1. 35 goes into 34 zero times with a remainder of 34. The remainder is 34.
2. A pentagon has 5 sides, a rectangle has 4 sides, and a triangle has 3 sides, so the answer is 4x5 + 1x4 + 6x3 = 20 + 4 + 18 = 42.
3. A = 4x4 = 16, so 5A = 5x16 = 80.
4. The 5 cancels out all the denominators, so the answer is W = 1 + 1 + 1 + 1 =4.
5. Since the Knights won 3 games, they must have not won 7 games. Hence 7 represents half of the final number of games, or 14. A = 14 - 10 = 4.
6. 32/16 = 2; 36/18 = 2; 40/20 = 2; 44/22 = 2 so the answer is 2x2x2x2 = 16.
7. The desired pair is 12 and 5, so a = 12 and the answer is 12 x 15 = 180.
8. The maximum is achieved when the alien puts the hand with 4 fingers behind his back and makes 3 of the fingers on the hand with 5 fingers invisible, leaving 2 visible.
9. Cross multiplication and division through by 'x' yields x = 10.
10. 20% of 500 is 100; 30% of 100 is 30; 500% of 30 is 150.
11. Note that 179 is prime, 180 = (10)(9)(2), 181 is prime, 182 = (2)(7)(13), and 183 = (3)(61). So 180 and a82 are supercomposite and the answer is 2.
12. The right hand side of the given equation will always be even. Hence the left hand side must be even as well, implying 'p' must be even. This means 'p' = 2 because 2 is the only even prime. So 42 = 6k, from which it follows that k = 7.
13. Reduce the two fractions on the left hand side so it becomes (1/4)(1/4), whisch evaluates tp 1/16. Hence x = 1.
14. We must find the arithmatic mean of the two numbers: (1/6 + 1/8)/2 = 7/48.
15. Divide by 2 ( or appropriate powers of 2) until obtaining an odd number. This gives us 3333.
16. "MATH IS FUN" has 9 letters, of which 3 are vowels. 3/9 to the nearest percent is 33%.
17. Multiplying both sides of the given equation by 'b' gives a = 3b. Multiplying through by 5 yields 5a = 15b so 5a - 15b = 0.
18. Each of the numbers in the multiplication contributes 1 zero except for 50 which, when combined with a 2 from another number, contributes 2 terminal zeros. Hence the answer is 7.
19. The Academy pays $35 + ($20)(2) = $75. There are (3)(5) = 15 players. So each player pays $75/15 = $5.
20. Note that 3! = 6. Dividing both sides through by 6 gives N! = 5! so N = 5.
21. The number either ends in 5 or 0. If it ends in 5, there are 8 choices for the first digit (it can't be 0), 8 choices for the second digit, 7 for the third, and 6 for the fourth, for a total of 8x8x7x6 = 2688. If it ends in 0, there are 9 choices for the first , 8 for the second, 7 for the third, and 6 for the fourth, for a total of 9x8x7x6 = 3024. The total count of numbers is therefore 2688 + 3024 = 5712.
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