gprep ps-3

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 379
Joined: Tue Sep 30, 2008 7:17 am
Location: NY
Thanked: 28 times
Followed by:11 members

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Jul 28, 2014 4:56 am
150, 200, 250, n
Which of the following could be the median of the 4 integers listed above?

I. 175
II. 215
III. 235


A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
Let m = the median.

Case 1: 150, 200, 250, n
This case will yield the greatest possible median.
Here, m = (200+250)/2 = 225.
Since it's not possible that m=235, eliminate any answer choice that includes statement III.
Eliminate D and E.

Case 2: 150, 200, n, 250.
Here, n must be between 200 and 250, inclusive.
Least possible median:
If n=200, m = (200+200)/2 = 200.
Greatest possible median:
If n=250, m = (200+250)/2 = 225.
Thus:
200 ≤ m ≤ 225.
Since it's possible that m=215, eliminate any remaining answer choice that does not include statement II.
Eliminate A.

Case 3: 150, n, 200, 250
Here, n must be between 150 and 200, inclusive.
Least possible median:
If n=150, m = (150+200)/2 = 175.
Since it's possible that m=175, eliminate any remaining answer choice that does not include statement I.
Eliminate B.

The correct answer is C.
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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 28, 2014 7:04 am
150, 200, 250, n
Which of the following could be the median of the 4 integers listed above?

I. 175
II. 215
III. 235


A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
In cases where there is an EVEN number of values (as there are in this question), the median will be the average of the two middlemost values when all values are arranged in ascending order.

We can already see that 200 will be one of the two middlemost values, so let's check the various options for median and see what the other number needs to be to get each target median.

I. 175
If the median is 175, then it must be the case that (200 + other number)/2 = 175
So, in this case, the other number must be 150.
This is entirely possible, if n < 150. For example if n = 100, then the values would be {100, 150, 200, 250}, in which case the median is 175.
So, option I is possible.

II. 215
If the median is 215, then it must be the case that (200 + other number)/2 = 215
So, in this case, the other number must be 230.
This is entirely possible, if n = 230. The values would be {150, 200, 230, 250}, in which case the median is 215.
So, option II is possible.

III. 235
If the median is 235, then it must be the case that (200 + other number)/2 = 235
So, in this case, the other number must be 270.
Here, we have a PROBLEM. If the other number is 270, then the values are {150, 200, 250, 270}, in which case 200 and 270 are NOT the two middlemost values. The two middlemost values are 200 and 250, giving us a median of 225 (not 235).
So, option III is NOT possible.

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Mon Jul 28, 2014 8:03 am
CONCEPT :
If Number of terms in set is ODD: Median is the Middle term when the terms are arranged in Ascending/Descending order
If Number of terms in set is EVEN: Median is the AVERAGE OF TWO Middle term when the terms are arranged in Ascending/Descending order


Terms in Set are : 150, 200, 250, n

Since the value of n is unknown therefore there are three cases

Case 1: n is the Biggest term of the set
Median = (200+250)/2 = 225


Case 2: n is the Smallest term of the set
Median = (150+200)/2 = 175


Case 3: n is the Greater than 150 and lesser than 250
then, 175 < Median < 225


Therefore,
Answer : Option C
"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

Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Fri Aug 01, 2014 6:42 pm

by peterparker » Sat Aug 02, 2014 10:51 pm
Median, middle element if the numbers are odd, else, for even set, the average of the two middle element.

Now, here, 150,200,250,n set are given, and we have to determine the median.

when median = 175, then, median = (200 + n)/2, which means, that n = 150, which is possible.

When median = 215, n = (430 - 200) = 230, a combination which is possible.

When median = 235, then n = 470 - 200 = 270 > 250, this option strikes out, because, median of 200 + 250 is 225,

So the correct answer is the option which has I and II