If i and d are integers, what is the value of i?
(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(2) The quotient when i is divided by (d+2) is d
What is the best way to tackle this kind of DS problems?
It can be done algebraically but picking numbers would probably be faster/easier.If i and d are integers, what is the value of i?
(1) The remainder when i is divided by (d+2) is the same as when i is divided by d --> let the remainder be 0 to simplify the case. So, we have that i is divisible by both d and d+2 --> if d=1 then d+2=3 and i can be ANY multiple of 3. Not sufficient.
(2) The quotient when i is divided by (d+2) is d --> let the remainder be 0 to simplify the case. Now, if d=2 then d+2=4, so i=8 (8/4=2: i=8 divided by d+2=4 yields the quotient of d=2) but if d=3 then d+2=5 and i=15 (15/5=3). Not sufficient.
(1)+(2) Notice that two values of i from (2) works for (1) as well: 8 is divisible d=2 and d+2=4 and 15 is divisible by d=3 and d+2=5.
Hope it's clear.
Can this somehow be done algebraically or conceptually
I had that first i/ (d+2) and i/d, yield the same remainder, but if both d and d+2, are larger than i, then 'i' could just take any value as the remainder.
Statement 2 we have that i = (d)(d+2) + r
Now, if we replace in first term, we have that (d)(d+2) + r / (d+2), gives d as quotient but still we are left with r as a remainder of d+2. while we also know that i/d gives the same remainder. Here we learn that 'i' must be greater than d+2 since if gives quotient d. However, we still have no clue as to what remainder the division can yield
Both together, i>d, i = d(d+2) + r, and 'r' here is equal to the remainder of i/d = d(d+2) / d.
So r/d = r/d+2, but still no information on the remainder
Hence answer is E