Question : Directions: Two numbers are named as Number A and Number B. The sum of Number A, its square, and its cube is 399. The sum of Number B, its square, and its cube is 819. What would be the square of the number obtained by adding numbers A and B?
Option 1: 256
Option 2: 289
Option 3: 225
Option 4: 324
Correct Answer: 256
Solution :
Given:
(I) The sum of Number A, its square, and its cube is 399
A + A
2
+ A
3
= 399
7 + 49 + 343 = 399
Thus, A = 7
(II) The sum of Number B, its square, and its cube is 819
B + B
2
+ B
3
= 819
9 + 81 + 729 = 819
Thus, B = 9
The square of the number obtained by adding Number A and Number B
( A + B )
2
= ?
( 7 + 9 )
2
= (16)
2
= 256
So, the number is 256. Hence, the first option is correct.
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