Problem Solving

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 to prior to the storm?

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

-- Since 138 billion gallons represents approx 82% of total capacity in the reservoir we can create an equation to solve for the total capacity of the tank.

82/100 = 124/X

X = TOTAL CAPACITY OF TANK = APPROX 168

billion gallons short of capacity prior to the storm --- 168 - 124 = 44

ANSWER = E

..... MY QUESTION HERE .... IS THEIR AN EASIER WAY TO SOLVE HERE? ANY SHORTCUTS/TRICKS?

factor26 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 to prior to the storm?

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

-- Since 138 billion gallons represents approx 82% of total capacity in the reservoir we can create an equation to solve for the total capacity of the tank.

82/100 = 124/X

X = TOTAL CAPACITY OF TANK = APPROX 168

billion gallons short of capacity prior to the storm --- 168 - 124 = 44

ANSWER = E

..... MY QUESTION HERE .... IS THEIR AN EASIER WAY TO SOLVE HERE? ANY SHORTCUTS/TRICKS?

It might be more efficient in this problem to use bounded estimates. From your initial observation about the capacity of the container, 82% capacity is 138 gallons. Rounding we have 80% capacity is 140 gallons, or that the container is 20% empty. We've rounded the capacity up but the percentage also, so our answer should be close to accurate. 20% of 140 is 28 (a much simpler calculation than you had above) and thus the rounded full capacity is 168. Subtract off 124 and you've got 44.

If you wanted a really quick and dirty way, you can ballpark from the answers noting that 125 plus the answer will be the full capacity. Right off the bat you can eliminate A and B. Why? Because if A were true after the rain the container would be over capacity and if B were true the container would be at capacity, not 82% of capacity. From there you could eliminate C also, because if 149 were the total capacity (124+25), that would be only 11 gallons over the 82% mark of 138, and you know that 11 is less than 22% of 138. At least now you've got a 1 in 2 chance of guessing correctly.

Luke, good call with the bounded estimates. For some reason, i always elect not to use this method when i could use it and save myself a lot of time. I think it's important for me, as well as other gmatters that while its a great feeling to find the exact answer ... it's better to use the tips/tricks to help us complete the exam in the alotted time...that's my biggest struggle ... time... as i frequently find myself with two minutes left and 10 questions to go!

factor26 wrote:Luke, good call with the bounded estimates. For some reason, i always elect not to use this method when i could use it and save myself a lot of time. I think it's important for me, as well as other gmatters that while its a great feeling to find the exact answer ... it's better to use the tips/tricks to help us complete the exam in the alotted time...that's my biggest struggle ... time... as i frequently find myself with two minutes left and 10 questions to go!

Oh for sure. I struggle with when to use estimates myself. But when you learn how to leverage them (which usually just comes with practice) its a SUPER powerful tool to solving problems quickly.

A note, this problem is extra friendly; it gives you a pretty good hint by using the word "approximately" in the question stem. When a problem has that word it in, it is usually safe to assume that the problem can be solved quickly using estimates at some stage of the numerical computation.

Hi,

I agree that estimating is a good strategy.

However, Luke made two errors in his post that happened to cancel each other out and lead to an answer that was correct:

We've rounded the capacity up but the percentage also, so our answer should be close to accurate.

1. If 82% is 138 gallons, estimating that 80% full is 140 gallons is actually rounding BOTH numbers in the direction of a BIGGER tank. If more gallons fill a smaller portion that means the tank has gotten bigger. We can verify this: 138/0.82 = about 168, while 140/0.8 = 175.

This 7-gallon difference could have mattered, since several of the answer choices are less than 7 apart (it happens that in this case the right answer is much bigger than the others).

20% of 140 is 28 (a much simpler calculation than you had above) and thus the rounded full capacity is 168.

2. If we do assume that 80% and 140 are good estimates, this math is also incorrect. If 80% of the tank is 140, we should add 25% of 140, NOT 20% of 140, to get the full capacity. This is because the missing amount is 20% of the FULL tank, not 20% of the partially full tank.

To get 20% of the full tank, we need to take 25% of the 80% full tank, because 0.25 * 0.8 = 0.2.
If we do this, we would get 140 * 0.25 = 35, and 140 + 35 = 175. This is exactly 7 more gallons than the 168 that was calculated.

Conclusion:
The first mistake led to an over-estimate of the tank size (+7), but adding only 20% instead of 25% of that overestimate was an underestimate (-7) that happened to lead to a number that was exactly right.

If you want to use estimation on this question, I recommend assuming that 140 (2 more gallons) is 5/6 (slightly more than 82%) of the tank. So, 5/6 * x = 140. Then, the whole tank is 140 * 6/5 = 168.

If you wanted to go in the other direction, you could say that 80% (slightly less than 82%) = 136 (slightly less than 138). So 4/5*x = 136, and x = 5/4 * 136 = 680/4 = 170.

Wowzer I apologize. I must have done that problem when uncaffeinated! I think my mind was correct but my hands didn't type what I was thinking.

Thanks for the correction.

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.