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beat this: number properties

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beat this: number properties

by sachindia » Fri Nov 02, 2012 7:50 pm
If k is a +ve integer, is (k+1)/k an integer?

1)When k is divided by 5, 1 is the remainder.


1 is sufficient or insufficient ?

OA: Insufficient
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Sach
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Nov 02, 2012 8:06 pm
sachindia wrote:If k is a +ve integer, is (k+1)/k an integer?

1)When k is divided by 5, 1 is the remainder.


1 is sufficient or insufficient ?

OA: Insufficient
Target question: Is (k+1)/k an integer?

Notice that (k+1)/k = k/k + 1/k = 1 + 1/k

So, we can rephrase the target question as: Is 1 + 1/k an integer?

Since 1 is already an integer, we can simplify the target question even further: Is 1/k an integer?

Statement 1: When k is divided by 5, 1 is the remainder.
There several possible values of k. Here are two:
Case a: k = 1, in which case 1/k is an integer
Case b: k = 6, in which case 1/k is not an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

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by Brent@GMATPrepNow » Fri Nov 02, 2012 8:10 pm
When it comes to remainders, we have a nice rule that says:

If N divided by D, leaves remainder R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

So, if k divided by 5 leaves a remainder of 1, then the possible values of k include 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), etc

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by sachindia » Fri Nov 02, 2012 8:23 pm
Amazing, Thanks a lot, Brent! This Qs is indeed from your Videos..

I never know R could also be the posssible value of N.

eg 1 divided by 5 will yield 0.2 .. if we go for decimal :D
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by Brent@GMATPrepNow » Fri Nov 02, 2012 8:28 pm
sachindia wrote:Amazing, Thanks a lot, Brent! This Qs is indeed from your Videos..

I never know R could also be the posssible value of N.

eg 1 divided by 5 will yield 0.2 .. if we go for decimal :D
Let's work backwards:
5 divides into 16 three times with remainder 1 [notice that (3)(5)+1=16]
5 divides into 11 two times with remainder 1 [notice that (2)(5)+1=11]
5 divides into 6 one time with remainder 1 [notice that (1)(5)+1=6]
5 divides into 1 zero times with remainder 1 [notice that (0)(5)+1=1]

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