OG problems

Question 1

If m is the average of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M-m?

Answer 1

0

In an evenly spread set, the mean and median will always be the same. As such, m=M, answer is 0.

Question 2

If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers. 
(A) (Q-1)/2 + 120
(B) Q/2 +119
(C) Q/2 +120
(D) (Q+119)/2
(E) (Q+120)/2

Answer 2

Use smart number Q=3

(A) (Q-1)/2 + 120  => 121, with median is 120, 121 is the largest number - yes!
(B) Q/2 +119 => not an integer
(C) Q/2 +120 => not an integer
(D) (Q+119)/2 => too small
(E) (Q+120)/2 => not an integer

Question 3

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. the actual number of miles per gallon that Cindy’s car got on this trip must have between?

Answer 3

L - 285/12.5 (lowest mile/highest gallons)

H - 295/11.5 (highest mile/lowest gallons)