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Each of the integers from 1 to 20 is written on the a seperate index

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Joined: 10 Jun 2014
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Kudos [?]: 15 [0], given: 119

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Each of the integers from 1 to 20 is written on the a seperate index [#permalink]

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New post 11 Sep 2016, 07:11
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Each of the integers from 1 to 20 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?

A) 19
B) 12
C) 11
D) 10
E) 3
[Reveal] Spoiler: OA

Kudos [?]: 15 [0], given: 119

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Director
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Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 622

Kudos [?]: 763 [1], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: Each of the integers from 1 to 20 is written on the a seperate index [#permalink]

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New post 11 Sep 2016, 07:58
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Out of the 20 integers: 10 are odd and 10 are even.
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 10 odd numbers first
2. 11th number will be the first even number
So we need to withdraw at least 11 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 11. (C)

Hope it helps!

azamaka wrote:
Each of the integers from 1 to 20 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?

A) 19
B) 12
C) 11
D) 10
E) 3

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Kudos [?]: 763 [1], given: 59

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Re: Each of the integers from 1 to 20 is written on the a seperate index [#permalink]

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New post 04 Oct 2017, 11:26
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Re: Each of the integers from 1 to 20 is written on the a seperate index   [#permalink] 04 Oct 2017, 11:26
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