Problem Solving

What number is 108 more than two-thirds of itself?

A. 72
B. 144
C. 162
D. 216
E. 324

E

AbeNeedsAnswers wrote:What number is 108 more than two-thirds of itself?

A. 72
B. 144
C. 162
D. 216
E. 324

We can PLUG IN THE ANSWERS.
When 108 is added to 2/3 of the correct answer choice, the resulting sum will be equal to the answer choice.

B: 144
(2/3)(144) = (2)(48) = 96.
96 + 108 = 204.
Here, the resulting sum is 60 greater than the answer choice.
Eliminate B.

D: 216
(2/3)(216) = (2)(72) = 144.
144 + 108 = 252.
Here, the resulting sum is 36 greater than the answer choice.
Eliminate D.

Notice the PATTERN implied by the portions in blue:
As the answer choice gets BIGGER, the resulting sum draws CLOSER to the answer choice.
Thus, for the resulting sum to be EQUAL to the answer choice, a value greater than D is needed,

The correct answer is E.

Algebraic solution:
Since adding 108 to 2/3 of the number must yield the number itself, we get:
108 + (2/3)x = x
108 = (1/3)x
324 = x.

The correct answer is E.