Integers - PSAT Math
Card 1 of 1267
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
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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
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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 →
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
← Didn't Know|Knew It →
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
← Didn't Know|Knew It →
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
← Didn't Know|Knew It →
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
← Didn't Know|Knew It →
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
← Didn't Know|Knew It →
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?
Tap to reveal answer
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
The prime digits are 2, 3, 5, and 7.
The perfect square digits are 0, 1, 4, and 9.
The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.
← 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
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