X number of books have to be distributed equally among a number of lib

Question

X number of books have to be distributed equally among a number of library shelves. If X is a multiple of both 9 and 6, which of the following statements must be true?
I The books can be distributed equally among 3 library shelves
II The books can be distributed equally among 27 library shelves
III The books can be distributed equally among 54 library shelves

A I only
B II only
C III only
D I, II and III
E None of the above

rajatchopra1994 · Answer

Answer is D.

As X is multiple of 9 and 6. It has to be multiple of 54.
54 multiple can be divided into 3 shelves. 
as for 1. 18 books in all or multiple.
2. 2 books per shelves or multiple.
3. 1 book per shelves or multiple.

pls give kudos if you find my answer explanation good.

thucanh1105 · Answer

X is a multiple of both 9 and 6 -> X may be 18, 36, 54, 72,...
-> X can be distributed equally among at least 3 libraries -> choose A

shashwat94 · Answer

As X is a multiple of 6 & 9, it can be one of the following :- 18, 36, 54, 72 ...
All of the above are divisible by 3 and not by 27 or 54, hence A should be the answer.

pearljiandani · Answer

This doesn't hold true for 18, which is a multiple of 9 and 6 but not a multiple of 27 or 54. It is a factor of 54 but not a multiple. So how would one divide 18 books equally among 27 or 54 shelves?

Kinshook  Can you please explain how OA is D?

Kinshook · Answer

OA is A

ScottTargetTestPrep · Answer

Solution:

Since X is a multiple of both 9 and 6, we can let X be the least common multiple of 9 and 6, which is 18. If X = 18, we see that the 18 books can be distributed equally among 3 shelves. However, they can’t be distributed equally among 27 or 54 shelves since some shelves will have at least one book while others will have no books. So II and III must be false.

Now, if X is not 18, then it must be a multiple of 18 since X is a multiple of both 9 and 6 (recall that if k is a multiple of m and n, then k is a multiple of the LCM of m and n). Since 18 is already a multiple of 3, any multiple of 18 will be also a multiple of 3; therefore, the number of books can be always distributed equally among 3 shelves. So I must be true.

Answer: A

Answer: A

sahilvermani · Answer

This is where I am confused. X can be 54, in which case books can be distributed equally among 27 library shelves.

So, II and III are also "possible" (since II and III denote "can" and not "must").

ScottTargetTestPrep · Answer

Response:
 
If I understand correctly, you are interpreting the second statement as “it is possible that the number of books is a multiple of 27.” In reality, the second statement is equivalent to saying “the number of books IS a multiple of 27.” The same thing goes for the third statement. Thus, we can say that statement two MUST be true if every value of X is a multiple of 27. Similarly, statement three MUST be true if every value of X is a multiple of 54. Since we can find a possible value for X which is neither a multiple of 27 nor a multiple of 54 (for instance, X = 18 or 36), neither statement two nor statement three must be true. Both statements CAN be true, but neither of them MUST be true.

X number of books have to be distributed equally among a number of lib

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X number of books have to be distributed equally among a number of lib

Prep Toolkit

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