A rainstorm increased the amount of water stored in State J reservoirs

Currently 138 billion which is 82% of capacity.
i.e.
Capacity*82%= 138 billion
Capacity=\(\frac{138}{82%}\)
Capacity=168.3 billion

Thus it was short of 168.3-124= 44 billion gallons

Since an approximation is needed, and we cannot use a calculator, I would take that 138 billion represents only 80 percent of the full capacity. I know that my answer will be a slight overshoot. So, if 138 is 80%, then 10% is 138/8 = 34.5/2 = 17.25, and 100% will be 172.5 billion. My overshot answer is 172.5-124=48.5.
So, the correct answer should be 44.
Just to be on the safe side: (124+30)*0.8=154*0.8=123.2 and (124+44)*0.8=168*0.8= 134.4, so definitely, 44 is the correct answer.

By a second thought, if we think of "ball parking", then all we need are the last two tests above. It is clear that the answer should be greater than 14 (124+14=138, which is just 82% of full capacity). No need to calculate the full capacity and then the required difference, it is sufficient to check that (124 + the answer) * 0.8 is the closest to 138.

Not a pretty question...

Answer E

Calculation approach:

1 % of capacity equals: 138/82 = 1.7 (rounded)gal (since 0.7*82 is slightly greater than 138). 100% of capacity = 100*1.7 = 170 = full capacity of tank.

170-124= 46 which is very close to E. Hence E.

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?

Solution:

82% * Cap =138
Cap = (138*100)/82
Using approximation:
Cap = (136*100)/80

Note: Den and Num decreased, Hence both cancel out each others effect.

Cap =136*(5/4) = 34*5 = 170

Now, 170-124 = 46 = ~44 (Nearest answer)

82% capacity = 138 Billion Gallons, so 100% =

\(138 * \frac{100}{82} = \frac{6900}{41}\)

Shortfall before rain =

\(\frac{6900}{41} - 124\)

\(= \frac{1816}{41}\)

= 44 (Approx)

Answer = E

After the reservoir is filled to 138 gallons the amount of water is at 82% or roughly 80% - which means that 20% of the reservoir is empty. To figure out what that 20% is approximate: 140 gallons /80 percent = x gallons /20 percent , therefore, x = 35 gallons , answer choices A,B,C,D are below 35 . We know that the reservoir must be short more than 35 gallons, therefore, the only possible choice is E.



Thinking about this question visually you see that the # of gallons that the reservoir was originally short = different b/w 138 & 124 + difference b/w total & 138
(138 gallons - 124 gallons) + (total gallons - 138 gallons)

Eliminate A & B, because the difference b/w 138 & 124 = 14, and after filling up to 138 gallons there is still 18% of space left in the reservoir. Knowing this we know that the answer choice has to be higher than 14 gallons. To figure out how much higher approximate:

138% = 82% we can derive that approximately 140 gallons = 80% ; remaining 20% = 140 * 20/80 = 35 gallons even without doing the calculation any further you can eliminate answer choices C & D because 35 gallons is higher than both C & D.

14 + 35 = 49 gallons

clumsy numbers in the problem..

138 is 82% of total. then total = (138*100)/82 = appro 168

before the storm it was 124 then 168-124 = 44

This is my first post on a question, but this question makes me feel really ignorant. I understand most of the concept for finding the answer, but my general math is not strong. When I see \((140/0.8)\), I feel like that is starting to get math heavy and don't have the skills to handle that in my head. Perhaps there is a concept you can point me too to help manipulate such a fraction in my head or another solution not calculation intensive?
I feel just as ignorant when I see \(138/82%\), otherwise I get how to solve the problem. Please forgive my ignorance, still new to the journey.

There are several ways:

\(\frac{140}{0.8}=\frac{1400}{8}= 175\);

\(\frac{140}{0.8}=\frac{140}{(\frac{4}{5})}= 140*\frac{5}{4}=175\).

That clears it up, thanks Bunuel. Recognizing 0.8 as 4/5 is a lot easier for me to handle this question.

Solution:

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.

Assume the total capacity = 100x billion gallons
Given that 138 billion gallons = 82x

x = 138/82 = 1.68
Total water = 168 billion gallons
Initial water level was 168 - 124 = 44 billion gallons short of the capacity

Correct Option: E

We can also approximate the values to get the answer approximately.
x = 138/82 = 140/80 = 1.7 (Note that since we have increased the numerator and decreased the denominator, the final value will be larger)
Total water = 170 billion gallons
Difference = 170 - 124 = 46 billion gallons.
Only option E is the closest.

so 82 % of total capacity = 138 gallons.

so Total capacity = (138 / 0.82)

Shortage = (138/0.82) - 124 = 172.5 - 124 = 48.

Answer : E

so 82 % of total capacity = 138 gallons.

so Total capacity = (138 / 0.82)

Shortage = (138/0.82) - 124 = 172.5 - 124 = 48.

Answer : E

Bunuel is my apprach corect ?

138= 80%
124 =x
cross multiply
x = 61%

hence 124= 61%

so 14 billion equals 19% percent increase then.... but in this case if initial number is 124 and it is 61 % and and 14 is abt 19 % then to reacg one 100% we need to double 14*2 which is abt 30:?

oops something went wrong where did i make mistake

pushpitkc hi can you please explain where am I wrong ?

Hi dave13

Please check your math on the highlighted portion - If 138 is 80%, 124 must be 72%(apprx)

This makes the difference of 14 about 8%. In order to bring the tank to capacity(100%),
we would need an increase of 20% - which is around 35+

The only answer option greater than 30 is Option E(44)

Hope this helps you!

Hi JeffTargetTestPrep
Could you tell where did you get IS in the question stem, please? Thanks__