130 passengers flying on a plane have stored a total of 250 pieces of

Question

130 passengers flying on a plane have stored a total of 250 pieces of luggage in the plane's cargo hold. If every passenger has stored at least 1 piece of luggage, how many of the passengers have stored exactly 2 pieces of luggage in the plane's cargo hold?

(1) 40 of the passengers stored only 1 piece of luggage in the cargo hold.

(2) None of the passengers stored more than 3 pieces of luggage in the cargo hold.

lovesuit · Answer

From 1 
we know that there are 40 passengers with only 1 luggage, but nothing about passengers with more than 1.
Not Sufficient 
From 2 
we know there are no passengers with more than 3 luggage, but nothing about the number of passengers carrying how much luggage.
Not Sufficient

By combining both 
we know that there 40 passengers with 1 luggage, so 90 passengers are left with 210 luggage. 60 *2 + 30* 3= 210
so there 60 passengers have stored exactly 2 pieces of luggage in the plane's cargo hold.
IMO C

gmatophobia · Answer

Number of extra luggage =  250 - 130 = 120

Statement 1

(1) 40 of the passengers stored only 1 piece of luggage in the cargo hold.

Number of people who stored more than 1 piece of luggage in the cargo hold = 130 - 40 = 90

However, we can't infer of these 90 passengers how many passengers stored exactly 2 pieces of luggage in the plane's cargo hold.

Hence, this statement alone is not sufficient and we can eliminate A, and D.

Statement 2

(2) None of the passengers stored more than 3 pieces of luggage in the cargo hold.

Let the number of passengers who stored exactly 2 pieces of luggage = x

Let the number of passengers who stored exactly 3 pieces of luggage = y

From the question premise, we know that  2x + 3y = 120

We have two variables and one equation; multiple possible combinations of x and y satisfy this equation. Hence, we cannot infer the values of x and y.

Hence, eliminate B

Combined

Let the number of passengers who stored exactly 2 pieces of luggage = x

Let the number of passengers who stored exactly 3 pieces of luggage = y

From the question premise, we know that  2x + 3y = 120

From statement 1, we can infer that  x + y = 90

Combining the two equations we can find the value of x, and y.

The statements combined are sufficient.

Option C

samarpan.g28 · Answer

Hi. While combining statements 1 and 2, I got y=-60, can we consider this? Kindly help to find my gap in understanding. Thank you in advance.

Bunuel · Answer

The equations in the solution you quoted are not correct. They should be 2x + 3y = 210  (40 of the passengers stored only 1 piece of luggage, thus 250 - 40 = 210 pieces of luggage were stored by the passengers who stored more than 1 piece)  and x + y = 90, which give x = 60 and y = 30.

bumpbot · Answer

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130 passengers flying on a plane have stored a total of 250 pieces of

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