Question : Directions: When a number X is added to the double of its cube, the number 1467 is obtained. Find the value of X.
Option 1: 6
Option 2: 9
Option 3: 7
Option 4: 8
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Correct Answer: 9
Solution :
Let the number be X
X + 2(X)
3
= 1467
Let's check each option –
First option:
6; 6 + 2 × (6)
3
= 6 + 2 × 216
6 + 432 = 438
438
≠ 1467
Second option:
9; 9 + 2 × (9)
3
= 9 + 2 × 729
9 + 1458 = 1467
1467 = 1467
Third option:
7; 7 + 2 × (7)
3
= 7 + 2 × 343
7 + 686 = 693
693
≠ 1467
Fourth option:
8; 8 + 2 × (8)
3
= 8 + 2 × 512
8 + 1024 =1032
1032
≠ 1467
So, the required number is 9. Hence, the
second option
is correct.
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