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

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Intern
Joined: 10 Jun 2014
Posts: 19
Each of the integers from 1 to 20 is written on the a seperate index  [#permalink]

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11 Sep 2016, 07:11
5
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:04) correct 21% (01:08) wrong based on 57 sessions

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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
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 612
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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11 Sep 2016, 07:58
1
Top Contributor
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If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number.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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Re: Each of the integers from 1 to 20 is written on the a seperate index  [#permalink]

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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 &nbs [#permalink] 04 Oct 2017, 11:26
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