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# John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical

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Math Expert
Joined: 02 Sep 2009
Posts: 64314
John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical  [#permalink]

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26 Nov 2017, 08:08
1
3
00:00

Difficulty:

15% (low)

Question Stats:

68% (01:00) correct 32% (01:33) wrong based on 122 sessions

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John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical pencils and 9 wood pencils. If John reaches into the drawer and selects randomly how many writing tools must he remove in order to ensure that he will select one of each type?

A. 23
B. 21
C. 20
D. 15
E. 4

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Joined: 02 Sep 2009
Posts: 64314
Re: John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical  [#permalink]

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26 Nov 2017, 08:10
Bunuel wrote:
John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical pencils and 9 wood pencils. If John reaches into the drawer and selects randomly how many writing tools must he remove in order to ensure that he will select one of each type?

A. 23
B. 21
C. 20
D. 15
E. 4

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Re: John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical  [#permalink]

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26 Nov 2017, 08:29
1
D. 15
Suppose he selects 5 black pens and then 6 blue pens and 3 mechanical pencils. To reach the wood pencil he should have chosen 14 items already and with the 15th item he chose he would have chosen one of each type.
Hence D

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Math Expert
Joined: 02 Aug 2009
Posts: 8632
Re: John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical  [#permalink]

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26 Nov 2017, 08:43
2
1
Sasindran wrote:
D. 15
Suppose he selects 5 black pens and then 6 blue pens and 3 mechanical pencils. To reach the wood pencil he should have chosen 14 items already and with the 15th item he chose he would have chosen one of each type.
Hence D

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hi..

your approach is correct but you could not take it to logical end..

Solution

5 black pens, 6 blue pens, 3 mechanical pencils and 9 wood pencils
we have to take the worst case scenario, so here think that you will get the LEAST numbered thing in the end, which here is 3 mechanical pencils..

so he picks up 5 black pens, 6 blue pens, 3 mechanical pencils and 9 wood pencils = 5+6+9=20
and then he picks up a mechanical pencil so 21

B
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Re: John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical  [#permalink]

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04 Aug 2019, 04:07
Bunuel wrote:
John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical pencils and 9 wood pencils. If John reaches into the drawer and selects randomly how many writing tools must he remove in order to ensure that he will select one of each type?

A. 23
B. 21
C. 20
D. 15
E. 4

(5+6+9) worst case + 1
therefore, 21
Re: John has a drawer containing 5 black pens, 6 blue pens, 3 mechanical   [#permalink] 04 Aug 2019, 04:07