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

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:11 am

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: A
Source: Official guide

A very fast solution is to see what happens when Q = 1.
This means that there's only ONE integer in the set.
So, if the median of the set is 120, then the set is {120}, which means the greatest value in the set is 120

So the correct answer choice should yield 120 when Q = 1.

a) (1-1)/2 + 120 = 120 PERFECT!
b) 1/2 + 119 = some non-integer
c) 1/2 + 120 = some non-integer
d) (1+119)/2 = 60
e) (1+120)/2 = some non-integer

Since only answer choice A yield the correct output, it is the correct answer.

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:11 am

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: A
Source: Official guide

Solution:

We are given that Q is an ODD NUMBER and that the median of Q CONSECUTIVE INTEGERS is 120. Let's choose a convenient number for Q, such as 3. We can now say:

The median of 3 consecutive integers is 120. Since 120 is the MEDIAN, or middle number of these integers, our 3 integers are the following:

119, 120, 121

Let’s now test each answer choice to see which gives us 121:

A) (Q-1)/2 + 120

(3-1)/2 + 120 = 1 + 120 = 121

This IS equal to 121.

We have found our answer.

Alternate solution:

Since Q is an odd number, we see that none of the choices B, C and E will yield an integer; so we can reject those answer choices. This leaves us with either choice A or D as the correct answer. By picking a small number for Q, e.g., Q = 3, we see that choice A will yield (3-1)/2 + 120 = 1 + 120 = 121 and choice D will yield (3+119)/2 = 122/2 = 61. Of course, the largest integer in the set has to be greater than the median of 120, so only choice A can be the right answer.

Answer: A