PSAT Math : Arithmetic
Study concepts, example questions & explanations for PSAT Math
All PSAT Math Resources
Example Questions
Example Question #121 : Fractions
If xy = 1 and 0 < x < 1, then which of the following must be true?
y = 1
y < x
y = x
y < 1
y > 1
y > 1
If x is between 0 and 1, it must be a proper fraction (e.g., ½ or ¼). Solving the first equation for y, y = 1/x. When you divide 1 by a proper fraction between 0 and 1, the result is the reciprocal of that fraction, which will always be greater than 1.
To test this out, pick any fraction. Say x = ½. This makes y = 2.
Example Question #2 : Operations With Fractions
Before going to school, Joey ran 1/3 of his daily total miles. In gym class, Joey did 2/3 of the remainder. What part of his daily total miles was left for after school?
2/3
1/3
7/9
2/9
4/9
2/9
Before school, Joey did 1/3 of the total miles. In school, Joey did 2/3 of the remaining 2/3, or 4/9 of the running. When added to his in school run, his before school run of 3/9 brings his completed miles to 7/9 of his dialy total. Thus, only 2/9 of the total miles are left for after school.
Example Question #2 : How To Multiply Fractions
Sally bought five computers for her office that cost $300, $405, $485, $520, and $555 respectively. She made a down payment of 2/5 the total cost and paid the rest in nine equal payments over the next nine months. Assuming no tax and no interest, what is the value of each of the nine payments?
151
906
1359
251
351
151
The total cost of the 5 computers is 2265.
2/5 of 2265 = 906, which is what Sally pays up front.
2265 – 906 = 1359, which is what Sally still owes.
1359/9 = 151, which is the value of each of the 9 equal payments.
Example Question #121 : Arithmetic
The price of a computer is reduced by 1/8. The new price is then reduced by 1/6. What fraction of the original price is the current price?
1/48
23/24
35/48
13/48
1/24
35/48
Let the original price = p.
After the first reduction, the price is (7/8)p
After the second reduction, the price is (5/6)(7/8)p = (35/48)p
Example Question #5 : Operations With Fractions
If a car travels at 30 mph, how many feet per second does travel?
264 ft/s
44 ft/s
2,640 ft/s
4,400 ft/s
440 ft/s
44 ft/s
30 miles / 1 hour * 5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec
Example Question #122 : Fractions
In a group of 20 children, 25% are girls. How many boys are there?
10
16
4
15
5
15
Since 
Example Question #121 : Fractions
Remember, when you multiply fractions, you can directly multiply their denominators and their numerators; therefore, you can begin this problem by making it into one large fraction:
Now, you could multiply all of this out and then divide. However, you can cancel things immediately. The 
Example Question #122 : Fractions
Simplify:
First, begin by remembering that 
Next, recall that you multiply fractions by multiplying the numerators and denominators by each other. It is very simple. This would give you:
Now, you can cancel the 
Next, you can reduce the 
You can also reduce the resulting 
Example Question #152 : Fractions
Jesse has a large movie collection containing X movies. 1/3 of his movies are action movies, 3/5 of the remainder are comedies, and the rest are historical movies. How many historical movies does Jesse own?
(3/9)*X
(11/15)*X
(2/5)*X
(4/15)*X
(7/12)*X
(4/15)*X
1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.
Example Question #1 : How To Add Fractions
If x = 1/3 and y = 1/2, find the value of 2x + 3y.
13/6
1
2
6/5
5/6
13/6
Substitute the values of x and y into the given expression:
2(1/3) + 3(1/2)
= 2/3 + 3/2
= 4/6 + 9/6
= 13/6
All PSAT Math Resources
