SAT Math - Whole and Part

1

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?

10

11

12

13

14

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.

2

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?

10

11

12

13

14

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.

3

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

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.

4

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?

45

30

35

40

50

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 $\dpi{100} \small 27\div 3=9$ ounces. Since there are $\dpi{100} \small 5$ fifths in the pitcher, it must hold $\dpi{100} \small 9\times 5=45$ ounces total.

5

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

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.

6

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?

45

30

35

40

50

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 $\dpi{100} \small 27\div 3=9$ ounces. Since there are $\dpi{100} \small 5$ fifths in the pitcher, it must hold $\dpi{100} \small 9\times 5=45$ ounces total.

7

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?

$10.00

$6.50

$4.00

$2.50

$1.00

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.

8

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?

$10.00

$6.50

$4.00

$2.50

$1.00