Math: b7e6394d

ID: b7e6394d

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: Think about units.

Method 1: The question is asking us about miles, so we want to make sure the answer would be in miles. This provides an excellent point of entry to evaluate the answers themselves.

(A) 25 (miles per gallon)/4 (dollars per gallon) * m (miles) = 95 (miles squared per dollar?)

Because this is a meaningless unit, we can eliminate this answer choice. In fact, (B) would give us the same nonsensical unit, so it can also fall by the wayside.

We can see that the left-hand side of (C) and (D) is identical, so it comes down to what this number on the right-hand side corresponds to. Straighten out (C) so that all the numbers are on the right-hand side, and you will see why it does not make sense either.

(C) (4/25)m = 95 --> 4m = 95 * 25 --> m = (95 * 25)/4

We do not need to be exact here, although we could plug in the above to a calculator readily enough. All we need to keep in mind is that the setup tells us that Alan currently drives an average of 100 miles each week, so if the question asks us to find how many fewer average miles he ought to drive, it cannot be any more than 100, since that would lead to 0 miles driven. If 400/4 = 100, then we can estimate that (95 * 25)/4 > 100, and this answer choice also makes no sense. The correct answer must be (D).

We could check it from top to bottom, of course.

(D) 4 (dollars per gallon)/25 (miles per gallon) * m (miles) = 5 (dollars)

Note that this $5 is the very amount Alan is hoping to save each week by cutting back on gas consumption. Also, this m would make sense within the context of the question.

(4/25) * m = 5

4m = 5 * 25

m = 125/4

Clearly, this quotient will be less than 100. Altogether, this chain of logic should allow you to answer (correctly) with confidence in under a minute.

Method 2: Graph each answer choice, using y for w, and keep an eye on that 100 from the setup: you are looking to answer how many fewer miles Alan could drive each week to save a few dollars, so the answer must be less than 100.

The only obvious outlier is the green line, so get rid of (C). Now, take a closer look at the others.

Keep in mind a few facts from the setup:

- the car Alan drives gets 25 miles per gallon

- Alan wants to save $5 each week by cutting back on driving miles

- gasoline costs $4 per gallon

- the question is asking about miles

Now, think about it: Alan must drive 25 miles fewer to save $4 for the 1 gallon he would otherwise use. The correct answer must therefore be a line that is greater than 25, and only the purple one qualifies. The correct answer must be (D).

Method 3: The only piece of information in the setup that is not a rate is $5, the target savings, so it stands to reason that this value will be on the right-hand side of the equation. Between (B) and (D), work out the algebra.

(B) (25/4)m = 5 --> 25m = 20 --> m = 20/25

That does not quite work. How will driving less than 1 mile less save Alan $5? Check (D) if you want to feel more confident in your answer.

(D) (4/25)m = 5 --> 4m = 125 --> m = 125/4 --> m = 31.25

Again, this makes sense: 31.25 miles will take 1 gallon of gasoline plus a bit more (a fourth, to be exact), and since gasoline costs $4 a gallon, the $5 in savings seems reasonable. The correct answer must be (D).