Is n divisible by 11 with no remainder?

Question

(1) n is divisible by m with integer result
(2) m is divisible by 5.5 with integer result

A. 1 alone, not 2 alone
B. 2 alone, not 1 alone
C. 1 and 2 together (need both)
D. 1 alone or 2 alone
E. 1 and 2 together are not sufficient

What do you think the answer is?

I think…

it is

E because if n is 5.5, it can be divisible by 5.5 but not divisible by 11. But the answer sheet seems to disagree with me.

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Archit3110 · Answer

Target is
11 factor of n

(1) n is divisible by m with integer result

M is factor of n
M may or may not be factor of 11
Insufficient

#2
 m is divisible by 5.5 with integer result

Value of M is a multiple of 5.5 or say 5&11
no info about N
Insufficient

From 1 &2
We can say since M is multiple of 5 &11 
So N has to be multiple of 11 as well
Sufficient Option C

sldisek783 · Answer

We know m is a multiple of 5.5, not a multiple of 11. If m is 5.5 and n is also 5.5, n won’t be divisible by 11.

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dzanum11 · Answer

A, B, D can be easily eliminated as either options alone do not provide any sufficient information. 
To decide between C and E, we can use the simple equation to get to the answer

(1) n is divisible by m with integer result
thus, n = m*k1 where k1 is some integer --- 1

(2) m is divisible by 5.5 with integer result
thus, m = 5.5*k2 where k2 is some integer -- 2

Combining both 1 and 2 we get

n = m*k1
 = 5.5*k2*k1
 = 5.5*k3 where k3 = k1*k2 and thus k3 is also an integer

Now, n/11 = 5.5*k3/11
 = (5.5/11) * k3

Since 11 divides 5.5 without leaving any remainder, 11 divides n without leaving any remainder

Thus Correct answer is C

sldisek783 · Answer

Oh I finally understood. The question asks if n is divisible by 11 with no remainder.. not if it is divisible by 11 with an integer result. Thanks.

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Tukkebaaz · Answer

This one has to be E. So ASSUME the # is 5.5/5 (is it divisible with no remainder)? or if we have 5.5/10 (is it divisible with no remainder)? Based on this logic, you can see where I am heading: Is 5.5/3, 7 or 8 divisible with no remainder. I can write say 1.8888 till infinity to claim it is divisible without a remainder. Basic concept of remainder is: x/n = x when xn where k is any +ve integer. I have never come across such a Question in the OG so doubt the credibility of the OA. I would stick with my answer of E here and wont overthink this question. Hope this helps

Is n divisible by 11 with no remainder?

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