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Difficulty:
95%
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Question Stats:
30% (02:48) correct
70%
(02:10)
wrong
based on 69
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A vending machine dispenses one drink at random from 48 drinks stocked inside. Each drink is either Coke or Pepsi, and each drink is either bottled or canned. What is the positive difference between the probability that the drink dispensed is a canned Pepsi and the probability that the drink dispensed is a bottled Coke?
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
(2) 9 of the drinks are bottled Pepsi.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
(2) 9 of the drinks are bottled Pepsi.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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M47-138
07 May 2026, 01:30
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GMAT Club Official Solution:
A vending machine dispenses one drink at random from 48 drinks stocked inside. Each drink is either Coke or Pepsi, and each drink is either bottled or canned. What is the positive difference between the probability that the drink dispensed is a canned Pepsi and the probability that the drink dispensed is a bottled Coke?
The question asks to find the value of |y/48 - x/48| = |y - x|/48. So, essentially, all we need to find is the value of y - x.
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
This gives:
So, we have that y = x - 4. Therefore, y - x = (x - 4) - x = -4 and the positive difference is thus 4/48. Sufficient.
(2) 9 of the drinks are bottled Pepsi.
This gives:
That is not enough to determine y - x. Not sufficient.
Answer: A.
A vending machine dispenses one drink at random from 48 drinks stocked inside. Each drink is either Coke or Pepsi, and each drink is either bottled or canned. What is the positive difference between the probability that the drink dispensed is a canned Pepsi and the probability that the drink dispensed is a bottled Coke?
| Coke | Pepsi | TOTAL | |
| Bottled | x | ||
| Canned | y | ||
| TOTAL | 48 |
The question asks to find the value of |y/48 - x/48| = |y - x|/48. So, essentially, all we need to find is the value of y - x.
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
This gives:
| Coke | Pepsi | TOTAL | |
| Bottled | x | = 24 - x | 24 |
| Canned | y = 20 - (24 - x) = x - 4 | = 48 -24 = 24 | |
| TOTAL | 28 | = 48 - 28 = 20 | 48 |
So, we have that y = x - 4. Therefore, y - x = (x - 4) - x = -4 and the positive difference is thus 4/48. Sufficient.
(2) 9 of the drinks are bottled Pepsi.
This gives:
| Coke | Pepsi | TOTAL | |
| Bottled | x | 9 | |
| Canned | y | ||
| TOTAL | 48 |
That is not enough to determine y - x. Not sufficient.
Answer: A.
General Discussion
03 May 2026, 20:22
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We need
|P(canned Pepsi) − P(bottled Coke)|,
total = 48.
(1) Coke = 28
⇒ Pepsi = 20.
Bottled = 24
⇒ canned = 24.
Let bottled Coke = x.
Then bottled Pepsi = 24 − x.
Canned Pepsi = 20 − (24 − x)
= x − 4.
P(canned Pepsi) = (x − 4)/48
P(bottled Coke) = x/48
Difference = |(x − 4 − x)/48|
= 4/48
= 1/12, fixed
⇒ sufficient.
(2) Bottled Pepsi = 9,
not enough to determine required probabilities
⇒ insufficient.
Answer: A
|P(canned Pepsi) − P(bottled Coke)|,
total = 48.
(1) Coke = 28
⇒ Pepsi = 20.
Bottled = 24
⇒ canned = 24.
Let bottled Coke = x.
Then bottled Pepsi = 24 − x.
Canned Pepsi = 20 − (24 − x)
= x − 4.
P(canned Pepsi) = (x − 4)/48
P(bottled Coke) = x/48
Difference = |(x − 4 − x)/48|
= 4/48
= 1/12, fixed
⇒ sufficient.
(2) Bottled Pepsi = 9,
not enough to determine required probabilities
⇒ insufficient.
Answer: A
