BTGmoderatorDC wrote: ↑Sun May 31, 2020 5:50 pm
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.
OA
D
Solution:
We can let a = 1, b = 2 and c = 3, we see that the value of the answer choices would be:
A) 1/100
B) 3/102
C) 4/103
D) 6/105
Since the denominators are really about the same, we see that choice D has the largest value. (Notice that if all the denominators are 100, their values would be 0.01, 0.03, 0.04, and 0.06, respectively.)
Now if we let a = 97, b = 98 and c = 99, the value of the answer choices would be:
A) 97/100
B) 195/198
C) 196/199
D) 294/297
Although each answer choice has a value approximately equal to 1, we see that each numerator is 3 less than its denominator. In that case, the fraction with the largest denominator would be the one that has the largest value. So again, choice D has the largest value.
Answer: D
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