Data Sufficiency

If z is a positive integer, is Z+1 is a factor of 105?

1. Z is a factor of 20.

2. 10 is a factor of z.

Factors of 105 are 1, 3,5,7,15,21,35,105.

Statement 1:
Z= Factors of 20 = 1,2,4,5,10,20
If z =4 then Z+1 is a factor of 105
But if Z= 5 then Z+1 is not a factor of 105

therefore not sufficient.

Statement 2:

10 is a factor of Z

In this case Z could be 20 then 21 is a factor of 105
But if Z =10 then 11 is not a factor of 105

therefore not sufficient.

Statement 1+2

Z= 1,2,4,5,10,20

And 10 is a factor of Z

therefore Z has to be either 10 or 20 then 11 is not a factor of 105 and 21 is a factor of 105
so not sufficient.

According to me the Answer is E,

I dont have the IMO for it, is E the right answer?

Hi Swati,

E is the right answer. The explanation is correct.

Thanks!