daviesj wrote:
If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50
(B) 30 ≤ y ≤ 50
(C) 10 ≤ y < 30
(D) 3 ≤ y < 10
(E) y = 2
(3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd.
Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are co-prime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1.
Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50.
Answer: A.
Similar question from GMAT Prep:
for-every-positive-even-integer-n-the-function-h-n-is-126691.htmlHope it helps.
I just wanted to undertsand in what case 2 can be a smallest prime factor. For Eg if the Q. said that the smallest prime in (3 Δ 47) + 1.Then, the no (3 Δ 47) + 1 will be odd+1=even. Can we say 2 will be the smallest prime in this case.
Also, 2 consecutive integers will also be co-prime and therefore none of the factors in (3 Δ 47) will be factors of (3 Δ 47) + 1.
Thanks for your reply to my queries earlier.