Arithmetic

If x and y are positive integers, is xy divisible by 6? (1) x is divisible by 3. (2) y is even.

Is the integer n odd? (1) n² is odd. (2) 2n is even.

What is the value of the positive integer n? (1) n² − 7n + 12 = 0. (2) n > 3.

If a and b are integers, is ab even? (1) a + b is odd. (2) a − b is odd.

Is the positive integer p prime? (1) p has exactly two positive divisors. (2) p > 2 and p is odd.

Each person on a committee with 40 members voted for exactly one of 3 candidates, F, G, or H. Did Candidate F receive the most votes from the 40 votes cast? (1) Candidate F received 11 of the votes. (2) Candidate H received 14 of the votes.

If @ represents one of the operations +, -, and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m? (1) k@1 is not equal to 1@k for some numbers k. (2) @ represents subtraction.

A certain expressway has Exits J, K, L, and M, in that order. What is the road distance from Exit K to Exit L ? (1) The road distance from Exit J to Exit L is 21 kilometers. (2) The road distance from Exit K to Exit M is 26 kilometers.

In Year X, 8.7 percent of the men in the labor force were unemployed in June compared with 8.4 percent in May. If the number of men in the labor force was the same for both months, how many men were unemployed in June of that year? (1) In May of Year X, the number of unemployed men in the labor force was 3.36 million. (2) In Year X, 120,000 more men in the labor force were unemployed in June than in May.­ ID: 700114

A retailer purchased a television set for x percent less than its list price, and then sold it for y percent less than its list price. What was the list price of the television set? (1) x = 15 (2) x - y = 5

□ +△ ___ ★ In the addition problem above, each of the symbols □, △, and ★ represents a positive digit. If □ < △,what is the value of △ ? (1) ★ = 4 (2) □ = 1

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

125% of 5 =

N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?

0.99999999 1.0001 − 0.99999991 1.0003 =

(1 2 − 1 3) + (1 3 − 1 4) + (1 4 − 1 5) + (1 5 − 1 6) =

For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation (a , b , c) Θ (d , e , f) = a d + b e + c f . What is the value of (1 , − 2 , 3) Θ (1 , − 1 2 , 1 3) (1 , − 2 , 3) Θ (1 , − 1 2 , 1 3) ?

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

If S = 1 + 1 2 + 1 3 2 + 1 4 2 + 1 5 2 + 1 6 2 + 1 7 2 + 1 8 2 + 1 9 2 + 1 10 2 , which of the following is true?

What is the value of √ 17 + √ 47 17 − √ + 47 − √ , to the nearest whole number?