GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Apr 2019, 05:41

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# 97 students take part in a test and the median score is 85.

Author Message
TAGS:

### Hide Tags

Intern
Joined: 04 Sep 2009
Posts: 41
97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

Updated on: 29 Dec 2013, 04:38
2
3
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:34) correct 46% (01:36) wrong based on 252 sessions

### HideShow timer Statistics

97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.

_________________
Aeros
"Why are you trying so hard to fit in when you were born to stand out?"
"Do or do not. There is no 'try'..."

Originally posted by aeros232 on 10 Oct 2012, 19:00.
Last edited by Bunuel on 29 Dec 2013, 04:38, edited 1 time in total.
Edited the OA.
Director
Joined: 22 Mar 2011
Posts: 599
WE: Science (Education)
Re: 97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

11 Oct 2012, 03:13
1
aeros232 wrote:
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.

You are right, the correct answer is not E.
If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.
The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions that "must be correct".

_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Intern
Joined: 08 Apr 2012
Posts: 7
GMAT 1: 650 Q51 V29
Re: 97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

29 Dec 2013, 01:52
I agree with the OA. We have exactly 49 students’ score are equal to or more than 85 and I & III must be true. With I, we cannot have 48 students’ score are equal to or more than 85 and with III, we cannot have 50 students’ score are equal to or more than 85. I & III must be true in this case.
Retired Moderator
Joined: 16 Jun 2012
Posts: 1006
Location: United States
Re: 97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

29 Dec 2013, 02:29
AnChu wrote:
I agree with the OA. We have exactly 49 students’ score are equal to or more than 85 and I & III must be true. With I, we cannot have 48 students’ score are equal to or more than 85 and with III, we cannot have 50 students’ score are equal to or more than 85. I & III must be true in this case.

Hello An

Evajager is correct, A is the answer. OA can't be E.
Let see an example:
Student 1: 50
Student 2: 51
Student 3: 51
...
...
Student 47: 84
Student 48: 85
Student 49: 85
Student 50: 85

Student 51: 86
....
....
Student 97: 90

Median is still 85
Clearly, we have 50 students who have test score higher than 85 --> We can't say "At most 49 students’ score are equal to or more than 85". Thus, E is not a "must be true" answer. Only A is correct.

Hope it helps.
_________________
Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMW Chief of Design.
Intern
Joined: 14 May 2015
Posts: 4
Re: 97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

24 Aug 2015, 15:28
aeros232 wrote:
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.

My solution process:

Step 1. Rephrase the question: The question is testing a simple concept, but the GMAC muddied the waters with convoluted statements and large #s. Therefore, I changed 'n' to 7 (see graphic below).

Step 2. Analyze the type of question: 'Must be true' ... Subsequently, I need to test the validity of the statements.
Attachments

Stats and Sets Prob.png [ 19.67 KiB | Viewed 1464 times ]

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9139
Location: Pune, India
Re: 97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

24 Aug 2015, 22:25
aeros232 wrote:
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.

Takeaway: Whenever you are given the median of a set and you need to consider cases of what the other numbers could be, never forget to take the case where all numbers are equal to the median.
_________________
Karishma
Veritas Prep GMAT Instructor

Board of Directors
Joined: 17 Jul 2014
Posts: 2556
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: 97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

23 Mar 2016, 19:08
aeros232 wrote:
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.

median is 85. it means 48 scored up to 85, INCLUSIVE. the 49th scored 85, and 48 scored at least 85 and more.

1. YES, at least 49 scored at least 85 or more. this one we know for SURE, since the 49th person in the middle scored 85, and there are 48 more people with either 85 or MORE. so I is true. we can eliminate B and C.
2. NO, even if everyone got a different score, there are 48 people who scored below 85. since the middle person, 49th one scored 49, and the rest 48 scored 85 or more, this case is never true. D eliminated.
3. at most 49 students got 85. this is a tempting one but NO. suppose all 97 students got 85. the median is still 85, but the statement is not true. E is eliminated, and only A stands.
Director
Joined: 13 Mar 2017
Posts: 723
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: 97 students take part in a test and the median score is 85.  [#permalink]

### Show Tags

19 Jul 2017, 00:38
aeros232 wrote:
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.

97 students take part in a test.
Median score is 85..
So it can be represented as below

(.........48 numbers........), 85, (...........48 numbers...........)

Now lets start going through options.
Option I : At least 49 students’ score are equal to or more than 85.
We see that the numbers on the right of median has to be greater than or equal to 85. So, 49 numbers including the median has to be greater than equal to 85.
There can be more numbers equal to 85 or less than 85 on the left hand side of the median.

So atleast 49 students score are equal or more than 85.
CORRECT

Option II : At least 49 students’ score are less than 85.
So for median to be 85.. THe numbers on the left has to be less than or equal to 85. So, atleast 49 students score should be less than or equal to 85.
INCORRECT

Option III : At most 49 students’ score are equal to or more than 85.
As we discussed in option I . There may be more numbers on the left hand side of median which may be equal to 85.
INCORRECT

P.S. : I did mistake in solving and got confused somehow between atmost and least. So such questions has to be tackled very carefully.
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Re: 97 students take part in a test and the median score is 85.   [#permalink] 19 Jul 2017, 00:38
Display posts from previous: Sort by