Last visit was: 11 Jul 2025, 08:42 It is currently 11 Jul 2025, 08:42
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: 11 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,414
 [105]
5
Kudos
Add Kudos
100
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,414
 [17]
4
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
General Discussion
User avatar
AdmitJA
Joined: 04 Jul 2014
Last visit: 26 Mar 2018
Posts: 276
Own Kudos:
1,203
 [1]
Given Kudos: 420
Location: India
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q49 V37
GPA: 3.58
WE:Analyst (Accounting)
Products:
GMAT 2: 710 Q49 V37
Posts: 276
Kudos: 1,203
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
740,414
 [4]
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,414
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
joseph0alexander
Bunuel
Set A consist of 10 terms, each of which is a reciprocal of a prime number, is the median of the set less than 1/5?


(1) Reciprocal of the median is a prime number.

(2) The product of any two terms of the set is a terminating decimal.

Hi again Bunuel! :)

This is how I am interpreting this question. Based on this interpretation when I read your explanation, I'm getting totally lost. Please help.

Prompt: A set consists of reciprocals of 10 different prime numbers (1/2, 1/3 ..... 1/101....). Is the sum of the 5 and 6th term less than 1.5?

Statement 1: Reciprocal of the average of the 5th and 6th term is also a prime number. I understand your explanation and this is clearly not sufficient.

Statement 2: 1/2 and 1/5 are the only numbers which are a part of this set (squares or cubes of these numbers also can't be a part of this set as the question states that the numbers are reciprocals of primes only). The 10 numbers could be 9 1/2's and 1 1/5 as well. So we don't know have sufficiency?

Is this understanding correct? IMHO answer is E

For (2) the set could be any combination of 1/2's and 1//5:
{1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2}
{1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5}
{1/5, 1/5, 1/5, 1/5, 1/5, 1/2, 1/2, 1/2, 1/2, 1/2}
....

Let me ask you: could the median of any of the sets above be less than 1/5?
User avatar
Ankur9
Joined: 25 May 2014
Last visit: 11 May 2016
Posts: 43
Own Kudos:
Given Kudos: 125
Products:
Posts: 43
Kudos: 50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Official Solution:


(1) Reciprocal of the median is a prime number. If all the terms equal 1/2, then the median=1/2 and the answer is NO but if all the terms equal 1/7, then the median=1/7 and the answer is YES. Not sufficient.

(2) The product of any two terms of the set is a terminating decimal. This statement implies that the set must consists of 1/2 or/and 1/5. Thus the median could be 1/2, 1/5 or (1/5+1/2)/2=7/20. None of the possible values is less than 1/5. Sufficient.


Answer: B


Hi Bunuel,
How can we get to be sure while solving the problem that ONLY 1/2 or 1/5 or combination of both results in terminating decimal.
Because there can be infinite # of cases of reciprocal of prime numbers in a set.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,414
 [20]
4
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
Ankur9
Bunuel
Official Solution:


(1) Reciprocal of the median is a prime number. If all the terms equal 1/2, then the median=1/2 and the answer is NO but if all the terms equal 1/7, then the median=1/7 and the answer is YES. Not sufficient.

(2) The product of any two terms of the set is a terminating decimal. This statement implies that the set must consists of 1/2 or/and 1/5. Thus the median could be 1/2, 1/5 or (1/5+1/2)/2=7/20. None of the possible values is less than 1/5. Sufficient.


Answer: B


Hi Bunuel,
How can we get to be sure while solving the problem that ONLY 1/2 or 1/5 or combination of both results in terminating decimal.
Because there can be infinite # of cases of reciprocal of prime numbers in a set.

THEORY:

A reduced fraction \(\frac{a}{b}\) (meaning that the fraction is already in its simplest form, so reduced to its lowest term) can be expressed as a terminating decimal if and only if the denominator \(b\) is of the form \(2^n5^m\), where \(m\) and \(n\) are non-negative integers. For example: \(\frac{7}{250}\) is a terminating decimal \(0.028\), as the denominator \(250\) equals \(2*5^3\). The fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and the denominator \(10=2*5\).

Note that if the denominator already consists of only 2s and/or 5s, then it doesn't matter whether the fraction is reduced or not.

For example, \(\frac{x}{2^n5^m}\), (where \(x\), \(n\), and \(m\) are integers) will always be a terminating decimal.

(We need to reduce the fraction in case the denominator has a prime other than 2 or 5, to see whether it can be reduced. For example, the fraction \(\frac{6}{15}\) has 3 as a prime in the denominator, and we need to know if it can be reduced.)

