Even / Odd Numbers - PSAT Math
Card 1 of 231
You are given that 
, 
, and 
are positive integers, and
In which of the following cases is 
odd?
I) Exactly one of 
is odd.
II) Exactly two of 
are odd.
III) Exactly three of 
are odd.
You are given that
In which of the following cases is
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of 
must have the same odd/even status. The sum of those two numbers must be even, and since it is a factor of 
, then 
itself must be even.
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
In which of the following cases is odd?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
In which of the following cases is
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of must have the same odd/even status. The sum of those two numbers must be even, and since it is a factor of , then itself must be even.
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
In which of the following cases is odd?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
In which of the following cases is
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of must have the same odd/even status. The sum of those two numbers must be even, and since it is a factor of , then itself must be even.
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of
← Didn't Know|Knew It →
You are given that 
, 
, and 
are positive integers, and
is odd.
Which of the following is possible?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
Which of the following is possible?
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
must be even, so for 
to be odd, 
must be odd. Similarly, for 
and 
to be odd, respectively, 
and 
must be odd.
Therefore, all three of 
, 
, and 
must be odd, and the correct response is III only.
For the product of three integers to be odd, all three integers must themselves be odd.
Therefore, all three of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
In which of the following cases is odd?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
In which of the following cases is
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of must have the same odd/even status. The sum of those two numbers must be even, and since it is a factor of , then itself must be even.
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
In which of the following cases is odd?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
In which of the following cases is
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of must have the same odd/even status. The sum of those two numbers must be even, and since it is a factor of , then itself must be even.
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
is odd.
Which of the following is possible?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
Which of the following is possible?
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
must be even, so for to be odd, must be odd. Similarly, for and to be odd, respectively, and must be odd.
Therefore, all three of , , and must be odd, and the correct response is III only.
For the product of three integers to be odd, all three integers must themselves be odd.
Therefore, all three of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
In which of the following cases is odd?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
In which of the following cases is
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of must have the same odd/even status. The sum of those two numbers must be even, and since it is a factor of , then itself must be even.
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
is odd.
Which of the following is possible?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
Which of the following is possible?
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
must be even, so for to be odd, must be odd. Similarly, for and to be odd, respectively, and must be odd.
Therefore, all three of , , and must be odd, and the correct response is III only.
For the product of three integers to be odd, all three integers must themselves be odd.
Therefore, all three of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
is odd.
Which of the following is possible?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
Which of the following is possible?
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
must be even, so for to be odd, must be odd. Similarly, for and to be odd, respectively, and must be odd.
Therefore, all three of , , and must be odd, and the correct response is III only.
For the product of three integers to be odd, all three integers must themselves be odd.
Therefore, all three of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
In which of the following cases is odd?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
In which of the following cases is
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of must have the same odd/even status. The sum of those two numbers must be even, and since it is a factor of , then itself must be even.
For the product of three integers to be odd, all three integers must themselves be odd.
At least two of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
is odd.
Which of the following is possible?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
Which of the following is possible?
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
must be even, so for to be odd, must be odd. Similarly, for and to be odd, respectively, and must be odd.
Therefore, all three of , , and must be odd, and the correct response is III only.
For the product of three integers to be odd, all three integers must themselves be odd.
Therefore, all three of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
is odd.
Which of the following is possible?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
Which of the following is possible?
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
must be even, so for to be odd, must be odd. Similarly, for and to be odd, respectively, and must be odd.
Therefore, all three of , , and must be odd, and the correct response is III only.
For the product of three integers to be odd, all three integers must themselves be odd.
Therefore, all three of
← Didn't Know|Knew It →
You are given that , , and are positive integers, and
is odd.
Which of the following is possible?
I) Exactly one of is odd.
II) Exactly two of are odd.
III) Exactly three of are odd.
You are given that
Which of the following is possible?
I) Exactly one of
II) Exactly two of
III) Exactly three of
Tap to reveal answer
For the product of three integers to be odd, all three integers must themselves be odd.
must be even, so for to be odd, must be odd. Similarly, for and to be odd, respectively, and must be odd.
Therefore, all three of , , and must be odd, and the correct response is III only.
For the product of three integers to be odd, all three integers must themselves be odd.
Therefore, all three of
← Didn't Know|Knew It →
, 
, 
, 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.
← Didn't Know|Knew It →
, , , 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.
← Didn't Know|Knew It →
, , , 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.
← Didn't Know|Knew It →
, , , 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.
← Didn't Know|Knew It →
, , , 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.
← Didn't Know|Knew It →
, , , 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.
← Didn't Know|Knew It →