If a = \frac{28}{31}, b =\frac{29}{30} and c =\frac{31}{33}. Which of the following is true?
I. a+b > 2
II. b+c-a > 1
III. a + b^2 - c^2 > 1
(A) I only
(B) I and II
(C) II and III
(D) II only
(E) I, II and III
I didn't understand really how to do this in 2-3 minutes. Is there any quick way to solve this or similar problems? Even creating common denominators for this to figure out II. took me a long time. The only statement I could evaluate quickly was I. as all fractions are smaller than 1 and therefore the sum of a+b is obviously not larger than 2. But I struggled with II. and III. Numerators and denominators are all "around 30". So maybe the trick lies in doing something with that information, or is that on purpose as a distraction? Thanks.![]()
I. a+b > 2
II. b+c-a > 1
III. a + b^2 - c^2 > 1
(A) I only
(B) I and II
(C) II and III
(D) II only
(E) I, II and III
I didn't understand really how to do this in 2-3 minutes. Is there any quick way to solve this or similar problems? Even creating common denominators for this to figure out II. took me a long time. The only statement I could evaluate quickly was I. as all fractions are smaller than 1 and therefore the sum of a+b is obviously not larger than 2. But I struggled with II. and III. Numerators and denominators are all "around 30". So maybe the trick lies in doing something with that information, or is that on purpose as a distraction? Thanks.