X is an integer, which of the following must be even?
Answer(s): C
You don’t know whether or not X is even. In answer C you have a multiplication of two consecutive numbers so one of them must be even and an even number multiplied by an odd number is always even.
P is divisible by 4.Q is divisible by 3. Which of the following is definitely odd?
Answer(s): E
P must be even but Q is either even or odd (3,6,…). None of the following answers are definitely odd although some can be.
A and B are integers. If 2A-B = B-A, than which of the following is true?
Answer(s): D
2A-B = B-A 3A = 2B. Therefore 3A must be an even number and since 3 is odd, A must be even and B can be either even or odd.In this question we are looking for an expression: odd/even, which can’t be an integer. In answer A: The numerator is odd and the denominator is even therefore it can’t be an integer.
The bus that travels from St. Louis to Chicago and back comes to St. Louis every 4 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o’clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
In order for both buses to meet again, we ought to look for the smallest common factor of 4 and 6, thus 12 hours. After 12 hours one of the buses will complete 3 roundtrips while the other will complete only 2, they will meet at (12:00 + 12 = 24:00).
Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn’t come but every one of the guests that did come ate six muffins and 3 muffins remained. How many guests did Monica plan on?
X is the number of guests that were supposed to show up at the party, and so Monica prepared 5X + 2 muffins. (X – 1) is the number of guests that did come to the party and the total number of muffins is 6(X – 1) + 3. The number of muffins that Monica prepared is equal to the total number of muffins and so we can compare the following expressions: 5X + 2 = 6(X – 1) +3 >X = 5.
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