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18 Sep 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:02) correct
30%
(01:37)
wrong
based on 247
sessions
History
Date
Time
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Not Attempted Yet
A drink contains only 7 oz. of soda and 3 oz. of juice. A second drink that contains only soda and juice is poured into the first. How many oz. of liquid were poured in?
(1) After the second drink is poured in, 40% of the entire beverage is juice.
(2) 30% of the second drink was soda.
(1) After the second drink is poured in, 40% of the entire beverage is juice.
(2) 30% of the second drink was soda.
This is a Data Sufficiency Butler Question
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19 Sep 2024, 10:40
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First drink: 7 oz. soda + 3 oz. juice = 10 oz. total
Second drink: contains only soda and juice, amount unknown
Let x be the number of ounces of liquid in the second drink.
Statement (1): After the second drink is poured in, 40% of the entire beverage is juice.
Statement (2): 30% of the second drink was soda.
Statement (1) alone:
We can set up an equation: 3 / (10 + x) = 0.4
Solving this: 3 = 0.4(10 + x)
7.5 = 10 + x
x = -2.5
This is impossible as we can't have negative volume.
Statement (1) alone is not sufficient.
Statement (2) alone:
We know 30% of the second drink is soda, so 70% must be juice.
But we don't know the total volume of the second drink.
Statement (2) alone is not sufficient.
Statements (1) and (2) together:
Let's say the second drink has y oz. of soda and z oz. of juice.
From (2), we know: y = 0.3x and z = 0.7x
From (1): (3 + 0.7x) / (10 + x) = 0.4
Solving this equation:
3 + 0.7x = 0.4(10 + x)
3 + 0.7x = 4 + 0.4x
0.3x = 1
x = 10/3 ≈ 3.33 oz.
With both statements, we can determine that approximately 3.33 oz. of liquid were poured in.
Therefore, the answer is C: Both statements (1) and (2) together are sufficient to answer the question.
Second drink: contains only soda and juice, amount unknown
Let x be the number of ounces of liquid in the second drink.
Statement (1): After the second drink is poured in, 40% of the entire beverage is juice.
Statement (2): 30% of the second drink was soda.
Statement (1) alone:
We can set up an equation: 3 / (10 + x) = 0.4
Solving this: 3 = 0.4(10 + x)
7.5 = 10 + x
x = -2.5
This is impossible as we can't have negative volume.
Statement (1) alone is not sufficient.
Statement (2) alone:
We know 30% of the second drink is soda, so 70% must be juice.
But we don't know the total volume of the second drink.
Statement (2) alone is not sufficient.
Statements (1) and (2) together:
Let's say the second drink has y oz. of soda and z oz. of juice.
From (2), we know: y = 0.3x and z = 0.7x
From (1): (3 + 0.7x) / (10 + x) = 0.4
Solving this equation:
3 + 0.7x = 0.4(10 + x)
3 + 0.7x = 4 + 0.4x
0.3x = 1
x = 10/3 ≈ 3.33 oz.
With both statements, we can determine that approximately 3.33 oz. of liquid were poured in.
Therefore, the answer is C: Both statements (1) and (2) together are sufficient to answer the question.
09 Dec 2025, 11:43
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