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## Comment on

Choosing Good Numbers## by choosing 1 you say that 1

## I can see how you might think

I can see how you might think that. However, if we think about remainders in the way you suggest, there would never been any remainders. For example, we'd just say that 7/2 = 3.5 (no remainder), when in fact, 2 divides into 7 three times with remainder 1.

Likewise, 1 divides into 5 zero times, with remainder 1.

For more on this, watch the video on remainders: https://www.gmatprepnow.com/module/gmat-integer-properties/video/842

## hi.. this is sujan and i have

## Good question.

Good question.

Some background information//examples first:

a) 3 divides evenly into 6 two times

b) 5 divides evenly into 20 four times

c) 2 divides evenly into 14 seven times

If a number does NOT divide evenly into another number then we have a REMAINDER.

Some examples:

d) 3 does not divide evenly into 17, so we have a remainder. 3 divides into 17 five times with remainder 2.

So, we can write: 17 = (5)(3) + 2

e) 2 does not divide evenly into 23, so we have a remainder. 2 divides into 23 eleven times with remainder 1.

So, we can write: 23 = (11)(2) + 1

Now onto your question....

5 does not divide evenly into 1, so there must be a remainder. What is that remainder?

5 divides into 1 ZERO times with remainder 1.

So, we can write: 1 = (0)(5) + 1

More here: https://www.gmatprepnow.com/module/gmat-integer-properties/video/842

## In the video, "When K is

## Hi linnn01,

Hi linnn01,

I'm not sure what you are asking.

Are you suggesting that (for statement 1) k could equal 4?

If so, then this is not correct, because 4 divided by 5 is 0 with remainder 4.

Please let me know if this is what you meant.

## Ref. to the second to last

## Your post: We can rephrase

Your post: We can rephrase the target question to ask : 'Is k a multiple of 5?'

CLOSE!!

The target question: Is (k + 5)/k an integer?

The expression will be an integer if k is a multiple of 5 OR if k = 1

So, the rephrased target question could be "Is k EITHER a multiple of 5 OR equal to 1?

----------------------------------

Your post: Similarly for the last question, we can rephrase the target question to ask:'Does k equal 2?

No, this would not be a correct rephrasing of the target question.

The target question: Is (k+1)/2 an integer?

In order for (k+1)/2 to be an integer, it must be the case that (k+1) is EVEN.

If (k+1) is EVEN, then it must be the case that k is ODD.

So, we can rephrase the target question to ask "Is k odd?"

Cheers,

Brent

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