Problem Solving

I have two questions that ask for the greatest/ maximum number of a quantity. Is there an easierway or set strategy to approach these kind of problems?

(1) Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.30?
(A) 426
(B) 430
(C) 443
(D) 460
(E) 486
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(2) An automobile’s gasoline mileage varies, depending on the speed of the automobile, between 18.0 and 22.4 miles per gallon, inclusive. What is the maximum distance, in miles, that the automobile could be driven on 15 gallons of gasoline?
(A) 336
(B) 320
(C) 303
(D) 284
(E) 270






Ans - (1) D, (2) A

Most of these questions just require you to apply some common sense and logic. To maximize what the question requires, what other quantities do we want to either maximize or minimize.

prees20 wrote:(1) Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.30?
(A) 426
(B) 430
(C) 443
(D) 460
(E) 486

The best rate is 1.5 cents each, from the $1.50/100 option. So let's buy as many envelopes as we can at the best rate.

$1.50 * 4 = $6.00, which is the best we can do.. so that's 400 envelopes.

Our 2nd best rate is 2 cents each, from the $1/50 option. With our remaining $1.30, we can buy one bunch of 50 envelopes for $1.

We have 30 cents left to spend on the single envelopes for 3 cents each - that's another 10 envelopes.

So: 400 + 50 + 10 = 460 envelopes.

(2) An automobile’s gasoline mileage varies, depending on the speed of the automobile, between 18.0 and 22.4 miles per gallon, inclusive. What is the maximum distance, in miles, that the automobile could be driven on 15 gallons of gasoline?
(A) 336
(B) 320
(C) 303
(D) 284
(E) 270

If we want to maximize the distance we can travel on 15 gallons, we want to choose the best possible mileage rate, which in this question is 22.4 mpg.

Distance = gallons * mpg = 15 * 22.4 = 330 and a bit more (we can just do 15*22 and see which answers are close): choose (A).