Bunuel wrote:
For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value?
A. a/100
B. (a+b)/(100+b)
C. (a+c)/(100+c)
D. (a+b+c)/(100+b+c)
E. The answer cannot be determined from the information provided.
a, b, c = Pos INTs
a < b < c < 100
Let's test numbers, Let try a =1, b =2, & b =3;
so we have
A. a/100 -------------------> 1/100
B. (a+b)/(100+b) ---------> 3/102
C. (a+c)/(100+c) ---------> 4/103
D. (a+b+c)/(100+b+c) ---> 5/105
E. The answer cannot be determined from the information provided.[/quote]
Let's try another integer values: a =97, b =98, c =99
A) 97/100 B) 195/198 C) 196/199 D) 294/297
Since option D has the highest numerator and highest denominator, and the denominator of each option is greater than the numerator by the same value, option D has the greatest value.
Now, assuming at this stage you need to compare each option against the other and you have to deal with big values, here's a shortcut i just found (hope, I'm right
):
For instance, let's check which is bigger, A or B: A) 97/100 vs. B) 195/198 ----> A) 198*97 vs B) 195*100,
just compare the positive differences of the multiplying figures and the option with the lower difference is likely to be bigger.
That is, since 195 - 100 = 97 is less than 199 - 97 = 102, option B is bigger (check!)
For B & C: B) 195/198 vs C) 196/199 ----> B) 199*195 vs. C) 198*196 ----> 199 - 195 = 4 > 198 - 196 = 2, option C is bigger
For C & D: C) 196/199 vs. D) 294/297 ----> C) 297*196 vs. 294*199 ----> 297 - 196 = 201 > 294 - 199 = 195, option D is bigger
Answer: D