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19 Dec 2023, 07:00
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A
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Difficulty:
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Question Stats:
45% (02:31) correct
55%
(02:28)
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based on 178
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
One liter of a Christmas cranberry mimosa cocktail consists of x% champagne and y% cranberry juice. A liter of champagne costs $12 and a liter of cranberry juice costs $2. Is the ratio of x to y greater than 3/2?
(1) If the cocktail consisted of y% champagne and x% cranberry juice, it would cost more than $6.
(2) The total cost of the cocktail is less than $10.
One liter of a Christmas cranberry mimosa cocktail consists of x% champagne and y% cranberry juice. A liter of champagne costs $12 and a liter of cranberry juice costs $2. Is the ratio of x to y greater than 3/2?
(1) If the cocktail consisted of y% champagne and x% cranberry juice, it would cost more than $6.
(2) The total cost of the cocktail is less than $10.
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20 Dec 2023, 06:50
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GMAT Club Official Explanation:
One liter of a Christmas cranberry mimosa cocktail consists of x% champagne and y% cranberry juice. A liter of champagne costs $12 and a liter of cranberry juice costs $2. Is the ratio of x to y greater than 3/2?
First, note that the cocktail is one liter, so x + y = 1. The question asks whether x/y > 3/2, or if x is more than 60% (since x/y > 60/40).
(1) If the cocktail consisted of y% champagne and x% cranberry juice, it would cost more than $6.
This implies 12y + 2x > 6. Substituting y with 1 - x gives 12(1 - x) + 2x > 6, which simplifies to x < 0.6. Hence, x is less than 60%. Sufficient.
(2) The total cost of the cocktail is less than $10.
This implies 12x + 2y < 10. Substituting y with 1 - x gives 12x + 2(1 - x) < 10, which simplifies to x < 0.8. Hence, x may or may not be more than 60%. Not sufficient.
Answer: A.
General Discussion
19 Dec 2023, 08:05
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A.
given x+y=100
1. y/100 *12 + x/100 *2 >6
6y+x>300
substituting x=100-y
y>40
means x<60
x/y has to be <3/2 SUFFICIENT
2. x/100 *12 +y/100*2 <10
6x+y<500
x<80...y>20
x/y can be greater or lesser than 3/2 NOT SUFFICIENT
given x+y=100
1. y/100 *12 + x/100 *2 >6
6y+x>300
substituting x=100-y
y>40
means x<60
x/y has to be <3/2 SUFFICIENT
2. x/100 *12 +y/100*2 <10
6x+y<500
x<80...y>20
x/y can be greater or lesser than 3/2 NOT SUFFICIENT
