If 41 is a factor of y, we can also say that y is a multiply of 41
Or we could say that y = 41k for some integer k

Now let's check each answer choice....

A. 82y + 82 = 82(41k) + 82
Is 82(41k) + 82 divisible by 41k? NO.
We know that 82(41k) is divisible by 41k, but it need not be the case that 82 is divisible by 41k
For example, if k = 3, then y = 41(3) = 123, and 82 is NOT divisible by 123

OR, here's another way to put it.
If 41 is a factor of y, then y COULD equal 123.
This means 82y + 82 = 82(123) + 82 = 10,168 and 10,168 is NOT divisible by 123

Statement A need not be true


B. 41y = (41)(41k)
Is (41)(41k) divisible by 41k?
YES
41k divides into (41)(41k) 41 times

Statement B IS true


C. 41 + y = 41 + 41k
Is 41 + 41k divisible by 41k?
NO.
For example, if k = 3, then we can ask: Is 41 + 41(3) divisible by 41(3)?
Simplify to get : Is 164 divisible by 123?
NO.

Statement C need not be true

D. y/41 = 41k/41 = k
Is k divisible by 41k?
NO.
If k = 3, then 3 is not divisible by 41(3)

Statement DC need not be true

Answer: B

Cheers,
Brent

You are correct to say that statement C is false.
If y = 82, then answer choice C becomes 82 + 41 = 123
Is 123 divisible by y?
In other words, is 123 divisible by 82?
No.
So, statement C need not be true.

Cheers,
Brent

I have edited the original post to display the correct answer.

Oops, definitely read that question as divisible by 41 and not y... Read the full question carefully, folks! Thanks for the full explanation.

You're not alone

Based on the original official answer, the original poster also misread y as 41.

Thank you @GreenlightTestPrep and @MyGuruStefan

Regards

The Option 'C' CAN BE true, but not MUST be true,
because as 41 is a factor of y,
So, 41x=y, here x can be 1,2,3 ... to find a positive integer y. So, let's say x=1, then y=41 [ a factor can be equal to its multiple 2*1=2.]
If we say, x=1, then (41+y)/y leads to 41/41+ y/y
as y=41, So, the result is 1+1, i.e. the condition of divisibility holds .
It's my understanding!
please correct me for my better understanding . Regards.

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