Number Properties

If d is a positive integer, is d √ 𝑑 an integer? (1) d is the square of an integer. (2) d √ 𝑑 is the square of an integer.

If Q is an integer between 10 and 100, what is the value of Q? (1) One of Q's digits is 3 more than the other, and the sum of its digits is 9. (2) Q < 50

If n is a positive integer, is n odd? (1) 3n is odd. (2) n + 3 is even.

Is the average (arithmetic mean) of x and y greater than 20? (1) The average (arithmetic mean) of 2x and 2y is 48. (2) x = 3y

The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 –n points if one of its runners finished in nth place, where 1 <= n <= 5. If all of the runners finished the race and if there were no ties, was each team awarded at least one point? (1) No team was awarded more than a total of 6 points. (2) No pair of teammates finished in consecutive places among the top five places. Show Spoiler

How many integers n are there such that r < n < s ? (1) s - r = 5 (2) r and s are not integers.

If r and s are integers, is r divisible by 7? (1) The product rs is divisible by 7. (2) s is not divisible by 7.

Can the positive integer n be written as the sum of two different positive prime numbers? (1) n is greater than 3. (2) n is odd. DS38602.01

If x and y are positive, what is the value of x? (1) 200% of x equals to 400% of y. (2) xy is the square of a positive integer.

If n is an integer, is n + 2 a prime number? (1) n is a prime number. (2) n + 1 is not a prime number.

Is the positive square root of x an integer? (1) x = n^4 and n is an integer (2) x = 16 Show Spoiler

Is the positive integer n a multiple of 24? (1) n is a multiple of 4. (2) n is a multiple of 6.

If n and k are greater than zero, is n/k an integer ? (1) n and k are both integers. (2) n^ 2 and k^2 are both integers

If x, y and z are positive integers, is x - y odd? (1) x = z^2 (2) y = (z - 1)^2

Is x an integer? (1) x/2 is an integer (2) 2x is an integer Show Spoiler

Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? (1) 31 < p < 37 (2) p is odd.

Is the integer P odd? (1) The sum of P, P + 4, and P+ 11 is even. (2) The sum of P – 3, P, and P+ 11 is odd.

If n is an integer, is n even? (1) n^2 - 1 is an odd integer. (2) 3n + 4 is an even integer.

If i and j are integers, is i + j an even integer? (1) i < 10 (2) i = j

If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?