The sum of x distinct integers greater than zero is less than 75.What is the greatest possible value of x?
A) 8
B) 9
C) 10
D) 11
E) 12
I combined tricks from multiple tricks (such as
Greenlight Test Prep - CMIIW).
First, since the answer choices are in ascending order. Pick Choice (C) 10 first as the middle point.
Sum of distinct integers from 1 to 10 = 10 x 11 / 2 = 55. Since the sum is less than 75 and the question is to find the
greatest possible value of x, we can eliminate Choice (A) 8 and Choice (B) 9 since the sum will be less than 55.
I test Choice (E) 12, the sum will be = 12 x 13 / 2 = 78. Choice (E) should be eliminated because the sum is greater than 75.
Choice (D) 11, the sum will be = 11 x 12 / 2 = 66. It is still less than 75 and greater than 55, thus the correct answer is Choice (D) 11.