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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.
(1) 28 of the drinks are Coke, and half of the 48 drinks are bottled.
(2) 9 of the drinks are bottled Pepsi.
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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
04 May 2026, 00:46
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We have 48 drinks arranged in a 2×2 grid: Coke vs Pepsi, and Bottled vs Canned. Let's call the four cells a (bottled Coke), b (bottled Pepsi), c (canned Coke), and d (canned Pepsi), where a + b + c + d = 48.
The question asks for |d/48 − a/48|, which simplifies to just finding |d − a|.
Statement 1 alone is sufficient
It tells us 28 drinks are Coke, so a + c = 28, meaning b + d = 20. It also tells us half the drinks are bottled, so a + b = 24, meaning c + d = 24. Now here's the elegant part — we don't need to solve for each variable individually. Notice that d − a = (b + d) − (a + b) = 20 − 24 = −4. So the positive difference is 4/48 = 1/12. Statement 1 gives a unique answer.
Statement 2 alone is insufficient
Knowing that 9 drinks are bottled Pepsi (b = 9) leaves us with three unknowns and only one equation (a + c + d = 39). For example, a = 10 and d = 15 gives a difference of 5/48, while a = 20 and d = 10 gives 10/48. Multiple valid scenarios exist, so no unique answer is possible.
The answer is A
The question asks for |d/48 − a/48|, which simplifies to just finding |d − a|.
Statement 1 alone is sufficient
It tells us 28 drinks are Coke, so a + c = 28, meaning b + d = 20. It also tells us half the drinks are bottled, so a + b = 24, meaning c + d = 24. Now here's the elegant part — we don't need to solve for each variable individually. Notice that d − a = (b + d) − (a + b) = 20 − 24 = −4. So the positive difference is 4/48 = 1/12. Statement 1 gives a unique answer.
Statement 2 alone is insufficient
Knowing that 9 drinks are bottled Pepsi (b = 9) leaves us with three unknowns and only one equation (a + c + d = 39). For example, a = 10 and d = 15 gives a difference of 5/48, while a = 20 and d = 10 gives 10/48. Multiple valid scenarios exist, so no unique answer is possible.
The answer is A
