Question 49 – ISRO-2007
April 16, 2024Question 1611 – ISRO CS 2015
April 16, 2024Question 188 – ISRO CS 2008
If (12x)3 = (123)x then the value of x is
Correct Answer: D
Question 19 Explanation:
Given, (12x)3 = (123)x
Since LHS has 3 as the base and RHS has ‘x’ base,
1 * 3*3 + 2 * 3 + x * 1 = 1 * x*x + 2 * x + 3
9 + 6 + x = x2 + 2x + 3
x2 + x – 12 = 0
x2 + 4x – 3x – 12 = 0
x( x + 4 ) – 3(x + 4) = 0
(x + 4)(x – 3) = 0
x = 3 and -4
But, both the values are infeasible.
Since LHS has 3 as the base and RHS has ‘x’ base,
1 * 3*3 + 2 * 3 + x * 1 = 1 * x*x + 2 * x + 3
9 + 6 + x = x2 + 2x + 3
x2 + x – 12 = 0
x2 + 4x – 3x – 12 = 0
x( x + 4 ) – 3(x + 4) = 0
(x + 4)(x – 3) = 0
x = 3 and -4
But, both the values are infeasible.
Alternative explanation :
According to the rules of number systems , the numbers present in a number system should not be greater than the base of the number system.
According to LHS , (12x)3 tells us that the value of x should be less than 3.
According to RHS , (123)x tells us that the value of x should be greater than 3 as largest digit in 123 is 3.
Therefore, any combination is not possible.
3
3 or 4
2
None of these
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