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If 41 is a factor of y which of the folllowing is divisible
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01 Oct 2018, 16:01

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If \(41\) is a factor of positive integer \(y\), which of the following MUST be divisible by \(y\)?

Indicate all possible values.

A. \(82y+82\)

B. \(41y\)

C. \(41+y\)

D. \(y/41\)

Indicate all possible values.

A. \(82y+82\)

B. \(41y\)

C. \(41+y\)

D. \(y/41\)

Re: If 41 is a factor of y which of the folllowing is divisible
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10 Jun 2019, 07:39

if y=82, then how can we divide (41+y) by y ?

As 41 is a factor of y, so y can be greater than or equal to 41, right?

I have little confusion about the option 'C'.

Can Somebody please clarify the issue? thank you.

As 41 is a factor of y, so y can be greater than or equal to 41, right?

I have little confusion about the option 'C'.

Can Somebody please clarify the issue? thank you.

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Re: If 41 is a factor of y which of the folllowing is divisible
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10 Jun 2019, 08:54

1

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jelal123 wrote:

if y=82, then how can we divide (41+y) by y ?

As 41 is a factor of y, so y can be greater than or equal to 41, right?

I have little confusion about the option 'C'.

Can Somebody please clarify the issue? thank you.

As 41 is a factor of y, so y can be greater than or equal to 41, right?

I have little confusion about the option 'C'.

Can Somebody please clarify the issue? thank you.

Absolutely!

Choice C can be factored to prove that 41 + y will always be divisible by 41, since we know that y is a multiple of 41.

Therefore, we can rewrite y as 41x and the expression in choice C as 41 + 41x.

Now, factor 41 from the quantity to determine that 41(1 + x).

So, as you can see no matter what is plugged in as a factor of 41, the full expression will be divisible by the 41 that is to be multiplied by the quantity (1 + x).

Hope this helps!

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Re: If 41 is a factor of y which of the folllowing is divisible
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10 Jun 2019, 09:06

1

sandy wrote:

If \(41\) is a factor of positive integer \(y\), which of the following MUST be divisible by \(y\)?

Indicate all possible values.

A. \(82y+82\)

B. \(41y\)

C. \(41+y\)

D. \(y/41\)

Indicate all possible values.

A. \(82y+82\)

B. \(41y\)

C. \(41+y\)

D. \(y/41\)

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

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Re: If 41 is a factor of y which of the folllowing is divisible
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10 Jun 2019, 09:09

1

jelal123 wrote:

if y=82, then how can we divide (41+y) by y ?

As 41 is a factor of y, so y can be greater than or equal to 41, right?

I have little confusion about the option 'C'.

Can Somebody please clarify the issue? thank you.

As 41 is a factor of y, so y can be greater than or equal to 41, right?

I have little confusion about the option 'C'.

Can Somebody please clarify the issue? thank you.

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

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Joined: **10 Apr 2015 **

Posts: **6218**

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Re: If 41 is a factor of y which of the folllowing is divisible
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10 Jun 2019, 09:10

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

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Re: If 41 is a factor of y which of the folllowing is divisible
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10 Jun 2019, 09:19

1

Expert Reply

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

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Re: If 41 is a factor of y which of the folllowing is divisible
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10 Jun 2019, 09:43

1

MyGuruStefan wrote:

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.

Re: If 41 is a factor of y which of the folllowing is divisible
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11 Jun 2019, 01:29

Expert Reply

Thank you @GreenlightTestPrep and @MyGuruStefan

Regards

Regards

Re: If 41 is a factor of y which of the folllowing is divisible
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11 Jun 2019, 06:30

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.

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.

Re: If 41 is a factor of y which of the folllowing is divisible
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26 Jul 2024, 20:59

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If 41 is a factor of y which of the folllowing is divisible [#permalink]

26 Jul 2024, 20:59
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