Question : Directions: The sum of a number's square, its cube, and its next number's cube is 205. What is the number?
Option 1: 3
Option 2: 5
Option 3: 4
Option 4: 6
Correct Answer: 4
Solution : Given: x 2 + x 3 + (x + 1) 3 = 205
By using the above equation let's check the option – First option: 3; 3 2 + 3 3 + (3 + 1) 3 = 9 + 27 + 64 = 100 ≠ 205 Second option: 5; 5 2 + 5 3 + (5 + 1) 3 = 25 + 125 + 216 = 366 ≠ 205 Third option: 4; 4 2 + 4 3 + (4 + 1) 3 = 16 + 64 + 125 = 205 Fourth option: 6; 6 2 + 6 3 + (6 + 1) 3 = 36 + 216 + 343 = 595 ≠ 205
So, the sum of the 4's square, its cube, and its next number's cube is 205. Hence, the third option is correct;
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