Questions testing this concept:
https://gmatclub.com/forum/does-the-dec ... 89566.html
https://gmatclub.com/forum/any-decimal- ... 01964.html
https://gmatclub.com/forum/if-a-b-c-d-a ... 25789.html
https://gmatclub.com/forum/700-question-94641.html
https://gmatclub.com/forum/is-r-s2-is-a ... 91360.html
https://gmatclub.com/forum/pl-explain-89566.html
https://gmatclub.com/forum/which-of-the ... 88937.html
User avatar
swanidhi
Joined: 11 Oct 2013
Last visit: 14 Jul 2023
Posts: 70
Own Kudos:
313
 [1]
Given Kudos: 137
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
GMAT 1: 600 Q41 V31
Posts: 70
Kudos: 313
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I was just about right, but made the usual mistake. The question asks, if mean is less than 1/5. And I deduced that it could be 1/5 too and marked E :'(
Great question!
avatar
PerseveranceWins
Joined: 23 Apr 2014
Last visit: 20 Apr 2017
Posts: 44
Own Kudos:
Given Kudos: 82
Location: United States
GMAT 1: 680 Q50 V31
GPA: 2.75
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation. Great question!!
User avatar
Senthil7
Joined: 31 Mar 2016
Last visit: 05 Mar 2017
Posts: 323
Own Kudos:
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
GMAT 1: 670 Q48 V34
Posts: 323
Kudos: 211
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
User avatar
zflodeen
Joined: 04 Sep 2017
Last visit: 17 Dec 2017
Posts: 19
Own Kudos:
Given Kudos: 10
Location: United States
Concentration: Finance
GMAT 1: 610 Q36 V36
GMAT 2: 680 Q40 V36
GPA: 3.3
WE:Consulting (Mutual Funds and Brokerage)
GMAT 2: 680 Q40 V36
Posts: 19
Kudos: 21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I can certainly see the logic in the explanation with this question, but I answered E. My basis for E is that all the terms could be 1/5 in which case the median is 1/5. My understanding of the wording of the question is the median has to be less than 1/5 to give a hard yes, but if you can have 1/5 as well as 1/2 and 7/20 as answers for #2, there is no clear yes or no. Am I overlooking something on this one?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,414
Kudos
Add Kudos
Bookmarks
Bookmark this Post
zflodeen
I can certainly see the logic in the explanation with this question, but I answered E. My basis for E is that all the terms could be 1/5 in which case the median is 1/5. My understanding of the wording of the question is the median has to be less than 1/5 to give a hard yes, but if you can have 1/5 as well as 1/2 and 7/20 as answers for #2, there is no clear yes or no. Am I overlooking something on this one?

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

The question asks: is the median of the list less than 1/5?

From (2) the median could be 1/2, 1/5 or 7/20. None of the possible values is less than 1/5. So, we have a definite NO answer to the question for all three possible values of the median. Sufficient.

Hope it's clear.
avatar
dileepsv
Joined: 25 Oct 2017
Last visit: 25 May 2020
Posts: 25
Own Kudos:
Given Kudos: 37
Location: Canada
GMAT 1: 720 Q47 V42
GPA: 2.9
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
avatar
Manick9
Joined: 25 May 2016
Last visit: 07 Jan 2025
Posts: 78
Own Kudos:
Given Kudos: 497
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V30
GMAT 1: 620 Q46 V30
Posts: 78
Kudos: 83
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why only 1/2 and 1/5 for statement two? It can also be 1/3, 1/7, 1/11 etc., right?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
740,414
 [2]
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,414
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Manick9
Why only 1/2 and 1/5 for statement two? It can also be 1/3, 1/7, 1/11 etc., right?

No. If there are reciprocals of other primes than 2 and 5, then the product of ANY two terms of the list won't be a terminating decimal. For example, if the list is {1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/5, 1/5, 1/5, 1/3}, then no pair with 1/3 will produce the product which is a terminating decimal: 1/2*1/3 = 1/6 = 0.1666666.... and 1/5*1/6 = 0.0333333............... (reduced fraction to be terminating its denominator must have only 2's and/or 5 in it).
User avatar
prabsahi
Joined: 09 Jun 2014
Last visit: 24 Mar 2025
Posts: 216
Own Kudos:
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Products:
Posts: 216
Kudos: 288
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question. Loved this questions!!
User avatar
shameekv1989
Joined: 14 Dec 2019
Last visit: 17 Jun 2021
Posts: 820
Own Kudos:
Given Kudos: 354
Location: Poland
Concentration: Entrepreneurship, Strategy
GMAT 1: 640 Q49 V27
GMAT 2: 660 Q49 V31
GMAT 3: 720 Q50 V38
GPA: 4
WE:Engineering (Consumer Electronics)
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Amazing question!! One that just blows your mind off!! Hats off Bunuel
avatar
sush147
Joined: 10 Aug 2020
Last visit: 11 Oct 2021
Posts: 23
Own Kudos:
Given Kudos: 24
Location: India
GMAT 1: 700 Q49 V35
GMAT 2: 730 Q51 V38
GPA: 2.5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,414
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
User avatar
BottomJee
User avatar
Retired Moderator
Joined: 05 May 2019
Last visit: 09 Jun 2025
Posts: 996
Own Kudos:
Given Kudos: 1,009
Affiliations: GMAT Club
Location: India
GMAT Focus 1: 645 Q82 V81 DI82
GMAT 1: 430 Q31 V19
GMAT 2: 570 Q44 V25
GMAT 3: 660 Q48 V33
GPA: 3.26
WE:Engineering (Manufacturing)
Products:
GMAT Focus 1: 645 Q82 V81 DI82
GMAT 3: 660 Q48 V33
Posts: 996
Kudos: 1,211
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
User avatar
Kartik2121
Joined: 16 Jan 2023
Last visit: 10 Jun 2025
Posts: 48
Own Kudos:
Given Kudos: 70
GMAT Focus 1: 645 Q82 V85 DI78
GMAT 1: 620 Q44 V31
GMAT 2: 680 Q47 V37
GMAT Focus 1: 645 Q82 V85 DI78
GMAT 2: 680 Q47 V37
Posts: 48
Kudos: 20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Poorly written question. The stem needs to make it clear that the terms can be repetitive.

Posted from my mobile device
 1   2   
Moderators:
Math Expert
102634 posts
Founder
41089 posts