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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