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GMAT - Problem Solving - Statistics

If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers? (more)

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

Let the first term be x

The largest term will be x + Q - 1

Median = (Q+1)/2 th term

Since the numbers are consecutive Median = x - 1 + (Q + 1)/2

120 = x - 1 + (Q+1)/2

x = 121 - (Q+1)/2

Largest term = x + Q - 1 = 121 - (Q+1)/2 - 1 = 120 + Q - Q/2 - 1/2 = 120 + (Q-1)/2

A is correct

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ? (more)

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m d ?

Ref. to the figure:

the question says the shaded portion between m-d and m+d = 68%

that means unshaded portion = 100 - 68 = 32%

since the curve is symmetric

% of population greater than m+d = 32/2 = 16%

the percentage of population below m+d = 100 - 16 = 84%