Lesson: Choosing Good Numbers

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by choosing 1 you say that 1/5 gives remainder 1...i am not able to understand it as 1/5 is 0.2 and no remainder.please explain me.
gmat-admin's picture

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 a doubt of one example in good numbers video. it is a data sufficiency example. that question is k+5/k is an integer?? in that question 1/5 leaves remainder 1 u said.. how is it possible?? can u explain again that question??
gmat-admin's picture

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 divided by 5", shouldn't be 4? May be the context is “When 5 is divided by K”?
gmat-admin's picture

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 question in the video, we can rephrase the target question to ask : 'is k a multiple of 5?'. Similarly for the last question, we can rephrase the target question to ask:'Does k equal 2?' Please let me know if my approach is correct. Thanks
gmat-admin's picture

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?

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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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