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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10152
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
One cup of sugar water was poured out of 300 g of 8% sugar water and t
[#permalink]
21 Aug 2019, 01:29
21 Aug 2019, 01:29
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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
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
Tutor
Joined: 04 Aug 2010
Posts: 1321
Given Kudos: 9
Schools:Dartmouth College
One cup of sugar water was poured out of 300 g of 8% sugar water and t
[#permalink]
Updated on: 23 Aug 2019, 03:24
Updated on: 23 Aug 2019, 03:24
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MathRevolution 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
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:
\(2 = \frac{8}{100}x\)
\(x = \frac{100}{8} = 25\)
Originally posted by GMATGuruNY on 21 Aug 2019, 03:36.
Last edited by GMATGuruNY on 23 Aug 2019, 03:24, edited 1 time in total.
Last edited by GMATGuruNY on 23 Aug 2019, 03:24, edited 1 time in total.
Re: One cup of sugar water was poured out of 300 g of 8% sugar water and t
[#permalink]
21 Aug 2019, 05:00
21 Aug 2019, 05:00
x..........2
......6.....
3...........1
x= 6+(4/3)= 22/3
the percentage of sugar after replacement=22/3%
\(V_R= V_I(1-\frac{x}{300)}\)
\(\frac{22}{3}*300=8*300(1-\frac{x}{300})\)
\((1-\frac{x}{300})= \frac{11}{12}\)
\(\frac{x}{300}= \frac{1}{12}\)
x=25
......6.....
3...........1
x= 6+(4/3)= 22/3
the percentage of sugar after replacement=22/3%
\(V_R= V_I(1-\frac{x}{300)}\)
\(\frac{22}{3}*300=8*300(1-\frac{x}{300})\)
\((1-\frac{x}{300})= \frac{11}{12}\)
\(\frac{x}{300}= \frac{1}{12}\)
x=25
MathRevolution 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
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
