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## Consecutive integers - complicated

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 0 member replies
AndreiGMAT Junior | Next Rank: 30 Posts
Joined
05 Apr 2016
Posted:
18 messages

#### Consecutive integers - complicated

Sun May 01, 2016 5:38 pm
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

I have no clue what this question is stating or asking and how to interpret the information.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Mon May 02, 2016 6:39 am
Quote:
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 answer.

Cheers,
Brent

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Sun May 01, 2016 11:03 pm
Hi AndreiGMAT,

Mitch's approach (TESTing VALUES) is a great way to answer this question; it's exactly how I would have approached this prompt.

This prompt is built around an interesting Number Property, which you could have used to answer the question without doing much math at all.

We're told that Q is an ODD number, we're dealing with CONSECUTIVE INTEGERS and we're asked for the LARGEST INTEGER..

Take a look at answer B. Since Q is ODD, will answer B EVER be an integer???
The answer is NO (we'd end up with a fraction, so B can't be the answer.

This same rule holds true for answer C and E. So, we've eliminated B, C and E.

Now look at D; we're taking (Q+119) and cutting it IN HALF. That math doesn't seem like it would produce the LARGEST INTEGER that we're looking for. Eliminate D.

The answer must be A. It would certainly give us an integer: (ODD - 1)/2 = INTEGER. Add THAT integer to 120 and you either get 120 or a bigger integer.

GMAT assassins aren't born, they're made,
Rich

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sun May 01, 2016 7:02 pm
Quote:
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?
1) (Q-1)/2 + 120
2) Q/2 + 119
3) Q/2 + 120
4) Q+119/2
5) Q+120/2
Let Q=3, implying that there are 3 consecutive integers.
Since the median is 120, the 3 integers are {119, 120, 121}.
The question stem asks for the largest integer: 121.
This is our target.
Now plug Q=3 into the answers to see which yields our target of 121.
Only A works:
(Q-1)/2 + 120 = (3-1)/2 + 120 = 121.

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