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One cup of sugar water was poured out of 300 g of 8% sugar w

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by Max@Math Revolution » Wed Aug 21, 2019 12:13 am
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[GMAT math practice question]

One cup of sugar water was poured out of 300 g of 8% sugar water and then the same amount of pure water was poured into the solution. After that 2% sugar water was added, resulting in 400 g of 6% sugar water. What weight of sugar water was initially poured out?

A. 20 g
B. 25 g
C. 30 g
D. 35 g
E. 40 g
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sugar water

by GMATGuruNY » Wed Aug 21, 2019 2:26 am
Max@Math Revolution wrote:[GMAT math practice question]

One cup of sugar water was poured out of 300 g of 8% sugar water and then the same amount of pure water was poured into the solution. After that 2% sugar water was added, resulting in 400 g of 6% sugar water. What weight of sugar water was initially poured out?

A. 20 g
B. 25 g
C. 30 g
D. 35 g
E. 40 g
Resulting amount of sugar = 6% of 400 grams = 24 grams.

Since the added sugar water increases the total volume from 300 grams to 400 grams, the amount of added sugar water = 400-300 = 100 grams
Since the added sugar water is 2% sugar, the weight of the added sugar = 2% of 100 = 2 grams.
Implication:
Before the 2% sugar water is added, the amount of sugar in the container = 24-2 = 22 grams.

Original amount of sugar in the container = 8% of 300 grams = 24 grams.
Since the removal process decreases the original amount of sugar from 24 grams to 22 grams, the amount of sugar removed = 24-22 = 2 grams.
Since the original solution is 8% sugar, these 2 grams must constitute 8% of the removed sugar water:
2 = (8/100)x
x = 100/8 = 25

The correct answer is B.
Last edited by GMATGuruNY on Fri Aug 23, 2019 2:13 am, edited 1 time in total.
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by Max@Math Revolution » Fri Aug 23, 2019 12:27 am
=>
Suppose x is the weight of sugar water poured out.
Then (8/100)(300-x) + (2/100)(400-300) = (6/100)(400) or 8(300-x) + 200 = 2400.
So, 8x = 200 and x = 25.

Therefore, B is the answer.
Answer: B
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