A vending machine dispenses one drink at random from 48 drinks stocked

Question

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.

M47-138

Bunuel · Accepted Answer

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?

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.

AdarshSambare · Answer

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

thisisakr · Answer

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

BongBideshini · Answer

Let:
 
  Pepsi canned = x  
  Coke bottled = y   
 we need to find |x-y|/48

Bottle 
 Can 
 Total 
 
  Coke 
 y

Pepsi 
  
 x

Total

48

Statement (1)

Bottle 
 Can 
 Total 
 
  Coke 
 y 
 24-x 
 28 
 
  Pepsi 
 24-y 
 x 
 20 
 
   Total  
  24  
  24  
 48

(24 − y) + x = 20
=> y − x =  4

Sufficient

Statement (2)

Bottle 
 Can 
 Total 
 
  Coke 
 y

Pepsi 
  9  
 x 
 9+x 
 
  Total

48

But no way to connect  x and y

Ans (A)

A vending machine dispenses one drink at random from 48 drinks stocked

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	Coke	Pepsi	TOTAL
Bottled	x	= 24 - x	24
Canned		y = 20 - (24 - x) = x - 4	= 48 -24 = 24
TOTAL	28	= 48 - 28 = 20	48

GMAT Data Sufficiency (DS) Questions

A vending machine dispenses one drink at random from 48 drinks stocked

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