For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value?

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

Source: Veritas Prep

Let's analyze each option one by one.

A. a/100: Since we know that a < 100, the value of a/100 < 1. We hold this option for further analysis.

B. (a+b)/(100+b): From option A, we know that a/100 < 1 and in the option B, we see that b > a is added to both numerator and denominator, so, the proportion of increment [(b/a)*100%] in the numerator (a) is greater than that [(b/100)*100%] in the denominator (100). Thus, (a+b)/(100+b) > a/100.

Option A is ruled out.

C. (a+c)/(100+c): Since c > b, the proportion of increment [(c/a)*100%] in the numerator (a) is greater than that [(c/100)*100%] in the denominator (100). Thus, (a+c)/(100+c) > (a+b)/(100+b).

Option B is ruled out.

D. (a+b+c)/(100+b+c): On similar reasoing, we can conclude that (a+c)/(100+c) > (a+b+c)/(100+b+c).

The correct answer: D

Hope this helps!

-Jay
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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