12 Days of Christmas GMAT Competition - Day 7: One liter of a Christma

Question

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.

Bunuel · Accepted Answer

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.

Shwetamed · Answer

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

Kinshook · Answer

Given: 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.

Asked: Is the ratio of x to y greater than 3/2?

The cost of 1 liter of the Christmas cranberry mimosa cocktail = 12*x% + 2*y%

(1) If the cocktail consisted of y% champagne and x% cranberry juice, it would cost more than $6.
The cost of 1 liter of the Christmas cranberry mimosa cocktail If the cocktail consisted of y% champagne and x% cranberry juice= 12*y% + 2*x% > 6
6y + x > 300
6 + x/y > 300/y
x/y < 6 - 300/y
Case 1: y = 60
x/y < 1
Case 2: y = 75
x/y < 2; x/y may or may not be greater than 3/2.
NOT SUFFICIENT

(2) The total cost of the cocktail is less than $10.
The total cost of 1 liter of the Christmas cranberry mimosa cocktail = 12*x% + 2*y% < 10
6x% + y% < 5
6x + y < 500
6x/y + 1 < 500/y
x/y < 500/6y - 1/6
Case 1: y = 10
x/y < 49/6 = 8 1/6; x/y may or may not be greater than 3/2.
Case 2: y = 50
x/y < 9/6 = 3/2
NOT SUFFICIENT

(1) + (2)
(1) If the cocktail consisted of y% champagne and x% cranberry juice, it would cost more than $6.
The cost of 1 liter of the Christmas cranberry mimosa cocktail If the cocktail consisted of y% champagne and x% cranberry juice= 12*y% + 2*x% > 6
6y + x > 300
6 + x/y > 300/y
x/y > 300/y - 6
(2) The total cost of the cocktail is less than $10.
The total cost of 1 liter of the Christmas cranberry mimosa cocktail = 12*x% + 2*y% < 10
6x% + y% < 5
6x + y < 500;
6x/y + 1 < 500/y
x/y < 500/6y - 1/6
300/y - 6 < x/y < 500/6y - 1/6
Case 1; y = 50
0 < x/y < 3/2 = 1.5
Case 2: y = 40
1.5 = 3/2 < x/y < 1.91
x/y may or may not be greater than 3/2.
NOT SUFFICIENT

IMO E

treeetravel · Answer

For 1 litre of cocktail, x+y=100....equation 1

from 1:

Total cost of cocktail, 12y/100 + 2x/100

Lets take total cost as $6

12y+2x = 600.......equation 2

Solving eq 1 and 2, x= 60 and y = 40. x/y = 3/2.

Now take any value greater than $6...lets take $7

12y+2x = 700....equation 3

solving equation 1 and 3, x= 50 and y=50, x/y =1

for any values to total cost greater than $6, x/y <3/2. Answer is NO.

For statement 2:

as total cost can be anything less than $10, lets take total cost $9

12x+2y = 900.....equation 4

Solving eq 1 and 4 gives x= 70 and y= 30, x/y= 7/3

as total cost can be anything less than $10, take total cost as $5

12x+2y= 500....equation 5

Solving eq 5 and 1, x= 30 and y =70, x/y= 3/7.

values of x/y can greater than or less than 3/2 . Not sufficient to answer.

Therefore final Answer is A

juancarlos12 · Answer

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?

Question x/y>1.5?
Assumes Total=100

(1) If the cocktail consisted of y% champagne and x% cranberry juice, it would cost more than $6.
(12y+2x)/100>6
6y+x>300
Test values:
Max value: y=100 and x=0 --> 600>300(ok) --> x/y =0/100=0>1.5 (False) --> we can answer the question
Min value: y=41and x=59--> 305>300(ok) --> x/y =59/41=1.43>1.5 (False) --> we can answer the question
Other Value : y=40and x=59--> 300>300(no ok)

--> Sufficient becase x/y is not greater than 1.5

(2) The total cost of the cocktail is less than $10.
(12x+2y)/100<10
6x+y<500
Test values:
Max value: x=0 and y=100 --> 100<500(ok) --> x/y =0/100=0>1.5 (False) --> we can answer the question
Max value: x=70 and y=30--> 450<500(ok) --> x/y =70/30=2.3>1.5 (True) --> we have 2 different answers
-->Not sufficient

Right answer:A

Kinshook · Answer

Bunuel 
Nowhere in the question it is mentioned that Christmas cranberry mimosa cocktail consists only of champagne and cranberry juice. 
Therefore, the relation
y% = 1 - x%
MUST NOT BE TRUE

Bunuel · Answer

I don't agree. The statement "the cocktail consists of x% champagne and y% cranberry juice" implies that the cocktail is made entirely of these two ingredients, so x% and y% together make up 100% of the cocktail.

Bunuel · Answer

For reference check  the following Official Guide question :

Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If  10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B , is x > y ?

(1) y > 4
(2) The cost of the 10 kilograms of Material K is less than $40.

Hope it helps.

Kinshook · Answer

bb 
The question could have been solved much more easily if the relation
x% = 100% - y%
was available.
With the language of the question, this relation can not be established. 
Please review and correct OA.

Bunuel · Answer

The question is correct as is.

For reference check  the following Official Guide question :

Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If  10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B , is x > y ?

(1) y > 4
(2) The cost of the 10 kilograms of Material K is less than $40.

Hope it helps.

Bunuel · Answer

I've already explained this earlier in the topic. So, please review the thread before posting.

The statement "the cocktail consists of x% champagne and y% cranberry juice" implies that the cocktail is made entirely of these two ingredients, so x% and y% together make up 100% of the cocktail.

Here is an  Official Guide question  with similar wording:

Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If  10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B , is x > y ?

(1) y > 4
(2) The cost of the 10 kilograms of Material K is less than $40.

Hope it helps.

bumpbot · Answer

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