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# Sam has a drawer full of exactly 59 packets, each containing a marker

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
Sam has a drawer full of exactly 59 packets, each containing a marker  [#permalink]

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22 Mar 2018, 07:33
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:00) correct 36% (02:18) wrong based on 90 sessions

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Sam has a big drawer full of exactly 59 packets, each containing a marker which is either black or blue or red in colour. All 59 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 59, 23 packets contain a black marker each. How many packets contain a blue marker?

(1) If Sam withdraws packets without looking at their contents, he needs to draw minimum 49 packets to ensure that he has at least one marker of each colour out of red, blue, black.

(2) Drawer has less packets containing red markers than those containing blue markers.
Intern
Joined: 02 Mar 2018
Posts: 10
Re: Sam has a drawer full of exactly 59 packets, each containing a marker  [#permalink]

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22 Mar 2018, 07:52
1
He has 59 packages:
- Black = 23
- Blue = x
- Red = y

(1) He has 23 red and 11 blue or 11 red and 25 blue. When he takes 49 packages: 23+25+1=49 he is sure that he has at least one of each color.
-Insufficient
(2) Clearly insufficient as it doesn't provide any numbers
-Insufficient

(1) + (2) From 1 we know that Blue =25 or Blue = 11. From (2) we know that Red < Blue. Then Blue = 25
SUFFICIENT (C)

Please, correct me if i'm wrong
Math Expert
Joined: 02 Aug 2009
Posts: 7992
Sam has a drawer full of exactly 59 packets, each containing a marker  [#permalink]

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22 Mar 2018, 07:57
amanvermagmat wrote:
Sam has a big drawer full of exactly 59 packets, each containing a marker which is either black or blue or red in colour. All 59 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 59, 23 packets contain a black marker each. How many packets contain a blue marker?

(1) If Sam withdraws packets without looking at their contents, he needs to draw minimum 49 packets to ensure that he has at least one marker of each colour out of red, blue, black.

(2) Drawer has less packets containing red markers than those containing blue markers.

Total - 59 packets
Black - 23 packets
so R + Blue = 59-23=36
Blue = ?

(1) If Sam withdraws packets without looking at their contents, he needs to draw minimum 49 packets to ensure that he has at least one marker of each colour out of red, blue, black.
49 packets means 49 = Max of two + only 1 of minimum..
so biggest 2 = 49-1=48
Black = 23, other larger qty = 48-23=25 and the least = 59-48=11
so Blue could be 25 or 11
insuff

(2) Drawer has less packets containing red markers than those containing blue markers.
R < Blue
insuff

combined
R<Blue ..
R and B could be 25 or 11
so Red = 11 and Blue = 25
suff
C
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Re: Sam has a drawer full of exactly 59 packets, each containing a marker  [#permalink]

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04 Oct 2019, 09:32
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Re: Sam has a drawer full of exactly 59 packets, each containing a marker   [#permalink] 04 Oct 2019, 09:32
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