Up Your Score (36 page)

3. On a map, if 1 inch represents 30 miles, then how many inches represent 75 miles?

This is a thinly disguised ratio problem—the key word here is
represent
. The problem can be translated to look like this:

1 inch : 30 miles :: x inches : 75 miles

Solving for
x
gives us
x
= 2½ inches.

It might be easier if you just think in your head, “Okay, the problem is asking how many times 30 goes into 75. That’s easy! 2½! God, I’m smart!” Sometimes problems are easier than they look.

4. Mary’s average salary for her first 6 years of work was $15,000; her average salary for the next 2 years was $16,000. What was her average salary over the entire 8 years?

Notice that
n
for this problem is 8; the average is

5. If Paul ate 300% more pizza than Manek ate, and Manek ate an entire pizza, then how many pizzas did Paul eat?

Paul ate
as many
pizzas as Manek
plus
300%.

So Paul ate ONE pizza PLUS 300% of one.

So Paul ate FOUR PIZZAS! (Paul, you glutton.)

6. Suppose JaJa took the SAT 8 times and her combined scores each time were 2230, 2230, 2280, 2300, 2340, 2400, 2400, 2400. What was her median score? What was the mode of her score?

Well, 2300 and 2340 are the 2 in the middle, so average them and you’ll see that the median equals 2320. And since 2400 shows up the most times, 2400 is the mode. Also, by the way, JaJa didn’t really take the SAT 8 times. She has a
way
cooler life than that.

Another thing to watch out for in word problems is common sense. Make sure you don’t pick an answer that says that Chris travels 200 miles an hour on his bike or that Amy ate 3,000 cookies in one day. The SAT isn’t creative enough to have outlandish answers.

These questions are famous. They have no relevance to anything, really, but they involve people making work for themselves by going places and coming back again for no apparent reason.

Example:

A man in a bus travels 4 miles in 3 minutes. Then he gets out of the bus and walks back to his starting point, taking
hour. What was his average speed for the whole trip?

Answer: 16 miles/hour

The best way to deal with this type of word problem is to plot it out, with distances and times:

4 miles in 3 min by bus + 4 miles in 27 min walking = 8 miles in 30 minutes total

Get it? Add up total miles, divide by total time, and you’ll like, totally get the answer. (Remember to convert 30 minutes to ½ hour in order to get the answer in miles/hour.)

Example:

A boat travels 3 miles north, 4 miles east, and then sinks. If it sank to a depth of 1 mile, then how far is it from its starting point?

Use the Pythagorean Theorem and a picture to get the answer. Point A is where the boat began. It sailed 3 miles north to point B, then 4 miles east to point C. It then sank 1 mile, to point D. The distance of the boat from its starting point is AD. So you must solve for AD, but first you must figure the distance of the hypotenuse, AC, of the triangle ABC.

Now you’re ready to solve for AD, the hypotenuse of triangle ACD:

So the distance of the boat from its starting point is
miles, or 5.1 miles.

Example:

A man’s goldfish swims around the edge of its cylindrical fish tank, which has a radius of 1 meter (it’s a big fish tank), at a rate of 1 lap per 30 seconds. How long does it take the fish to swim 32π meters, if after every 4 laps the fish takes a 5-second break to eat some McNuggets? (Include the final break.)

(A) 16 minutes

(B) 500 minutes

(C) 8⅓ minutes

(D) 32 minutes

(E)
π minutes

JaJa says: Make a list of key points from the word problems so you don’t have to go back and reread the question. Saves time and effort!

Since the circumference of a circle is π times diameter, then each lap is 2π meters. The fish swims 32π meters, or 16 laps: