PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Find The Ratio Of A Fraction

You have a bag filled with red and green apples. If there are 9 red apples and 12 green apples, what is the probability of choosing a red apple out of the bag?

Possible Answers:

Correct answer:

Explanation:

To find the probability we need to set up a ratio. The ratio will be how many red apples are in the bag over the total number of apples (both red and green) in the bag.

 

We can now reduce this fraction:

Example Question #2 : How To Find The Ratio Of A Fraction

A pie is made up of   crust,  apples, and  sugar, and the rest is jelly. What is the ratio of crust to jelly?

Possible Answers:

Correct answer:

Explanation:

A pie is made up of   crust,  apples,  sugar, and the rest is jelly. What is the ratio of crust to jelly?

To compute this ratio, you must first ascertain how much of the pie is jelly. This is:

Begin by using the common denominator :

So, the ratio of crust to jelly is:

This can be written as the fraction:

, or 

Example Question #1 : How To Find The Ratio Of A Fraction

In a solution,  of the fluid is water,  is wine, and  is lemon juice. What is the ratio of lemon juice to water?

Possible Answers:

Correct answer:

Explanation:

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying: 

Example Question #41 : Proportion / Ratio / Rate

If  and , what is the ratio of  to ?

Possible Answers:

Correct answer:

Explanation:

To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:

Recall that division of fractions requires you to multiply by the reciprocal:

which is the same as:

This is the same as the ratio:

Example Question #81 : Fractions

The price of 10 yards of fabric is c cents, and each yard makes q quilts. In terms of q and c, what is the cost, in cents, of the fabric required to make 1 quilt?

Possible Answers:

(c )/(10q )

(10c )/(q )

(cq )/(10 )

10cq

Correct answer:

(c )/(10q )

Explanation:

We create a conversion ratio that causes yards to cancel out, leaving only cents in the numerator and quilts in the denominator. This ratio is ((c cent )/(10 yard))((1 yard)/(q quilt))=(c )/(10q ) cent⁄quilt . Since the ratio has cents in the numerator and quilts in the denominator, it represents the price in cents per quilt.

Example Question #2 : How To Find Proportion

Susan is doing a bake sale for her sorority. One third of the money she made is from blueberry cupcakes, which cost 50 cents each. A quarter of her sales is from cinnamon cream pies, which cost $1 each. And the rest are from her chocolate brownies, which cost 25 cents each. She made a total of $60 at the end of her bake sale, how many brownies did she sell?

Possible Answers:

130

140

100

150

120

Correct answer:

100

Explanation:

1/3 of sales from cupcakes = $20, ¼ of sales from cream pies = $15 and the rest are from brownies = $60-$20-$15 = $25. Since each brownie costs 25 cents, Susan will have sold 100 of them.

Example Question #1 : How To Find Proportion

In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly? 

Possible Answers:

8

5

9

6

12

Correct answer:

8

Explanation:

Consider

(Bill + 7) = 2 x (Amy + 7)

(Amy – 2) = 1.5 x (Molly – 2)

Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.

Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1

Substitute this into the first equation:

(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12

Solve for Molly:

Bill + 7 – 12 = 3 x Molly

Molly = (Bill – 5) ¸ 3

Substitute Bill = 29

Molly = (Bill – 5) ¸ 3 = 8

Example Question #1 : How To Find Proportion

When Christina opens a bag of white and milk chocolate pieces, 20% of the chocolate pieces are white. After Christina eats 10 milk chocolate pieces, the ratio of brown chocolate to white chocolate is 2 to 3. How many pieces of chocolate are left in the bag?

Possible Answers:

2

15

12

3

5

Correct answer:

5

Explanation:

Let original white chocolate pieces = W and original milk chocolate pieces = M. So the total number of pieces in the original bag is M + W.

From the first sentence: (M + W) x 0.2 = W or

0.2 M = 0.8 W or [M = 4W]

Once Christina has eaten 10 milk chocolate pieces, there are W pieces of white chocolate, (M – 10) pieces of milk chocolate and (M + W – 10) pieces total. According to the second sentence:

W ¸ (M – 10) = 3 ¸ 2

Or 2W = 3M - 30

Insert the equation in brackets: 2W = 3[4W] + 30 = 12W – 30

10W = 30 or W = 3 and M = 12

We want “How many pieces of chocolate are left in the bag” or (M – W – 10).

So (M +W – 10) = 3 + 12 – 10 = 5 

Example Question #2 : How To Find Proportion

You are buying a new car.  The car gets 33 miles per gallon in the city and 39 miles per gallon on the highway.  You plan on driving 30,000 miles over three years and 10,000 of that will be city driving.  If gas costs $3.50 per gallon, how much will you pay in gas over the three year period (round to the nearest cent)?

Possible Answers:

$3181.81

$2692.31

$2855.47

$1060.60

$1794.87

Correct answer:

$2855.47

Explanation:

Cost = ( Miles driven / Miles per gallon) * 3.50

Total Mileage = City Miles + Highway Miles

30,000 = 10,000 + Highway Miles

Highway Miles = 20,000

Cost City = ( 10,000 miles / 33 miles per gallon ) * 3.50

Cost City = 303.03 * $3.50 = $1060.60

Cost Highway = ( 20,000 miles / 39 miles per gallon ) * 3.50

Cost Highway = 512.82 * $3.50 = $1794.87

Total Cost = Cost City + Cost Highway = $1060.60 + $1794.87 = $2855.47

Example Question #2 : How To Find Proportion

A class room of 8th graders is 1/3 boys. Of all the students 4/5 of them are aged 14 while the others are aged 13. If there are 20 girls in the class, approximately how many boys are age 13?

Possible Answers:

8

6

4

2

5

Correct answer:

2

Explanation:

If 20 students are girls, this is 2/3 of the class, giving 30 students total with 10 of them being boys. 4/5 of the boys will be 14, leaving 1/5 of the boys age 13. 1/5 of 10 is 2. 

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