Integers

Hi guys can you help me to understand the attached question? Why the answer is A)...
Thanks,
ES

(A+B)=i*(C+D) where i is integer as much as possible; (A+B) the largest possible is (9+8)=17 prime. Next large one to these numbers' sum is (9+7)=16; 16=i*(C+D) ---> i is maximized when (A+B) is minimized. So (A+B) can be (1+3)=4 and 16/4=4 OR i=4. Let's try another pair of numbers, as we can also get i=5, when (A+B)=(1+2)=3 and (C+D)=15 or (C+D)=(8+7)=(9+6). Pick D

diehard_gmat wrote:Letters A, B, C, and D represent four different digits selected from 1, 2, ..., 9. If (A+B)/(C +D) is an integer that is as large as possible, what is the value of A + B?

A) 3
B) 5
C) 11
D) 15
E) 17

@monge1980: it says 450y=n^3 correct? Also n,y>0
So prime factorization of 450=2^1*3^2*5^2 and we know that 450y is n^3 where n is +ve integer. The only way 450y can be equal to n^3 is when the missing parts in 450 itself can be represented as (...)^3 OR put this 450*(2^2*3^1*5^1). So we must have at least y/(2^2*3^1*5^1) condition, where this ratio is both +ve and integer (at least). Otherwise 450y can't be equal to n^3 or a^3, actually can't be derived the root power of 3

2^2*3^1*5^1 is the part of y here, which completes 410 and help our statement 410y=n^3, because Root^3(410) isn't good, and we look for possible Root^3(410y)...

ok?

monge1980 wrote:Hi guys can you help me to understand the attached question? Why the answer is A)...
Thanks,
ES

Thanks!!