RahulVohra
I am not able to understand how you have reached to the answer..... here people don't explain but write down some vague statements.... which we are not able to understand.... you can call me dimwit..... but explain it properly..... reasoning behind each and every step.....
Regards
Rahul Vohra
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
Would suggest you to go through
Math Theory once so that it may help you comprehend certain concepts, if that's the issue you're facing. Best way to ask when you don't understand certain explanation is to highlight the statement of the explanation, share what you didn't understand and request to explain it with more clarity.
Regarding this question, since y is the smallest prime factor of (3 Δ 47) + 2, (3 Δ 47) + 2 should be divisible by y
Now, \(3 Δ 47 = 47*45*43*41*39*...........*7*5*3\)
Since (3 Δ 47) + 2 should be divisible by y: \(\frac{47*45*43*41*39*...........*7*5*3}{y}\) + \(\frac{2}{y}\) = integer
y cannot be any prime number from 47 to 3, as \(\frac{2}{y}\) won't be an integer and y cannot be 2 as \(\frac{47*45*43*41*39*...........*7*5*3}{y}\) won't be an integer. y also cannot be 48, 49, or 50 since they are not prime numbers.
Therefore,
y > 50Hope it helps.