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

Question

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

Lampard42 · Answer

2A=B and 3B=C; Combining both gets 6A=3B=C (Equation *3); So A+B+C=A+2A+6A=9A; so the total books must be divisible by 9; IMO C 90 books

CareerGeek · Answer

Let the number of books of Andy = x
--> Number of books of Bill = 2*x = 2x
--> Number of books of Charlie = 3*2x = 6x

Total number of books = x + 2x + 6x = 9x

So, the total SHOULD be a multiple of 9

Only Option C satisfies

IMO Option C

Pls Hit Kudos if you like the solution

Archit3110 · Answer

given
A=B/2; 2A
B= C/3=2A
C=2B= 6A
A+2A+6A ; 9A
multiple of 9 is answer
IMO C

Nikhilaery · Answer

Let books with Charlie be x.

Therefore, Bill is (x/3) and Andy has half the number of books Bill has, which is (x/6)

For all of them to have an integer number of books, min(x) = 6 so that that the number of books with Andy is an integer value = 1.

The number of books with Andy, Bill and Charlie are in the ratio 1:2:6

The minimum number of books with all three therefore equals = 1+2+6 = 9.

Thus, the sum total of the books all three hold must be a multiple of 9.

From the options, min and the only value workable is (C) 90

Posted from my mobile device

Prep Toolkit