A and B are integers. The expression (A+1)(B+1) is even. What can be said about A and B?
Answer(s): C
Because the given expression is even, at least one of the phrases in one of the parenthesis must be even therefore either A or B must be odd.
In orange county one fifth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
Answer(s): D
The answer must be a number that is divisible by both seven and four. The only possible number is 140.
Danny can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows Danny has in his herd?
Answer(s): A
The number of cows is divisible by 5 and 6 but not by 9. Meaning it must end with a 5 or a 0 and be divisible by 3 (the sum of its digits is divisible by 3). That leaves answers C and A only. However, 180 is also divisible by 9 and is ruled out.
The number of bunnies in Peter’s yard increases by 4 times every week. How many weeks will it take for the number of bunnies to be divisible by 8 assuming that he started out with 3 bunnies?
Answer(s): B
In the beginning he has 3, one week later he has12 and two weeks later he has 48 and that can be equally divided by 8.
If X = 23 x 52 x 7, then the expression X/8 is not divisible by:
From the given expression we learn that X/8 = 25 x 7, which is not divisible by 2.
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