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# There are 10 books of different colours lying on a table. Is the proba

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Math Expert
Joined: 02 Aug 2009
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There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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24 Jan 2017, 06:08
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55% (hard)

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59% (01:28) correct 41% (01:24) wrong based on 266 sessions

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There are 10 books of different colours lying on a table. Is the probability of picking a red book more than $$\frac{1}{10}$$?

1) there are 9 books which are either Red or Blue.
2) there are 7 books which are either Blue or Yellow.

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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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11 Feb 2017, 05:15
3
hotshot02 wrote:
chetan2u wrote:
There are 10 books of different colours lying on a table. Is the probability of picking a red book more than $$\frac{1}{10}$$?

1) there are 9 books which are either Red or Blue.
2) there are 7 books which are either Blue or Yellow.

Hi,

Prob of 1/10 in 10 books means "are red books more than 1?

Let's see the statements..
) there are 9 books which are either Red or Blue.
You do not know how many are red or blue in these 10..
Insufficient

2) there are 7 books which are either Blue or Yellow.
Red could be 0,1,2,3..
Insufficient

Combined...
R + B =9... (I)
B + Y =7....(II)..
But total are 10...
To make red the least let's take blue the max, so from (II) , blue can be 7 at the most..
But red + blue is 9, so red is ATLEAST 9-7=2..
So our answer will be YES..
C
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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24 Jan 2017, 06:37
rephrasing the question: is R>=2?

st1. if 9 books either red or blue we don't know exactly how many are red. insuff.
st2. if 7 books are either blue or yellow it imply that 3 are red so it is sufficient.

B
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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24 Jan 2017, 06:53
AMahmoodi wrote:
rephrasing the question: is R>=2?

st1. if 9 books either red or blue we don't know exactly how many are red. insuff.
st2. if 7 books are either blue or yellow it imply that 3 are red so it is sufficient.

B

how can you be sure that there are only 3 colours ?
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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24 Jan 2017, 07:10
hotshot02 wrote:
AMahmoodi wrote:
rephrasing the question: is R>=2?

st1. if 9 books either red or blue we don't know exactly how many are red. insuff.
st2. if 7 books are either blue or yellow it imply that 3 are red so it is sufficient.

B

how can you be sure that there are only 3 colours ?

hmm. you are absolutely right.

then It must be 1&2 combined. from 2 if we assume that there is just 1 yellow book then there should be 6 blue books to add up to 7. then if there are 6 blue books from st1 we can conclude that there are 3 red books. and then we can conclude that there is 3 or more red books. suff
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There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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Updated on: 10 Feb 2017, 06:58
N is the number of Red books, so we are asked whether N is greater or equal to 2

Statement 1: Can be 8 red, 1 blue and 1 other; in this case the answer is yes. But can be also 1 red, 8 blue and 1 other; in this case the anwer is no. Insufficient
Statement 2: Provide no information about red books, so insufficient

Taking both Statements together the answer is no. From Statement 2 we know that maximum value of blue books is 6 and combining this with Statement 1 we can infer that the number of red books must be at least 3. Sufficient

Originally posted by KVKA on 10 Feb 2017, 04:09.
Last edited by KVKA on 10 Feb 2017, 06:58, edited 2 times in total.
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There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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10 Feb 2017, 06:52
chetan2u wrote:
There are 10 books of different colours lying on a table. Is the probability of picking a red book more than $$\frac{1}{10}$$?

1) there are 9 books which are either Red or Blue.
2) there are 7 books which are either Blue or Yellow.

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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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12 Feb 2017, 22:04
1
chetan2u wrote:
There are 10 books of different colours lying on a table. Is the probability of picking a red book more than $$\frac{1}{10}$$?

1) there are 9 books which are either Red or Blue.
2) there are 7 books which are either Blue or Yellow.

(1) INSUFFICIENT. red books could be any number ranging from 1 to 8.
(2) INSUFFICIENT. red books could be any number ranging from 0 to 3.

(1)+(2) SUFFICIENT.
From (1),there could be only one book with different color from red and blue.
From (2),we have yellow.Hence,we have 1 yellow,6 blue and 3 red.
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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15 Feb 2017, 09:39
How do we know that there are only 3 colors present in the population? If there was one other color wouldn't that make the result choice E?
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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15 Feb 2017, 10:51
emockus wrote:
How do we know that there are only 3 colors present in the population? If there was one other color wouldn't that make the result choice E?

Hi,from statement 1 we know that the total number of red and blue is nine.
Statement 2 introduce another color-yellow.
So far,we have 10 books,nine is either red or blue.Hence,there is only a room left for yellow book.
If we add another color,then the total number of books must be greater than 10.
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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01 Sep 2018, 05:54
statement 1: there are 9 either red or blue books. So to satisfy the condition if the table consists of 1 red book and 8 blue books.The probability of picking red book is 1/10
Then answer to the question is no.
.But if the number of red books become 2,3 or so on then the probability will be 1/5,3/10 ,so on. Then the answer to the question is yes.
Hence the statement 1 is insufficient.

statement 2: the statement doesn't say anything about the number of red books.

combining statement 1&2 there are 9 red or blue books and 7 blue or yellow books. Now the maximum number of blue books that can be on the table is 7 hence there will be minimum of 2 red books on the table. hence the probability of picking up red books will be minimum 2/10 = 1/5 >1/10.So sufficient.
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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01 Sep 2018, 07:20
chetan2u wrote:
There are 10 books of different colours lying on a table. Is the probability of picking a red book more than $$\frac{1}{10}$$?

1) there are 9 books which are either Red or Blue.
2) there are 7 books which are either Blue or Yellow.

I dont understand what i am missing :S . If there are 10 books of different colours how can R+B=9, B+Y=7?
Shouldn't there be 10 different colours?
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Re: There are 10 books of different colours lying on a table. Is the proba  [#permalink]

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01 Sep 2018, 23:12
goforgmat wrote:
chetan2u wrote:
There are 10 books of different colours lying on a table. Is the probability of picking a red book more than $$\frac{1}{10}$$?

1) there are 9 books which are either Red or Blue.
2) there are 7 books which are either Blue or Yellow.

I dont understand what i am missing :S . If there are 10 books of different colours how can R+B=9, B+Y=7?
Shouldn't there be 10 different colours?

Please understand that it is given that the number of books are 10 but they have different colours. What I construed is that those 10 might have 3,4,5 or more different colours. Details regarding their colours can be inferred from the statements provided.
Re: There are 10 books of different colours lying on a table. Is the proba   [#permalink] 01 Sep 2018, 23:12
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