PS - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

PS

Expert replies

jaspreetsra: Master | Next Rank: 500 Posts; Posts: 164; Joined: Sat Sep 20, 2014 10:26 pm; Thanked: 1 times

by jaspreetsra » Sun Jan 04, 2015 2:19 am

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

Didn't get this question. Help plz.

Hard work brings success!

Like this post

Source: Beat The GMAT — Problem Solving | Sun Jan 04, 2015 2:19 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 04, 2015 4:36 am

jaspreetsra wrote: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.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sun Jan 04, 2015 5:33 am

jaspreetsra wrote: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

Didn't get this question. Help plz.

Another way to do it is by seeing the logic of it.

First you can look at the answer choices to see what they are looking for and see that they all involve using Q along with some number related to the median, 120.

Then figure out what makes sense, which is this.

We have Q consecutive integers. Since they are consecutive, they are all evenly spaced 1 apart from each other.

120 is the median and the number of integers, Q, is odd. So 120 is in the exact middle of the set, and the rest of the set is composed of an even number of integers, Q - 1, half of which are higher than 120 and the other half of which are lower than 120.

So in the set, other than 120 there are Q - 1 integers, and half of them are greater than 120. This means there are (Q - 1)/2 integers that are greater than 120.

This is already looking like one of the answer choices, but just to be sure that's the right choice let's finish the math.

How high is the highest one? Well we know that they are evenly spaced 1 apart, so to get to the highest one we can start at 120 and add the number of higher integers to get (Q - 1)2 + 120, and that exactly matches one of the answer choices.

Choose 1.

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 04, 2015 8:49 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

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 - Creator of GMATPrepNow.com

Like this post

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Mon Jan 05, 2015 7:12 am

Holy moly Brent. That's genius.

Like this post

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Jan 05, 2015 7:32 am

jaspreetsra wrote: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

Didn't get this question. Help plz.

Let, Q=3

Median of 3 consecutive Integer{a, a+1, a+2} = a+2
i.e. a+1 = 120
i.e. a = 119
i.e. Largest = a+2 = 121

Substitute Q=3 in options,

Answer: Option A

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Jan 05, 2015 10:26 am

Let's do something other than substitution, for a change of pace. (The other three answers are all substitution, which is fine but also kinda fast food math: instantly gratifying, but not satisfying or particularly good for you.

)

Since Q is an odd number, we can write Q = 2*(some integer) + 1. It doesn't matter what that integer is, so let's call it k, and say that Q = 2k + 1.

Since Q = 2k + 1, we have 2k + 1 integers in our set. There will be k integers greater than the median, k integers less than the median, and 1 integer that's the median itself.

Since the median is 120, we know that the GREATEST integer in the set is k integers greater than 120, or 120 + k. The answers are in terms of Q, so let's fix this. We know 2k + 1 = Q, so k = (Q - 1)/2.

Hence the greatest integer is 120 + k, or 120 + (Q-1)/2. Voila!

Save $100 on any VP online course!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review