PSAT Math : Whole and Part

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #1 : Whole And Part

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

Possible Answers:

$2.50

$6.50

$1.00

$4.00

$10.00

Correct answer:

$2.50

Explanation:

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

Example Question #1 : How To Find The Whole From The Part

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from.  If after the 2nd bounce the ball reaches  39.96 ft, what was the initial height the ball was dropped from? 

Possible Answers:

66 ft

135 ft

150 ft

100 ft

111 ft

Correct answer:

111 ft

Explanation:

We know the height of the initial bounce, so work backwards to find the initial height.  39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

Example Question #3 : Whole And Part

A pitcher of water is filled \dpi{100} \small \frac{2}{5} of full.  An additional 27 ounces of water is added.  Now the pitcher of water is completely full.  How much water does the pitcher hold?

Possible Answers:

40

50

45

35

30

Correct answer:

45

Explanation:

If \dpi{100} \small 27 ounces fills the pitcher, then it must equal the volume of \dpi{100} \small \frac{3}{5} of the pitcher.  If \dpi{100} \small \frac{3}{5} of a pitcher equals 27 ounces, then \dpi{100} \small \frac{1}{5} of a pitcher equals \dpi{100} \small 27\div 3=9ounces.  Since there are \dpi{100} \small 5 fifths in the pitcher, it must hold \dpi{100} \small 9\times 5=45 ounces total.

Example Question #1 : How To Find The Whole From The Part

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

 

Possible Answers:

Correct answer:

Explanation:

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

 

 

Example Question #4 : Whole And Part

A certain bakery makes chocolate, vanilla, red velvet, and carrot cupcakes in a ratio of 2:3:5:1. If that bakery makes 63 vanilla cupcakes in one day, what is the total number of cupcakes that the bakery made that day?

Possible Answers:

Correct answer:

Explanation:

Because the bakery makes 63 vanilla cupcakes in one day, start by dividing the 63 by the vanilla part of the ratio, which is 3. . That means that the bakery made 21 times the basic set of 2 chocolate, 3 vanilla, 5 red velvet, and 1 carrot cupcakes.

Now add up the parts of your ratio: . If the bakery only made 3 vanilla cupcakes, then it would have made 11 cupcakes that day. But, because the bakery made 21 times that number of vanilla cupcakes, it made 21 times the total number of cupcakes over the course of the day. To find the total number of cupcakes the bakery made that day, you multiply  to get 

Example Question #5 : Whole And Part

A circle is divided into various sized slices. One slice has an interior angle of  and an area of . What is the circumference of the circle?

Possible Answers:

Correct answer:

Explanation:

In order to find the circumference of the cirlce, we will need to find the radius of the circle. We know that a slice with a 40-degree angle has an area of . There are 360 degrees in a circle. Therefore, the slice of the circle with an angle of 40 dgrees is one-ninth of the entire circle.

Multiply  by 9 to find the area of the circle

The area of the circle is . Now use the formula for area to find the radius

The radius of the circle is 9. Use the formula for circumference to find the circumference of the circle:

The circumference of the circle is .

Example Question #1 : How To Find The Part From The Whole

If a TV show is 45 minutes long, what fraction of the show is completed 5 minutes after it begins?

Possible Answers:

1/4

1/9

1/3

1/2

1/10

Correct answer:

1/9

Explanation:

5 minutes out of 45 have been completed. We can represent this as a fraction: 5/45. When simplified, this yields 1/9. 

Example Question #2 : How To Find The Part From The Whole

A birthday cake is cut into 8 pieces.  On the first night three pieces are eaten.  On the second night, 20% of the remaining cake was eaten.  On the third night, half of the remaining cake was eaten.  How many slices were left to eat on the fourth night?

Possible Answers:

1

3

2

4.5

1/2

Correct answer:

2

Explanation:

First night: 8 – 3 = 5 remaining.

Second night: 20% of 5 remaining = .2 * 5 = 1 slice Therefore 4 remaining.

Third night: ½ of the 4 remaining = ½*4 = 2 slices remaining

Example Question #3 : How To Find The Part From The Whole

There was a malfunction at a candy factory and the machines only put red, purple, and green candy into the bags.  If 1/4 of the candies were red and 3/8 were green, how many purple candies were in the bag, if each bag can hold 16 pieces?

Possible Answers:

6

8

10

4

3

Correct answer:

6

Explanation:

Since 1/4 of the 16 are red: 16 * 1/4 = 4 red candies.  With 3/8 being green:

16 X 3/8 = 6 green candies.   16 – 4 – 6 = 6 candies remain, which must be purple.

Example Question #1 : Whole And Part

In the 30-day month of January, for every three days it snowed, there were seven days it did not snow. The number of days in January on which it did not snow was how much greater than the number of days in January on which it snowed?

Possible Answers:

11

14

10

13

12

Correct answer:

12

Explanation:

The question tells us that for every ten-day period in January (a three-day period plus a seven-day period), it snowed on 3 of those days and did not snow on 7 of those days. Since January has 30 days, it has 3 ten-day periods, so we multiply the numbers given for the 10-day period by 3 to find the  number of days with and without snow during the 30-day period. Doing this, we see that it snowed 3 * 3 = 9 days and did not snow 7 * 3 = 21 days during the 30-day period. Since the question asks how much greater the number of days on which it did not snow is than the number of days on which it snowed, we subtract as follows: number of days it did not snow - number of days it snowed = 21 – 9 = 12.

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