Arithmetic - PSAT Math
Card 1 of 4032
How many elements of the set 
are less than 
?
How many elements of the set
Tap to reveal answer
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set 
are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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How many elements of the set are less than ?
How many elements of the set
Tap to reveal answer
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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How many elements of the set are less than ?
How many elements of the set
Tap to reveal answer
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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, 
, 
, and 
are positive integers.
is odd.
Which of the following is possible?
I) Exactly two of 
are odd.
II) Exactly three of 
are odd.
III) All four of 
are odd.
Which of the following is possible?
I) Exactly two of
II) Exactly three of
III) All four of
Tap to reveal answer
If exactly two of 
are odd, then exactly one of the seven expressions being added is odd - namely, the only one that does not have an even factor (for example, if 
and 
are odd, then the only odd number is 
). This makes 
the sum of one odd number and six even number and, subsequently, odd.
If exactly three of 
are odd, then exactly three of the seven expressions being added are odd - namely, the three that do not include the even factor (for example, if 
, 
, and 
are odd, then the three odd numbers are 
, 
, and 
). This makes 
the sum of three odd numbers and four even numbers and, subsequently, odd.
If all four of 
are odd, then all of the seven expressions being added, being the product of only odd numbers, are odd. This makes 
the sum of seven odd numbers, and, subsequently, odd.
The correct choice is that all three scenarios are possible.
If exactly two of
If exactly three of
If all four of
The correct choice is that all three scenarios are possible.
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How many elements of the set are less than ?
How many elements of the set
Tap to reveal answer
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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, , , and are positive integers.
is odd.
Which of the following is possible?
I) Exactly two of are odd.
II) Exactly three of are odd.
III) All four of are odd.
Which of the following is possible?
I) Exactly two of
II) Exactly three of
III) All four of
Tap to reveal answer
If exactly two of are odd, then exactly one of the seven expressions being added is odd - namely, the only one that does not have an even factor (for example, if and are odd, then the only odd number is ). This makes the sum of one odd number and six even number and, subsequently, odd.
If exactly three of are odd, then exactly three of the seven expressions being added are odd - namely, the three that do not include the even factor (for example, if , , and are odd, then the three odd numbers are , , and ). This makes the sum of three odd numbers and four even numbers and, subsequently, odd.
If all four of are odd, then all of the seven expressions being added, being the product of only odd numbers, are odd. This makes the sum of seven odd numbers, and, subsequently, odd.
The correct choice is that all three scenarios are possible.
If exactly two of
If exactly three of
If all four of
The correct choice is that all three scenarios are possible.
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How many elements of the set are less than ?
How many elements of the set
Tap to reveal answer
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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, , , and are positive integers.
is odd.
Which of the following is possible?
I) Exactly two of are odd.
II) Exactly three of are odd.
III) All four of are odd.
Which of the following is possible?
I) Exactly two of
II) Exactly three of
III) All four of
Tap to reveal answer
If exactly two of are odd, then exactly one of the seven expressions being added is odd - namely, the only one that does not have an even factor (for example, if and are odd, then the only odd number is ). This makes the sum of one odd number and six even number and, subsequently, odd.
If exactly three of are odd, then exactly three of the seven expressions being added are odd - namely, the three that do not include the even factor (for example, if , , and are odd, then the three odd numbers are , , and ). This makes the sum of three odd numbers and four even numbers and, subsequently, odd.
If all four of are odd, then all of the seven expressions being added, being the product of only odd numbers, are odd. This makes the sum of seven odd numbers, and, subsequently, odd.
The correct choice is that all three scenarios are possible.
If exactly two of
If exactly three of
If all four of
The correct choice is that all three scenarios are possible.
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How many elements of the set are less than ?
How many elements of the set
Tap to reveal answer
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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, , , and are positive integers.
is odd.
Which of the following is possible?
I) Exactly two of are odd.
II) Exactly three of are odd.
III) All four of are odd.
Which of the following is possible?
I) Exactly two of
II) Exactly three of
III) All four of
Tap to reveal answer
If exactly two of are odd, then exactly one of the seven expressions being added is odd - namely, the only one that does not have an even factor (for example, if and are odd, then the only odd number is ). This makes the sum of one odd number and six even number and, subsequently, odd.
If exactly three of are odd, then exactly three of the seven expressions being added are odd - namely, the three that do not include the even factor (for example, if , , and are odd, then the three odd numbers are , , and ). This makes the sum of three odd numbers and four even numbers and, subsequently, odd.
If all four of are odd, then all of the seven expressions being added, being the product of only odd numbers, are odd. This makes the sum of seven odd numbers, and, subsequently, odd.
The correct choice is that all three scenarios are possible.
If exactly two of
If exactly three of
If all four of
The correct choice is that all three scenarios are possible.
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, , , and are positive integers.
is odd.
Which of the following is possible?
I) Exactly two of are odd.
II) Exactly three of are odd.
III) All four of are odd.
Which of the following is possible?
