Last visit was: 08 Jul 2025, 20:30 It is currently 08 Jul 2025, 20:30
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,581
 [97]
5
Kudos
Add Kudos
92
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,756
Own Kudos:
34,032
 [34]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,756
Kudos: 34,032
 [34]
18
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
User avatar
manpreetsingh86
Joined: 13 Jun 2013
Last visit: 19 Dec 2022
Posts: 219
Own Kudos:
1,147
 [9]
Given Kudos: 14
Posts: 219
Kudos: 1,147
 [9]
7
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
rohitmanglik
Joined: 24 Jul 2011
Last visit: 22 May 2025
Posts: 127
Own Kudos:
116
 [1]
Given Kudos: 93
Location: India
GMAT 1: 570 Q50 V19
GMAT 2: 650 Q49 V28
GMAT 3: 690 Q50 V34
WE:Information Technology (Finance: Investment Banking)
Products:
GMAT 3: 690 Q50 V34
Posts: 127
Kudos: 116
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there.


It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week).

We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat).
=> 3* odd is again odd.


2 * age of students is always even.

So final equation is even +odd = odd.

Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 08 Jul 2025
Posts: 21,064
Own Kudos:
26,107
 [6]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,064
Kudos: 26,107
 [6]
2
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
Bunuel

Tough and Tricky questions: Statistics.



During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer?

(A) 0%
(B) 10%
(C) 20%
(D) 30%
(E) 40%

Let’s analyze the number each students gets. When 7 raised to any positive integer power, the result will be odd. When that result is multiplied by 3, the result will be odd again. Finally, when that result is added to doubled age of the student’s age (which is an even number), the final result will always be an odd number. So each student will get an odd number regardless of his/her favorite day of the week and his/her age.

We are given that there are 28 students in the class. The median will the be the average of the the 14th and 15th numbers if the numbers are in ascending (or descending) order. However, since each number is odd and the average of two odd number is always an integer, the probability that the median number will be a non-integer is 0.

Answer: A
User avatar
m7runner
User avatar
Kellogg School Moderator
Joined: 15 May 2023
Last visit: 08 Jul 2025
Posts: 35
Own Kudos:
Given Kudos: 79
Posts: 35
Kudos: 19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
→ There are 28 sample values
→ Thus there are two middle terms
→ Note that the calculation of each term is of the form: 3(7^x) + 2k, where is x = {1,.....,7}, and k is the value of the student. The first term here will ALWAYS be odd and the second term will ALWAYS be even. When added, the resultant will ALWAYS be ODD. Thus the entire sample will consist of a set of ODD samples.
→ Since we know there are 28 terms and there will be two middle terms, hence the average of these terms will be the median. Thus ODD + ODD / 2 = EVEN / 2 = EVEN, hence there will be a 0% probability of the median lucky number being a non-integer.
User avatar
AnjaliSK
Joined: 01 May 2024
Last visit: 31 Jan 2025
Posts: 2
Given Kudos: 2
Posts: 2
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi All,

I have opted for a lil different perspective here,

Since, we have got 28 students and they can choose the values only from 1^7 to 7^7, there are only 7 values to choose from and median for odd number of values is always an integer, so that way the answer has to be 0%.

Please let me know if this way of thinking for such questions is right.

Thank you for any help in advance.
Moderators:
Math Expert
102594 posts
PS Forum Moderator
679 posts