OG 11 PS #37.
If a positive integer n is divisible by both 5 an 7, then n must also be divisible by which of the following?
I. 12
II. 35
III. 70
(A) None (B) I only (C) II only (D) I and II (E) II and III
I understand the OG explanation (Since 5 and 7 are prime numbers, if n is divisible by both, then n must also be divisible by 35...and they look for numbers that will be factor of 35). However, I have been referring to MGMAT guide and they have a different concept. I solved it following the below method...following MGMAT number properties...where did I understand it wrong?
To check divisibility, first step prime factorization.
12 -> 2, 2, 3
35 -> 5, 7
70 -> 2, 5, 7
n is divisible by 5 and 7...so the other number should have 5 and 7 in them...then they could also be factors of n. So, from this concept, 35 and 70 could be factors (I chose E, but the OA is C).
When I read OG explanation, I understand it....but it conflicts with the above concept. Need some help understanding the basics here!
Thanks in advance.
If a positive integer n is divisible by both 5 an 7, then n must also be divisible by which of the following?
I. 12
II. 35
III. 70
(A) None (B) I only (C) II only (D) I and II (E) II and III
I understand the OG explanation (Since 5 and 7 are prime numbers, if n is divisible by both, then n must also be divisible by 35...and they look for numbers that will be factor of 35). However, I have been referring to MGMAT guide and they have a different concept. I solved it following the below method...following MGMAT number properties...where did I understand it wrong?
To check divisibility, first step prime factorization.
12 -> 2, 2, 3
35 -> 5, 7
70 -> 2, 5, 7
n is divisible by 5 and 7...so the other number should have 5 and 7 in them...then they could also be factors of n. So, from this concept, 35 and 70 could be factors (I chose E, but the OA is C).
When I read OG explanation, I understand it....but it conflicts with the above concept. Need some help understanding the basics here!
Thanks in advance.
