### All PSAT Math Resources

## Example Questions

### Example Question #1 : Sale Prices

Maria was shopping for a camera and found one that was on sale for 30% off. As she went to pay for it, the store announced an instant sale that took an additional 10% off all items. If the final price Maria paid was $207.27, what was the original price (before all discounts) of the camera?

**Possible Answers:**

$329.00

$518.18

$767.67

$290.18

$82.91

**Correct answer:**

$329.00

To reconstruct an original price from a sale price, use:

Original Price – Original Price * Mark-down-percent = Sale Price, or

Original Price * (1 - Mark-down-percent) = Sale Price

To do a double mark-down problem, we must do this twice. For the 10%:

Original Sale Price * (1 – 10%) = $207.27

Original Sale Price = $207.27/0.9 = $230.30.

For the pre-all-discount price,

Original Price * (1 – 30%) = $230.30

Original Price = $230.30/0.7 = $329.00.

### Example Question #2 : Sale Prices

An mp3 player costs $100 on day one. On day two, the shop owner decides to decrease the price by 10% of the day one price. However, on day three the owner changes her mind and raises the price by 10% of the day two price. What is the new price of the mp3 player?

**Possible Answers:**

$102

$100

$99

$98

$101

**Correct answer:**

$99

10% of the day one price = 0.1(100) = $10.

Therefore the day two price = 100 - 10 = $90.

10% of the day two price = 0.1(90) = $9.

Therefore the day three price = 90 + 9 = $99.

### Example Question #3 : Sale Prices

The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?

**Possible Answers:**

44%

40%

56%

50%

48%

**Correct answer:**

44%

Let us assume that the original purse is $100. The price after the first reduction is $80. After the second reduction the price is now $56. The difference between 100 and 56 is 44, giving 44% off.

### Example Question #4 : Sale Prices

A store is having a sale. If you buy one widget for the regular price of $20, you can buy a second widget for 40% off the regular price. How much per widget does a customer save by buying two widgets during the sale instead of buying two widgets at the regular price?

**Possible Answers:**

4

8

20

12

32

**Correct answer:**

4

Widget 1 costs $20.

Widget 2 is on sale for 40%($20) off, or $8 off, or $20 – $8 = $12.

Two widgets during the sale cost $20 + $12 = $32.

Two widgets at regular price cost $20 + $20 = $40.

The total amount saved during the sale is $40 – $32 = $8.

This is the savings for two widgets, so the savings for one widget is $8/2 = $4.

### Example Question #5 : Sale Prices

A $225 dress goes on sale for 75% off. It is then discounted again for 10% off. How much money was saved on by the final purchase?

**Possible Answers:**

191.25

16.88

174.37

33.75

50.63

**Correct answer:**

174.37

The answer is $174.37.

The dress originally cost $225 but when it went on sale for 75% off we multiply the sale cost by 0.75. We see that through the sale we save $168.75 makeing the new cost of the dress $56.25.

Now we take the new cost of the dress ($56.25) and multiply that by 0.10 to represent the 10% discount. From this we see we save an additional $5.63 making the final cost of the dress $50.63.

The total savings on the dress sum up to $174.37.

### Example Question #6 : Sale Prices

A stove is regularly priced for $300. What is the difference one would pay when buying it at a 20% discount rather than a 10% discount, with an additional 10% discount off the sale price?

**Possible Answers:**

$20

$3

$5

$30

**Correct answer:**

$3

Buying the stove at a 20% discount would be $240. If one buys it at a sale of 10%, with another 10% off then the price would be $243, so the difference is $3

20% of 300 is 0.2 * 300 = 60 → 300 – 60 = 240

10% of 300 is 0.1 * 300 = 30 → 300 – 30 = 270

10% of 270 is 0.1 * 270 = 27 → 270 – 27 = 243

243 – 240 = 3

### Example Question #7 : Sale Prices

Mark sells his car to Mike for 95% of the amount he originally paid. Mike then discounts the car 20% and sells it to Max. Max paid $300. How much did Mark buy his car for (rounded to the nearest dollar)?

**Possible Answers:**

280

265

395

355

335

**Correct answer:**

395

Apply your percentage knowledge. Starting value times percentage equals end value. $300/(1 – 0.2) = $375. $375/0.95 = $395.

### Example Question #8 : Sale Prices

The costs for Lizzie’s party are as follows: $6000 to cater, $1200 for the DJ, $2000 for decorating, and $2200 for the venue rental. Lizze can choose to apply a discount of 10% for the caterer and decorating but is then charged an additional 30% for the DJ and venue. What is the minimum price she will pay?

**Possible Answers:**

$12,160

$11,400

$12,440

$10,800

$11,000

**Correct answer:**

$11,400

The discounts are not worth the extra cost. The answer is $11,400.

### Example Question #9 : Sale Prices

Mr. Glatfelter trains hunting dogs for a price of $4000 per dog. If it costs him $15,000 per month to keep his business open and each dog costs $1000 to train, how many dogs per month must he train to make a profit?

**Possible Answers:**

5

7

8

6

9

**Correct answer:**

6

The answer is 6. 6 hunting dogs gives him a net profit of $3000. If you picked 5, that’s where Glatfelter breaks even (he doesn’t make a profit or a loss).

### Example Question #10 : Sale Prices

A dress was originally priced at $70. In January, it was put on sale for 20% off. Then in February, the sale price was lowered an additional $10 off of January's price. How much is the dress currently being sold for?

**Possible Answers:**

$52

$50

$46

$34

$60

**Correct answer:**

$46

The dress started at $70. In January, it was marked down 20%. $70 * 0.2 = $14, so it was being sold for $70 – $14 = $56. Then we're told its price is again lowered, this time by $10. Now the price is $56 – $10 = $46.

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