SAT Math Problem with Solution

Today I would like to provide you with a sample question and solution for the revised SAT. This one is a Level 2 Problem Solving question.

Level 2 Problem Solving

A chemist has a supply of 5.2 liter bottles of a certain solvent that must be shipped to a central warehouse. The warehouse can accept the solvent at the rate of 3 hectoliters per minute for a maximum of 8 hours per day. If 1 hectoliter equals 100 liters, what is the maximum number of bottles that the warehouse could receive from the chemist each day.

(A)   461
(B)   462
(C)   27,692
(D)   83,200

Solution: The warehouse can receive  3 ∙ 60 ∙ 8 hectoliters of the solvent per day, or equivalently, 1440 ∙ 100 = 144,000 liters of the solvent per day. Therefore the number of bottles that can be accepted each day is 144,000/5.2 which is approximately 27,692.30769. The maximum number of bottles that the warehouse can accept in one day is therefore 27,692, choice (C).

Notes: (1) Since there are 60 minutes in an hour, “3 hectoliters per minute” is the same as  3 ∙ 60 = 180  hectoliters per hour.

Similarly, since the warehouse can accept the solvent for a maximum of 8 hours per day, “180 hectoliters per hour” is equivalent to a maximum of  180 ∙ 8 = 1440 hectoliters per day.

(2) In the above solution we combined the two conversions given in note 1 into a single conversion: “3 hectoliters per minute” is equivalent to a maximum of  3 ∙ 60 ∙ 8 = 1440 hectoliters per day.

(3) Since 1 hectoliter equals 100 liters, we can convert hectoliters to liters by multiplying by 100. So 1440 hectoliters is equal to 1440 ∙ 100 = 144,000 liters.

(4) We can convert between hectoliters and liters more formally by setting up a ratio. The two things being compared are “liters” and “hectoliters.”

 liters     100        x
hectoliters    1        1440

Now draw in the division symbols and equal sign, cross multiply and divide the corresponding ratio to find the unknown quantity x.

100/1 = x/1440

1x = 100 ∙ 1440

x = 144,000

(5) Instead of converting 1440 hectoliters to 144,000 liters, and then dividing by 5.2, we can instead convert 5.2 liters to  hectoliters, and then divide 1440/.052, giving the same answer of 27,692, choice (C).

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