmetic?
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by Patrick_GMATFix » Sat Jan 18, 2014 10:48 am
The solution below is taken from the GMATFix App.


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by GMATGuruNY » Sat Jan 18, 2014 2:31 pm
BlueDragon2010 wrote:A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

A) 9
B) 14
C) 25
D) 30
E) 44
Do only as much math as necessary.

138 billion gallons is approximately 80% of the reservoir's capacity.
Implication:
The reservoir's capacity must be more than 150 billion gallons.
Test easy values greater than 150:
80% of 160 = 128.
80% of 170 = 136.
Success!

Thus:
The reservoir's capacity ≈ 170 billion gallons.
The amount of water lacking before the storm ≈ 170-124 ≈ 46.

The correct answer choice is E.
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by [email protected] » Sat Jan 18, 2014 2:49 pm
Hi BlueDragon2010,

Mitch's explanation is right on point. As you continue to study, it's important to note the way that GMAT questions are worded. Oftentimes a particular word, phrase or other "clue" will provide a tip-off as to the most efficient way to tackle the question. In this prompt, the word "approximately" is hinting that you should "round off" the numbers to make the basic math easier to finish. Keep an eye out for this exact situation, as it's likely to occur at least once in the Quant section on Test Day.

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by Scott@TargetTestPrep » Thu Mar 15, 2018 9:25 am
BlueDragon2010 wrote:A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

A) 9
B) 14
C) 25
D) 30
E) 44
We are given that the water increased from 124 billion gallons to 138 billion gallons. We also know that 138 billion gallons is 82% of the total capacity. Let's translate this information into an equation, where T = total capacity. We translate the sentence "138 billion gallons is 82% of total capacity" as 138 = (0.82)T, remembering that "is" means "equals" and "of" means "multiply."

However, we are told to APPROXIMATE. So, instead of using the equation 0.82T = 138, we can instead use 0.8T = 136. Note that I chose 136 because I know that it is divisible by 8, but you could just as easily use 138 and ignore the decimal values. Now we need to solve for T.

T = 136/0.8
T = 1360/8
T = 170

The total capacity is approximately 170 billion gallons. It follows that the reservoirs were approximately 170 - 124 = 46 billion gallons short of capacity prior to the storm.

From our approximated answer, we see that answer choice E (44) is closest.

Answer: E

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