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# A drawer contains 32 buttons, of which 20 are blue and 12 are brown. I

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4127
GPA: 3.39
A drawer contains 32 buttons, of which 20 are blue and 12 are brown. I  [#permalink]

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25 May 2017, 09:38
00:00

Difficulty:

55% (hard)

Question Stats:

58% (00:56) correct 42% (01:53) wrong based on 48 sessions

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A drawer contains 32 buttons, of which 20 are blue and 12 are brown. If 7 of the buttons are removed, how many of the buttons left in the drawer are brown?

(1) The difference between the number of blue buttons removed and the number of brown buttons removed is 1.
(2) Each of the first 4 buttons removed are brown.

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Posts: 323
Re: A drawer contains 32 buttons, of which 20 are blue and 12 are brown. I  [#permalink]

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25 May 2017, 09:48
1
Statement (1) The difference between the number of blue buttons removed and the number of brown buttons removed is 1.

As per this statement,

Buttons removed can be :

Blue=4 Brown=3 or Blue=3 Brown=4

This statement is not sufficient.

Statement (2) Each of the first 4 buttons removed are brown.

We do not know about the color of the last 3 buttons removed, hence this statement is not sufficient.

Combining both statements we get Buttons removed Blue=3 Brown=4

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Re: A drawer contains 32 buttons, of which 20 are blue and 12 are brown. I  [#permalink]

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20 Feb 2018, 00:36
1
Very tricky question.
Let a = number of blue buttons removed, b = number of brown buttons removed., a + b = 7

Statement 1: The difference between the number of blue buttons removed and the number of brown buttons removed is 1.
=> a - b = 1, so a = 4, b = 3
Looks like sufficient to tell number of browns left after removal process.

But wait, we get b = 3 (number of brown buttons removed) which contradicts statement 2 (which says first b >= 4, first four buttons removed are brown).
so we are missing something.

oh ya, it could be other way round , b - a = 1? yes it is , if so, b = 4 and a = 3, which aligns with Statement 2. so we need both the statements to answer => (C)

Take away: when we get answer from one of the statements, always better to verify that answer by plugging into the other statement. If it aligns with another statement, our answer is correct. Otherwise, we are missing something from our analysis.
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Joined: 20 Dec 2017
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A drawer contains 32 buttons, of which 20 are blue and 12 are brown. I  [#permalink]

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20 Feb 2018, 04:09
Quite simple but both statements are tricky:

(1) We know that the ratio between the colours is 4:3. But we do not know which colour has 4 and which has 3. Insufficient

(2) We only know the colour of the first 4 buttons (red) and nothing about the remaining 3. Insufficient

(1) & (2) We can match the first 4 red picks to the 4:3 ratio. Since there are no other colours, brown has to be 3 quantities. Sufficient

A drawer contains 32 buttons, of which 20 are blue and 12 are brown. I   [#permalink] 20 Feb 2018, 04:09
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