PSAT Math : Arithmetic

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

\(\displaystyle \small 2, 3, 5, 9, 17, x, 65, 129....\)

\(\displaystyle \small \textup{In the above number sequence, what is the value of}\,x?\)

Possible Answers:

\(\displaystyle \small 35\)

\(\displaystyle \small 31\)

\(\displaystyle \small 32\)

\(\displaystyle \small 34\)

\(\displaystyle \small 33\)

Correct answer:

\(\displaystyle \small 33\)

Explanation:

Each term in the sequence is one less than twice the previous term.

So, \(\displaystyle \small x=2\left ( 17\right )-1\) 

\(\displaystyle \small x=33\)

Example Question #2 : How To Find The Next Term In An Arithmetic Sequence

What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?

Possible Answers:

37

40

32

41

35

Correct answer:

35

Explanation:

The series is defined by n2 – 1 starting at n = 1. The sixth number in the series then equal to 62 – 1 = 35.

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

A sequence of numbers is as follows:

\(\displaystyle 3, 8, 18, 38, 78, . . .\)

What is the sum of the first seven numbers in the sequence?

Possible Answers:

1529

490

248

719

621

Correct answer:

621

Explanation:

The pattern of the sequence is (x+1) * 2.

We have the first 5 terms, so we need terms 6 and 7:

(78+1) * 2 = 158

(158+1) * 2 = 318

3 + 8 + 18 +38 + 78 + 158 + 318 = 621

Example Question #391 : Arithmetic

Find the \(\displaystyle \small 7th\) term in the sequence

\(\displaystyle \small 3 , 7 , 11 , 15 , ...\)

Possible Answers:

\(\displaystyle \small 27\)

\(\displaystyle \small \small \small 23\)

\(\displaystyle \small 19\)

\(\displaystyle \small 31\)

Correct answer:

\(\displaystyle \small 27\)

Explanation:

Notice that in the sequence 

\(\displaystyle \small 3 , 7 , 11 , 15 , ...\)

each term increases by \(\displaystyle \small 4\).

It is always good strategy when attempting to find a pattern in a sequence to examine the difference between each term.

We continue the pattern to find:

The \(\displaystyle \small 5th\) term is \(\displaystyle \small 19\)

The \(\displaystyle \small \small 6th\) term is \(\displaystyle \small \small 23\)

The \(\displaystyle \small \small \small 7th\) term is \(\displaystyle \small \small \small 27\)

It is useful to note that the sequence is defined by,

\(\displaystyle \small S(n) = 4n -1\)

where n is the number of any one term.

We can solve

\(\displaystyle \small \small S(7) = 4(7) -1 = 28 - 1 = 27\)

to find the \(\displaystyle \small 7th\) term.

 

Example Question #1 : How To Find The Sale Price

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:

$767.67

$82.91

$329.00

$518.18

$290.18

Correct answer:

$329.00

Explanation:

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 #1 : How To Find The Sale Price

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:

$99

$101

$100

$102

$98

Correct answer:

$99

Explanation:

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 : How To Find The Sale Price

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:

56%

50%

48%

40%

44%

Correct answer:

44%

Explanation:

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 #1 : How To Find The Sale Price

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:

8

12

32

4

20

Correct answer:

4

Explanation:

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 #4 : How To Find The Sale Price

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:

50.63

16.88

33.75

174.37

191.25

Correct answer:

174.37

Explanation:

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 #1 : How To Find The Sale Price

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:

$30

$5

$3

$20

Correct answer:

$3

Explanation:

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

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