PSAT Math : Basic Operations
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Example Questions
Example Question #1 : Basic Operations
Kacey works 5 hours per day on Monday, Tuesday, and Wednesday, as well as 9 hours on Thursday and Friday. She does not work on Saturday or Sunday. Her total earnings per week is $363. How much does she earn per hour in dollars?
8
9
12
11
11
Kacey works 5 hours a day for 3 days and 9 hours a day for 2 days. (5)(3) = 15 and (2)(9) = 18. 15 + 18 = 33 hours worked a week. $363/33 hours = $11/hr.
Example Question #1 : How To Divide Integers
When k is divided by 2, the remainder is 1. If k is divided by 3, the remainder is 0. And if k is divded by 5, the remainder is 3. Which of the following is a possible value for k?
Since the remainder when k is divided by 2 is 1, this means that k is not an even number. Therefore, we can immediately eliminate 30 from our possible answer choices.
Because the remainder when k is divded by 3 is 0, we know that k must be a multiple of 3. This means we can eliminate 23 from our answer choices.
The only choices left are 63, 27, and 57. When 27 and 57 are divded by five, the remainder is two. Thus, only 63 works, because when 63 is divded by five, the remainder is three.
The answer is 63.
Example Question #1 : How To Divide Integers
The result of a number divided by 2 is the same as the result of that number divided by 10. What is that number?
1
0
2
10
0
0 is the only choice that yields the same answer (0) when divided by 2 and 10. You can check this easily by plugging a few of the answer choices into a fraction:
1/2 ≠ 1/10
2/2 ≠ 2/10 etc.
Example Question #2 : How To Divide Integers
If x and y are positive integers and 2y = 16x, what is the value of y/x?
4
1/2
1/4
2
4
Making the equation even yields y = 4 and x = 1, since 24 = 16. This makes y/x = 4.
Example Question #2 : How To Divide Integers
If 
1
9
8
5
2
8
For this problem, you need to use process of elimination.
When
The remainder of 
Example Question #1 : Basic Operations
The annual number of cellular phones purchased from a company is illustrated in the following graph. How many more phones were sold in 2009 than 2011?
6
17,000
17
6,000
3,000
6,000
In 2009, 32,000 phones were sold (according the the label on the y-axis, each number is equal to 1,000 phones). In 2011, 26,000 phones were sold.
Example Question #1 : How To Multiply Integers
If the mass is increased by 3 three times the original and the acceleration is increased by 7 times the original, how many times greater is the new force than the original force?
We simply multiply the new mass by the new acceleration to obtain a new force that is 21 times greater than the original.
Example Question #1 : How To Multiply Integers
An office wants to buy 22 computers at $900 each. The budget is $20,000 and the tax on computers is 9%. How many computers can the office afford?
The office can only afford 20 computers.
1.09 * 900 = $981 is the actual price of each computer, with tax.
Divide:
20,000/981 = 20.39
Since the office cannot purchase a partial computer, we round down to 20 computers.
Example Question #1 : Basic Operations
What property of arithmetic is demonstrated below?
Commutative
Symmetric
Associative
Transitive
Distributive
Distributive
The statements demonstrates that the product of a number and a sum can be found by multiplying the number by each of the addends and adding the products. This is the distributive property of multiplication over addition.
Example Question #2 : How To Multiply Integers
What property of arithmetic is demonstrated here?
Associative
Transitive
Commutative
Symmetric
Associative
The symbols express the idea that if three numbers are multiplied, the same product results regardless of which numbers are multiplied first. This is the associative property of multiplication.
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