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09 Jul 2024, 23:02
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D
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Difficulty:
95%
(hard)
Question Stats:
35% (02:27) correct
65%
(02:06)
wrong
based on 113
sessions
History
Date
Time
Result
Not Attempted Yet
12 litres of water is drawn from a container containing 60 litres of water and replaced with wine. Find the minimum number of replacements like this needed for the barrel to hold more than 65% of the wine.
A. 2
B. 3
C. 4
D. 5
E. 6
A. 2
B. 3
C. 4
D. 5
E. 6
10 Jul 2024, 01:35
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Given,
12 litres of water is drawn from a container containing 60 litres of water and replaced with wine.
12 lts = 20% of 60 lts
=> For each replacement ,
previous existing Volume of Wine or Water is diluted by 20% & replaced by 20% wine to keep the total volume same (i.e 60 Lts)
Initially -> 0% Wine
1st Replacement -> 20% Wine
2nd Replacement -> {0.8*20} + 20 = 16 + 20 = 36% Wine [ 0.8*Previous Wine %age ---- as 20% gets diluted with replacement]
3rd Replacement -> {0.8*36} + 20 = 28.8 + 20 = 48.8% Wine
4th Replacement -> {0.8*48.8} + 20 = 39 + 20 = 59% Wine [still the concentration of wine is <65%]
5th Replacement -> {0.8*59} + 20 = 47.2 + 20 = 67.2% Wine > 65%
Therefore, Minimum of 5 Replacements are required to reach to 65% of Wine in the mixture.
Answer: D
“One may walk over the highest mountain one step at a time.”
All The Best for GMAT
12 litres of water is drawn from a container containing 60 litres of water and replaced with wine.
12 lts = 20% of 60 lts
=> For each replacement ,
previous existing Volume of Wine or Water is diluted by 20% & replaced by 20% wine to keep the total volume same (i.e 60 Lts)
Initially -> 0% Wine
1st Replacement -> 20% Wine
2nd Replacement -> {0.8*20} + 20 = 16 + 20 = 36% Wine [ 0.8*Previous Wine %age ---- as 20% gets diluted with replacement]
3rd Replacement -> {0.8*36} + 20 = 28.8 + 20 = 48.8% Wine
4th Replacement -> {0.8*48.8} + 20 = 39 + 20 = 59% Wine [still the concentration of wine is <65%]
5th Replacement -> {0.8*59} + 20 = 47.2 + 20 = 67.2% Wine > 65%
Therefore, Minimum of 5 Replacements are required to reach to 65% of Wine in the mixture.
Answer: D
“One may walk over the highest mountain one step at a time.”
All The Best for GMAT
01 Oct 2025, 21:31
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Let's dive into a simpler way to solve this question, with minimum calculations
From a solution of 60l, 12l is removed every time, that means our Multiplication Factor (MF) should be = 48/60 = 4/5 =0.8
We need the barrel to hold more than 65% of the wine, i.e. less than 35 % of water
100% * (MF) < 35%
(0.8)^n < 0.35
where n is number of operations
(0.8)^1 = 0.8
(0.8)^2 = 0.64
(0.8)^3 ~ 0.5
(0.8)^4 ~ 0.4
(0.8)^5 ~ 0.32, which is less that 0.35
Therefore, total number of operations needed will be 5
From a solution of 60l, 12l is removed every time, that means our Multiplication Factor (MF) should be = 48/60 = 4/5 =0.8
We need the barrel to hold more than 65% of the wine, i.e. less than 35 % of water
100% * (MF) < 35%
(0.8)^n < 0.35
where n is number of operations
(0.8)^1 = 0.8
(0.8)^2 = 0.64
(0.8)^3 ~ 0.5
(0.8)^4 ~ 0.4
(0.8)^5 ~ 0.32, which is less that 0.35
Therefore, total number of operations needed will be 5
sahilsahh
