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A certain number of books are to be divided by students. If the number

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A certain number of books are to be divided by students. If the number  [#permalink]

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New post Updated on: 21 Mar 2019, 10:44
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A
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D
E

Difficulty:

  45% (medium)

Question Stats:

58% (02:04) correct 42% (01:45) wrong based on 31 sessions

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A certain number of books are to be divided by students. If the number of the books is less than 50, how many books are
there?
(1) If the books are evenly divided by 7 students, 3 books will be remained.
(2) If the books are evenly divided by 4 students, 2 books will be remained.



A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Originally posted by MBA20 on 21 Mar 2019, 10:00.
Last edited by MBA20 on 21 Mar 2019, 10:44, edited 1 time in total.
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Re: A certain number of books are to be divided by students. If the number  [#permalink]

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New post 21 Mar 2019, 10:15
If the question is rephrased, it’s a simple “MULTIPLE OF A NUMBER” question.
If n is less than 50, n=?
Statement 1: if n is divided by 7, remainder is 3.
Statement 2: if n is divided by 4, reminder is 2.

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Re: A certain number of books are to be divided by students. If the number  [#permalink]

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New post 21 Mar 2019, 10:28
1
Statement 1: Insufficient
Total number of books can MULTIPLE numbers.
N=3,10,17 ........
(No UNIQUE number is found)

Statement 2: Insufficient
Total number of books can be a lot of numbers.
N=2,6,10 ........
(No fixed number is found)

Combining both statements
If common number found from both statements is 10.
TO FIND OUT SECOND COMMON NUMBER THAT SATISFIES STATEMENT 1 & 2, ADD LCM OF TWO GIVEN MULTIPLES WITH FIRST COMMON NUMBER.

Here,
First common number that satisfies both statements=10.
LCM of 2 MULTIPLES (4,7)=28.
So, SECOND common number that satisfies both statements=10+28=38.

So, possible number of total books (n)=10 or 38 (both are less than 50).

My answer is E.

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Re: A certain number of books are to be divided by students. If the number  [#permalink]

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New post 21 Mar 2019, 10:38
From S1:

When n is divided by 7, the remainder is 3.
n can be 10,17,24...45.
Hence Insufficient.

From S2:

When n is divided by 4, the remainder is 2.
n can be 6,10,14,....46
Hence Insufficient.

Combining both:
n can be 10 or 38.
Insufficient.

E is the answer.
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Re: A certain number of books are to be divided by students. If the number   [#permalink] 21 Mar 2019, 10:38
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