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

It is currently 17 Oct 2019, 13:30

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

A retailer sells products that belong to different categories, A to F,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Marshall & McDonough Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1685
Location: India
GMAT ToolKit User
A retailer sells products that belong to different categories, A to F,  [#permalink]

Show Tags

New post 02 Apr 2016, 19:49
1
5
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (01:49) correct 28% (01:52) wrong based on 168 sessions

HideShow timer Statistics

A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product sold last week belonged to Category D?

(A) 2/27

(B) 4/27

(C) 5/27

(D) 8/27

(E) 15/27

Question: Self Made
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7971
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

Show Tags

New post 02 Apr 2016, 20:19
3
Vyshak wrote:
A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?

(A) 2/27

(B) 4/27

(C) 5/27

(D) 8/27

(E) 15/27

Question: Self Made
OA after 24 hours


Hi,
there are 6 distinct categories..
Since each category has to have atleast 2 products..
let A have 2 and each thereafter has ONE more than previous..
so A,B,C,D,E, and F will have minimum 2+3+4+5+6+7 = 7*8/2 -1 = 28-1 =27..
therefore ONLY possiblity of products in each due to restriction of TOTAL as 27 is 2,3,4,5,6,7 so D will have 5 products..
Probability = 5/27

C
_________________
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4776
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

Show Tags

New post 03 Apr 2016, 06:22
1
Vyshak wrote:
A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?

(A) 2/27

(B) 4/27

(C) 5/27

(D) 8/27

(E) 15/27

Question: Self Made
OA after 24 hours


Since there are 2 products in any category , we can write as under -

A = 2n
B = 2n+1
C = 2n+2
D = 2n+3
E = 2n+4
F = 2n+5

Given

Quote:
1. a total of 27 products were sold last week
2. at-least 2 products are sold in any category


So the minimum value of n must have to be 1 ( To satisfy condition 2 above)

Further while solving the problem, the possible number of products sold can be as follows

A = 2*1 => 2
B = 2*1+1 => 3
C = 2*1+2 => 4
D = 2*1+3 => 5
E = 2*1+4 => 6
F = 2*1+5 => 7

Thus we find D has minimum 5 products ( Satisfying conditions 1 and 2 above)

So the required probability is 5/27

Answer is (C)

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Intern
avatar
Joined: 22 Nov 2015
Posts: 3
GMAT ToolKit User
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

Show Tags

New post 04 Apr 2016, 21:05
1
Vyshak wrote:
A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?

(A) 2/27

(B) 4/27

(C) 5/27

(D) 8/27

(E) 15/27

Question: Self Made
OA after 24 hours


Going by the options I marked this answer as C = 5/27 solving in the same manner as explained by others.

But I find a glitch here. Question says - "What is the probability that a product was sold from Category D last week"? - means whether a product was sold or not from category D last week. In all the outcomes a product was definitely sold from category D.
By arranging the figures I can certainly say that a product was sold, for sure, from category D. Doesn't that makes the probability as 1?

If the question were - "If a product was bought by me then what is the probability that it belonged to category D?" then I believe that answer C would be the correct option.
Can anybody help me here understand whether my thinking is correct or not?

Thanks!
Marshall & McDonough Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1685
Location: India
GMAT ToolKit User
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

Show Tags

New post 04 Apr 2016, 23:49
inventgm wrote:
Vyshak wrote:
A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?

(A) 2/27

(B) 4/27

(C) 5/27

(D) 8/27

(E) 15/27

Question: Self Made
OA after 24 hours


Going by the options I marked this answer as C = 5/27 solving in the same manner as explained by others.

But I find a glitch here. Question says - "What is the probability that a product was sold from Category D last week"? - means whether a product was sold or not from category D last week. In all the outcomes a product was definitely sold from category D.
By arranging the figures I can certainly say that a product was sold, for sure, from category D. Doesn't that makes the probability as 1?

If the question were - "If a product was bought by me then what is the probability that it belonged to category D?" then I believe that answer C would be the correct option.
Can anybody help me here understand whether my thinking is correct or not?

Thanks!


Thanks inventgm. I have corrected the question to ensure better understanding.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13243
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

Show Tags

New post 02 Sep 2018, 05:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: A retailer sells products that belong to different categories, A to F,   [#permalink] 02 Sep 2018, 05:51
Display posts from previous: Sort by

A retailer sells products that belong to different categories, A to F,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne