# SAT Mathematics : SAT Math

## Example Questions

### Example Question #41 : Sat Math

A particular ball always bounces back to  of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 625 millimeters. Approximately how high (in inches) will it reach after its fifth bounce?

9.6 millimeters

16 millimeters

6.4 millimeters

24 millimeters

16 millimeters

Explanation:

If the ball begins at a height of 250 millimeters after the first bounce, we can apply the change for each bounce to arrive at the height after the 5th bounce by multiplying each height by  .

So, the heights after each bounce are as follows:

After the first bounce - 625

After the second bounce - 250 (625 * )

After the third bounce - 100 (250 * )

After the fourth bounce - 40 (100 * )

After the fifth bounce - 16 (40 * )

Keep in mind, our starting value is already after the first bounce, so we're only applying our multiplier of  four times. The common mistake in this question is to assume that because we're looking for the "fifth bounce," we should apply the multiplier five times. Be sure to pay close attention to the wording and, if needed, take things step by step!

### Example Question #41 : Sat Math

Portia purchased a laptop for $480, but after checking the merchant's website realized that she had been overcharged by 20%. By how much, in dollars, was she overcharged? Possible Answers:$80

$48$24

$96 Correct answer:$80

Explanation:

In any percent problem, it is crucial that you know exactly which value the percent is to be taken of. Here Portia is overcharged by 20%, meaning that she paid 20% more than the item should have cost. That means that the amount she paid, $480, equals 20% more than she should have paid: , where is the price she should have paid. To solve for , divide both sides by : This means that she should have paid$400 but instead paid $480, so she overpaid by$80.

Note that a common mistake on percent problems is taking the percent of the wrong value: here you might be tempted to simply take 20% of 480, for example. The SAT test makers know that, and will often set up problems so that you're given the result of the percent change (here the result is Portia paying $480) and need to work your way back to the start value as you did here. Always pause to ensure that you know which value (or variable) gets multiplied by the percent change. ### Example Question #42 : Sat Math Over the course of a single week, the price of a company’s stock rose by 10%. If the following week the company’s stock rose by 10% of the new price, by what percent did the stock increase over the two week period? Possible Answers: 21% 120% 20% 19% Correct answer: 21% Explanation: This problem rewards students who do the work rather than just looking at a problem and going with what “looks right.” Whenever you see a problem that asks you to find the percent difference between two unknowns, you can probably pick your own numbers to make the problem easier since the problem is asking for a relationship rather than a value. In this case, since you are dealing with percents, it is a good idea to start with the number 100. If you increase 100 by 10%, you will get after the first increase. During the second week, you are told, the price of the stock increases by 10% of the new value. Be careful here to take the percent of the correct value, 110, rather than the original value. If you increase 110 by 10%, you get: . To find the percent increase from there, you find the difference and then divide by the original before multiplying by 100: ### Example Question #3 : Applying Percents To Word Problems A store buys a shirt for$60, then marks it up by 50%, then offers customers a 20% discount off the marked up price. What price do consumers pay?

$72$108

$78$90

$72 Explanation: Remember that when you are dealing with taking the percent of a number and then taking the percent of the result, that you must be careful to take the percent of the correct number. In this case, that means increase$60 by 50% and then taking 20% off that new number. What you cannot do is either take off 20% of 60 or just increase 60 by 30% rather than doing each step in order. Doing either will lead to a trap that the Testmaker has left for you.

The first step you’re given is to increase $60 by 50%. This is the same as taking 150% of$60, or as multiplying it by 1.5. If you do this you get;

From there, you now need to find what 20% off 90 is in order to get your solution. You can do this by first finding 10% of 90 by moving the decimal point one place to the left to get 9 and then doubling it to get 18.

### Example Question #7 : Applying Percents To Word Problems

After the first week of training for an upcoming race, Dinesh begins the second week of his training program by increasing his weekly running mileage by 50%. After three weeks, he catches a cold and has to reduce his current weekly mileage by 40% for the final week of training. By what percent did Dinesh's weekly mileage change from the first week to the final week?

10% decrease

10% increase

15% decrease

20% increase

10% decrease

Explanation:

Algebraically, if Dinesh started at  miles, he increases to  miles in the second week, and decreases to  for the final week -- a 10 percent decrease from his starting point.

### Example Question #8 : Applying Percents To Word Problems

In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts?

35%

28%

24%

30%

30%

Explanation:

You can set this problem up algebraically by recognizing what you're really solving for, which is essentially a ratio of doughnuts () to total (). You're given that the ratio of glazed () to doughnuts () is 70/100, and you're given that glazed () to total () is 21/100. Knowing that, you can set up:

and

And since  has to be equal in each of those equations, you can set the equations equal:

From there, your goal is to solve for , so you'll divide both sides by  to get:

And then multiply both sides by  to cancel the fraction on the left and move all the numbers to the right. Now you have:

Now you should see how cleanly the terms on the right factor, leaving you with:

. If  out of  is  out of , that means that the answer is .

### Example Question #3 : Applying Percents To Word Problems

During a clearance sale, a retailer discounted the original price of its TVs by 25% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?

60%

55%

40%

45%