I'm practicing some GRE math problems which I don't have answers for. Would you please correct my answers if they're wrong?
Q1.
You have 4 books, A and B and C and D. In how many ways you can arrange them on a shelf and keep book A and book C next to each other?
A.
2*1*2*1 = 4
Q2.
Anne closet contain 11 pants, 4 of them are blue. 7 hats, 3 of them are blue. 8 shirts, 2 of them are blue. What's the probability that Anne would grab a blue pants, a blue hat and a blue shirt?
A.
1/4 * 1/3 * 1/2 = 1/24
Q3.
A set of 7 different integers, it's range is 12, and it's median is 86. What's the lease possible of the first integer in the set?
A.
integers after median in the set would be: {,,,86,87,88,89} and 89-12=77 So answer is 77.
(1) Consider 'AC' as a single object. There are 3! ways in which to arrange three objects 'AC', B and D. Then multiply by 2 because A and C are still next to each other if it's 'CA'. Answer: 12 ways.
(2) Answered in Comment by @JMoravitz
(3) "77, two intermediate digits, 86, two intermediate digits, 89" has 7 digits, median 86, range 89 - 77 = 12, and s0 satisfies the requirements.
But if the integers didn't need to be DIFFERENT, we could have "75, 77, 79, 86, 87, 87, 87" for a smaller minimum number.