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# A man intends to purchase nine units each of pens, pencils and books

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Joined: 23 Apr 2019
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A man intends to purchase nine units each of pens, pencils and books  [#permalink]

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Updated on: 22 Sep 2019, 19:38
1
00:00

Difficulty:

25% (medium)

Question Stats:

86% (01:43) correct 14% (02:31) wrong based on 14 sessions

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A man intends to purchase at least nine units each of pens, pencils and books during a sale. He purchases more pencils than pens and more books than pencils for a total of 32 items. What is the possible number of pencils purchased?

(A) 4

(B) 6

(C) 8

(D) 10

(E) 12

Originally posted by Hovkial on 22 Sep 2019, 13:49.
Last edited by chetan2u on 22 Sep 2019, 19:38, edited 1 time in total.
Corrected the Q
Math Expert
Joined: 02 Aug 2009
Posts: 8004
Re: A man intends to purchase nine units each of pens, pencils and books  [#permalink]

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22 Sep 2019, 19:37
Hovkial wrote:
A man intends to purchase atleastnine units each of pens, pencils and books during a sale. He purchases more pencils than pens and more books than pencils for a total of 32 items. What is the possible number of pencils purchased?

(A) 4

(B) 6

(C) 8

(D) 10

(E) 12

The question is of course missing the word ATLEAST. You cannot have all buying 9 units each and still having more books then pencils and so on..

Now, it is given that books > pencils > pens $$\geq{9}$$..
If we take pens as 10, pencils will be atleast 11 and books 12... Total =10+11+12=33....NOT possible, so pens have to be 9.

This means books + pencils = 32-9=23.
let us check for possibilities..
pencils is 10, so books = 23-10=13..Possible
pencils is 11, so books = 23-11=12..Possible
pencils is 12, so books = 23-12=11.. NOT Possible, as books have to be GREATER than pencils..

Possible values of pencils -- 10 and 11

D
_________________
Re: A man intends to purchase nine units each of pens, pencils and books   [#permalink] 22 Sep 2019, 19:37
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