I) Exactly two of
II) Exactly three of
III) All four of
Tap to reveal answer
If exactly two of are odd, then exactly one of the seven expressions being added is odd - namely, the only one that does not have an even factor (for example, if and are odd, then the only odd number is ). This makes the sum of one odd number and six even number and, subsequently, odd.
If exactly three of are odd, then exactly three of the seven expressions being added are odd - namely, the three that do not include the even factor (for example, if , , and are odd, then the three odd numbers are , , and ). This makes the sum of three odd numbers and four even numbers and, subsequently, odd.
If all four of are odd, then all of the seven expressions being added, being the product of only odd numbers, are odd. This makes the sum of seven odd numbers, and, subsequently, odd.
The correct choice is that all three scenarios are possible.
If exactly two of
If exactly three of
If all four of
The correct choice is that all three scenarios are possible.
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How many elements of the set are less than ?
How many elements of the set
Tap to reveal answer
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set are less than this positive number.
The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,
All four (negative) numbers in the set
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, , , and are positive integers.
is odd.
Which of the following is possible?
I) Exactly two of are odd.
II) Exactly three of are odd.
III) All four of are odd.
Which of the following is possible?
I) Exactly two of
II) Exactly three of
III) All four of
Tap to reveal answer
If exactly two of are odd, then exactly one of the seven expressions being added is odd - namely, the only one that does not have an even factor (for example, if and are odd, then the only odd number is ). This makes the sum of one odd number and six even number and, subsequently, odd.
If exactly three of are odd, then exactly three of the seven expressions being added are odd - namely, the three that do not include the even factor (for example, if , , and are odd, then the three odd numbers are , , and ). This makes the sum of three odd numbers and four even numbers and, subsequently, odd.
If all four of are odd, then all of the seven expressions being added, being the product of only odd numbers, are odd. This makes the sum of seven odd numbers, and, subsequently, odd.
The correct choice is that all three scenarios are possible.
If exactly two of
If exactly three of
If all four of
The correct choice is that all three scenarios are possible.
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, , , and are positive integers.
is odd.
Which of the following is possible?
I) Exactly two of are odd.
II) Exactly three of are odd.
III) All four of are odd.
Which of the following is possible?
I) Exactly two of
II) Exactly three of
III) All four of
Tap to reveal answer
If exactly two of are odd, then exactly one of the seven expressions being added is odd - namely, the only one that does not have an even factor (for example, if and are odd, then the only odd number is ). This makes the sum of one odd number and six even number and, subsequently, odd.
If exactly three of are odd, then exactly three of the seven expressions being added are odd - namely, the three that do not include the even factor (for example, if , , and are odd, then the three odd numbers are , , and ). This makes the sum of three odd numbers and four even numbers and, subsequently, odd.
If all four of are odd, then all of the seven expressions being added, being the product of only odd numbers, are odd. This makes the sum of seven odd numbers, and, subsequently, odd.
The correct choice is that all three scenarios are possible.
If exactly two of
If exactly three of
If all four of
The correct choice is that all three scenarios are possible.
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A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
Tap to reveal answer
The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
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The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?
The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?
Tap to reveal answer
Let us assume that the original purse is $100. The price after the first reduction is $80. After the second reduction the price is now $56. The difference between 100 and 56 is 44, giving 44% off.
Let us assume that the original purse is $100. The price after the first reduction is $80. After the second reduction the price is now $56. The difference between 100 and 56 is 44, giving 44% off.
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Julie goes shopping at Gap. There is a storewide sale of 30% off. She buys a sweater on clearance that gets an additional 50% off. If the sweater was originally $50, how much did she pay?
Julie goes shopping at Gap. There is a storewide sale of 30% off. She buys a sweater on clearance that gets an additional 50% off. If the sweater was originally $50, how much did she pay?
Tap to reveal answer
The original price was $50. First you take 30% off (50 * (100 - 30)/100 = $35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)
The original price was $50. First you take 30% off (50 * (100 - 30)/100 = $35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)
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Alan is twice as old as Betty. He will be twice as old as Charlie in 10 years. If Charlie is 2 years old, how old is Betty?
Alan is twice as old as Betty. He will be twice as old as Charlie in 10 years. If Charlie is 2 years old, how old is Betty?
Tap to reveal answer
If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.
If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.
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The ratio of 10 to 14 is closest to what value?
The ratio of 10 to 14 is closest to what value?
Tap to reveal answer
Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
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A baker has four different types of frosting, three different kinds of sprinkles, and 8 different cookie cutters. How many different cookie combinations can the baker create if each cookie has one type of frosting and one type of sprinkle?
A baker has four different types of frosting, three different kinds of sprinkles, and 8 different cookie cutters. How many different cookie combinations can the baker create if each cookie has one type of frosting and one type of sprinkle?
Tap to reveal answer
Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. 4 x 3 x 8 = 96
Multiplying each of the possible choices together.
Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. 4 x 3 x 8 = 96
Multiplying each of the possible choices together.
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