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PSAT Math : PSAT Mathematics

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Example Questions

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

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:

Correct answer:

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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Example Question #2 : Whole And Part

Mikey has one full box of cereal. On Saturday, he eats 1/3 of the the box. On Sunday he eats 2/3 of what is left. How much of the box is still left?

Possible Answers:

4/9

2/9

none

2/3

5/9

Correct answer:

2/9

Explanation:

If Mikey eats 1/3 of the box, he is left with 1 – 1/3 = 2/3.

When he eats 2/3 of what remains, he is eating 2/3 of 2/3, or 4/9 of the box.

2/3 – 4/9 = 2/9

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Example Question #3 : Whole And Part

What is the remainder when 27 is divided by 6?

Possible Answers:

0.5

4.5

Correct answer:

Explanation:

Long division is the fastest way: 6 goes into 27 four times. 6 times four is 24. 27 – 24 = 3.

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

Graph

The above graph represents the results of a general election for mayor of Kingston.

If 6,239 people voted in the election, which is closest to the number of people who voted for Johns?

Possible Answers:

1,500

500

1,000

2,000

2,500

Correct answer:

1,000

Explanation:

The dark purple wedge, which represents Johns, is about one-sixth of the circle, so roughly one-sixth of the voters chose him. This is about

$\frac{1}{6} \times 6,239 \approx 1, 040$

so 1,000 is the best choice among the ones given.

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

Kim weighs two-thirds as much as Jim. Jim weighs 50 pounds more than Tim. Together, Kim, Jim and Tim weight 430 pounds. How much do Jim and Kim weigh together?

Possible Answers:

$300\ \text{lbs}$

$180\ \text{lbs}$

$250\ \text{lbs}$

$330\ \text{lbs}$

$310\ \text{lbs}$

Correct answer:

$300\ \text{lbs}$

Explanation:

Create an equation to represent the combined weights, in pounds, of Kim, Jim and Tim.

Kim+Jim+Tim = 430

Now, taking the other information we are given, put the weights of Kim and Tim in terms of Jim:

Kim weighs two-thirds of Jim:

$Kim=\frac{2}{3}Jim$

Jim weighs 50 pounds more than Tim is the same as saying that Tim weighs 50 pounds less than Jim:

Tim = Jim-50

Replace the variables of Kim and Jim in the equation with their substitutions:

Kim+Jim+Tim = 430

$\frac{2}{3}Jim+Jim+(Jim-50) = 430$

Solve for Jim's weight. To combine the fractions, put all variables in terms of thirds and combine like variables:

$\frac{2}{3}Jim+Jim+Jim-50=430$

$\frac{2}{3}Jim+\frac{3}{3}Jim+\frac{3}{3}Jim-50=430$

$\frac{8}{3}Jim - 50=430$

$\frac{8}{3}Jim=480$

$Jim = 480*(\frac{3}{8})$

Jim =180

Jim weighs 180 pounds. Kim weighs two-thirds of 180:

$Kim=\frac{2}{3}*Jim=\frac{2}{3}*180= 120$

Kim = 120

The combined weight of Jim and Kim is equal to:

180+120=300

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

There are 60 ties on a rack in the department store. One-third are blue, two-fifths are green, and the remainder are red. How many red ties are on the rack in the department store?

Possible Answers:

Correct answer:

Explanation:

Begin by finding how many blue and green ties there are in the department store. If one-third of 60 ties are blue, then there are 20 blue ties:

$\small 60*\frac{1}{3}=20$

Addtionally, if two-fifths of the ties are green, then there are 24 green ties:

$\small \small 60*\frac{2}{5}=24$

To find the number of red ties, subtract the green and blue ties from the total number:

$\small =\small 60-20-24$

$\small =16$

There are 16 red ties in the department store.

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Example Question #1 : Whole And Part

A pitcher is currently $\dpi{80} \frac{4}{5}$ of the way full of water. If $\dpi{80} 3$ ounces are poured out, then the pitcher would be $\frac{3}{4}$ of the way full. How many ounces of water are in the pitcher before the $\dpi{80} 3$ ounces are poured out?

