Problem Solving

Is the integer n a multiple of 15?

1) n is a multiple of 20

2) n + 6 is a multiple of 3

Answer is C. Appreciatte a detailed explanation.

tutonaranjo wrote:Is the integer n a multiple of 15?

1) n is a multiple of 20

2) n + 6 is a multiple of 3

Answer is C. Appreciatte a detailed explanation.

To be divisible by 15 it must have factors 3 and 5

From 1 we know that n i divisble by 20 so it could be 20,40,80 or maybe 60
Thus n has factors 5 and 4 for sure and probably 3 but not known

From 2 we know that is divisble by 3 since (n+6)/3 = n/3 +6/3 and this is still a multiple
So n has a factor 3 for sure but we dont know if it has 5 as a factor.

Combining both, we get that n has factors 3, 4 and 5 thus ensuring that it is a multiple of 15

Neo2000 wrote:

tutonaranjo wrote:Is the integer n a multiple of 15?

1) n is a multiple of 20

2) n + 6 is a multiple of 3

Answer is C. Appreciatte a detailed explanation.

To be divisible by 15 it must have factors 3 and 5

From 1 we know that n i divisble by 20 so it could be 20,40,80 or maybe 60
Thus n has factors 5 and 4 for sure and probably 3 but not known

From 2 we know that is divisble by 3 since (n+6)/3 = n/3 +6/3 and this is still a multiple
So n has a factor 3 for sure but we dont know if it has 5 as a factor.

Combining both, we get that n has factors 3, 4 and 5 thus ensuring that it is a multiple of 15

1st stmt -> 20,40,60......

2nd stmt -> n+6 is a multiple of 3 -> n is a multiple of 3
for n = 54
n+6 = 60 (which is a multiple of 20 n 15 too)

This implies C is the answer.

I hope it explained the soln.

Keep Neo's method of solving in mind - it'll help on tons of other DS problems

( I'm not implying the other solutions are bad - just that Neo's solution is easily applicable to other problems )

What is the number??

There is not only one answer.
We just need to know that n is a multiple (or not) of 15 to answer the question.
It could be 0 or 60 or 120 or ...