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If Q is an odd number and the median of Q consecutive

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Intern
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Joined: 25 Feb 2017
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Re: If Q is an odd number and the median of Q consecutive  [#permalink]

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New post 01 May 2017, 17:49
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

My 2 cents.
Plug in.

Assume that Q = 3
119,120,121, the largest is 121

Plug in.
a) (3-1)/2 + 120 = 121 check.
all others, just by briefly looking at them, you know that they are out.

A.
Intern
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If Q is an odd number and the median of Q consecutive  [#permalink]

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New post 15 Oct 2017, 08:50
You need to study the arithmetic sequence formulas , which should get it straight forward

Xn=a+(n-1)d , n=numbers in sequence , a=first number and d=differnce
Xq=a+(q-1)-->1
(Xq+a)/2 =120 -->2 Median=Arithmetic mean equation

from 2&1 , x=2(120)-X+Q-1 , 2X=2(120)+Q-1

X=120 + (Q-1)/2

most of the replies tell to test numbers , but in the real exam testing number could be very hard and confusing , remember the formulas
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Re: If Q is an odd number and the median of Q consecutive  [#permalink]

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New post 20 Apr 2018, 14:08
Top Contributor
Walkabout wrote:
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


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
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Re: If Q is an odd number and the median of Q consecutive  [#permalink]

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New post 06 Jun 2018, 05:28
(120-n)<---------->(120+n) this is the Greatest number equation for series
...............120.............,
Consider,
integers to the left of 120= n
intergers to the right of 120= n
Therefore, Q= n+1+n, (*note that 120 is also another integer in the series of Q Odd numbers)
Q= 2n+1
Q-1= 2n
(Q-1)/2= n,

Therefore the greatest number = (Q-1)/2+ 120 Which is same as 120+n..
GMAT Club Bot
Re: If Q is an odd number and the median of Q consecutive &nbs [#permalink] 06 Jun 2018, 05:28

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