Possible Answers:

60oz

64oz

48oz

52oz

56oz

Correct answer:

48oz

Explanation:

Let p represent the total capacity of the pitcher. The current volume in the pitcher is $\dpi{80} \frac{4}{5}p$ . If this volume is depleted by $\dpi{80} 3$ ounces, it becomes $\dpi{80} \frac{3}{4}p$ . In other words:

$\dpi{80} \frac{4}{5}p - 3 = \frac{3}{4}p$

Solve this equation for $\dpi{80} p$ and get:

$\dpi{80} \frac{4}{5}p-\frac{3}{4}p=3$

$\dpi{80} \frac{16}{20}p-\frac{15}{20}p=3$

$\dpi{80} \frac{1}{20}p=3$

$\dpi{80} p=60$

Remember, $\dpi{80} p$ represents the total capacity of the pitcher, or 60 ounces. The question asks how many ounces are in the pitcher at the beginning of the problem, so evaluate $\dpi{80} \frac{4}{5}p=\frac{4}{5}\times 60=48$ .

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Example Question #1651 : Psat Mathematics

Define an operation $\bigstar$ as follows:

For all real a, b ,

$a \bigstar b = 2a - 3b$ .

Evaluate $\frac{4}{5} \bigstar \frac{3}{10}$ .

Possible Answers:

$-\frac{1}{10}$

$-\frac{21}{50}$

$-1\frac{4}{5}$

$1\frac{11}{25}$

$\frac{7}{10}$

Correct answer:

$\frac{7}{10}$

Explanation:

$a \bigstar b = 2a - 3b$

$\frac{4}{5} \bigstar \frac{3}{10} = 2 \cdot \frac{4}{5} - 3 \cdot \frac{3}{10}$

$= \frac{2}{1} \cdot \frac{4}{5} - \frac{3}{1} \cdot \frac{3}{10}$

$= \frac{8}{5} - \frac{9}{10}$

$= \frac{16}{10} - \frac{9}{10}$

$= \frac{7}{10}$

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Example Question #2 : How To Subtract Fractions

Define an operation $\triangleright$ as follows:

For all real a, b ,

$a \triangleright b = 7 - ab$ .

Evaluate $5 \triangleright \left ( - \frac{5}{3}\right )$ .

Possible Answers:

$15 \frac{1}{3}$

$10\frac{2}{3}$

$-1 \frac{1}{3}$

Correct answer:

$15 \frac{1}{3}$

Explanation:

$a \triangleright b = 7 - ab$

$5 \triangleright \left ( - \frac{5}{3}\right ) = 7 - 5 \left ( - \frac{5}{3}\right )$

$= 7 - \frac{5}{1} \left ( - \frac{5}{3}\right )$

$= 7 - \left ( - \frac{25}{3}\right )$

$= \frac{21}{3} + \frac{25}{3}$

$= \frac{46}{3}$

$=15 \frac{1}{3}$

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Example Question #1 : Operations With Fractions

Define an operation $\Cup$ as follows:

For all real a, b ,

$a \Cup b = a - b^{2}$

Evaluate $5\frac{1}{2} \Cup 1 \frac{1}{3}$ .

Possible Answers:

$4\frac{5}{18}$

$17\frac{13}{36}$

$\frac{1}{6}$

$3 \frac{13}{18}$

$\frac{5}{7}$

Correct answer:

$3 \frac{13}{18}$

Explanation:

$a \Cup b = a - b^{2}$

$5\frac{1}{2} \Cup 1 \frac{1}{3} = 5\frac{1}{2} -\left ( 1 \frac{1}{3} \right )^{2}$

$= \frac{11}{2} -\left ( \frac{4}{3} \right )^{2}$

$= \frac{11}{2} -\left ( \frac{4^{2}}{3^{2}} \right )$

$= \frac{11}{2} - \frac{16}{9}$

$= \frac{99}{18} - \frac{32}{18}$

$= \frac{67}{18}$

$=3 \frac{13}{18}$

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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

Example Question #2 : Whole And Part

Example Question #3 : Whole And Part

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

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

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

Example Question #1 : Whole And Part

Example Question #1651 : Psat Mathematics

Example Question #2 : How To Subtract Fractions

Example Question #1 : Operations With Fractions

All PSAT Math Resources

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