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Andy has half as many books as Bill, who has one third as many books

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Andy has half as many books as Bill, who has one third as many books [#permalink]

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New post 14 Oct 2017, 08:21
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Difficulty:

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Question Stats:

82% (01:20) correct 18% (00:40) wrong based on 21 sessions

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Andy has half as many books as Bill, who has one third as many books as charlie. which of these can be total number of books three of them have?

(A) 30
(B) 60
(C) 90
(D) 120
(E) 150
[Reveal] Spoiler: OA

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Re: Andy has half as many books as Bill, who has one third as many books [#permalink]

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New post 14 Oct 2017, 08:51
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My approach
assume 3 variables
Andy - a
Bill - b
charlie - c

a= 1/2 b -----> i.e b=2a
b= 1/3 c -----> i.e c=3b = 3*2a = 6a


Total = a + b + c
= a + 2a + 6a
=9a

hence the total should be divisible by 9
only option is 90 Hence C

Just have a query what if 2 options are divisible by 9 :oops:
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Re: Andy has half as many books as Bill, who has one third as many books [#permalink]

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New post 14 Oct 2017, 09:04
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Let A has X books. Therefore, B has 2X books, since number of books with A is half that of B.

In the same vein, number of books with C is thrice that of B. Therefore, C has 3(2X) = 6X books.

Therefore, the total number of books with A, B and C combined is X+2X+6X = 9X.

Only one of the given options is divisible by 9.

Thus, the answer is C.

Kudos [?]: 7 [1], given: 246

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Re: Andy has half as many books as Bill, who has one third as many books [#permalink]

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New post 14 Oct 2017, 09:05
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akshata19 wrote:
My approach
assume 3 variables
Andy - a
Bill - b
charlie - c

a= 1/2 b -----> i.e b=2a
b= 1/3 c -----> i.e c=3b = 3*2a = 6a


Total = a + b + c
= a + 2a + 6a
=9a

hence the total should be divisible by 9
only option is 90 Hence C

Just have a query what if 2 options are divisible by 9 :oops:


To answer your query, I suppose if more than one option is divisible by 9, the test-makers might include a condition such as, "the maximum/minimum number of books they could have together"

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Re: Andy has half as many books as Bill, who has one third as many books [#permalink]

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New post 14 Oct 2017, 09:37
Let A has X books. Therefore, B has 2X books, since number of books with A is half that of B.

In the same vein, number of books with C is thrice that of B. Therefore, C has 3(2X) = 6X books.

Therefore, the total number of books with A, B and C combined is X+2X+6X = 9X.

Only one of the given options is divisible by 9.

Thus, the answer is C.

Kudos [?]: 7 [0], given: 182

Re: Andy has half as many books as Bill, who has one third as many books   [#permalink] 14 Oct 2017, 09:37
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