If m and n are distinct positive integers such that n is divisible by

Question

If m and n are distinct positive integers such that n is divisible by m, and m is divisible by 3, which of the following statements must be true?

I. n is divisible by 3
II. n = 3m
III. n has more than 3 positive factors

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III

callmeDP · Answer

If m and n are distinct positive integers such that n is divisible by m, and m is divisible by 3, which of the following statements must be true?

I. n is divisible by 3
II. n = 3m
III. n has more than 3 positive factors

Let, 
 m = k*3   (where K is a natural number)

n = Q*m  ( where Q is an integer greater than 1, as n and m are distinct )

thus, n = Q*(k*3) ...  thus, I satisfies  (by plugging m)

n = 3*m or n = 5*m...  thus II does not satisfies

assume Q=3, m=3 and k=1, thus n =  3^2

and n has 3 factors ....  III doesnot satisfies.

IMO A only I

dushyanta · Answer

IMO (A)

if m and n are distinct positive integers such that n is divisible by m, and m is divisible by 3, which of the following statements must be true?

n is divisible by m, and m is divisible by 3
=>(1) m=3a
=>(2) n=mb=3ab

I. n is divisible by 3
As per (2) - always true

II. n = 3m
As per 2, b could be anything.. for e.g. 
n = 6 and b = 3
n=18 and b = 6
- Not always true

III. n has more than 3 positive factors

if m=3 => 
1) n=6
2) 369963. anything
- not always true

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III

CEdward · Answer

I think the answer is A.

Statement 1 - n/3
As a general rule, any integer x that is divisible by another integer y is also divisible by the factors of integer y.
e.g. n = 6, m = 3 YES
e.g. n = 9, m = 3 YES

Statement 2 - n = 3m
Let's take test case from statement 1.
e.g. n = 6, n = 3 --> 6/3 = 2 SO NO

Statement 3 - n has more than 3 positive factors
e.g. n = 6 ; positive factors are 1, 2, 3, 6 YES
e.g. n = 9 ; positive factors are 1, 3, 9 NO

TarunKumar1234 · Answer

If m and n are distinct positive integers such that n is divisible by m, and m is divisible by 3, which of the following statements must be true?

I. n is divisible by 3
II. n = 3m
III. n has more than 3 positive factors

Let,
m = k*3 (where K is a natural number)

n = Q*m ( where Q is an integer greater than 1, as n and m are distinct )

thus, n = Q*(k*3) ... thus, I satisfies (by plugging m)

n = 3*m or n = 5*m... thus II does not satisfies

assume Q=3, m=3 and k=1, thus n = \(3^2\)

and n has 3 factors .... III doesnot satisfies.

IMO A only I

akadiyan · Answer

If m and n are distinct positive integers such that n is divisible by m, and m is divisible by 3, which of the following statements must be true?

I. n is divisible by 3
If m is divisible by 3, then since n is divisible by m , we know that n is divisible by 3. so statement I is true.

II. n = 3m
If m = 3, n =9 , and satisifies the condition n = 3m
If m = 3, n = 6, n is divisble by m but n is Not equal to 3m
Statement II is  NOT always true

III. n has more than 3 positive factors
If m =3 and n =6, then n has 4 (>3) positive factors 
Consider m=3 and n=9, then n has 3 positive factors 
Statement III is  NOT always true

Only Statement I is true always

Ans  A

bumpbot · Answer

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If m and n are distinct positive integers such that n is divisible by

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If m and n are distinct positive integers such that n is divisible by

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