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Consecutive integers - complicated

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

Post 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.

Please, help

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Post 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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Post 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.

Final Answer: A

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

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Contact Rich at Rich.C@empowergmat.com

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Thanked by: AndreiGMAT
Post 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

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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Thanked by: gary391
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