CAT Practice : Exponents and Logarithms

Value of x

Q.13: 46+12+18+24+…+6x = (0.0625)-84, what is the value of x?
1. 7
2. 6
3. 9
4. 12

Choice A. 7

Detailed Solution

Take right side expression
(0.0625)-84 = $\frac{1}{16}$-84

= (4-2)-84
= 4168

Take left side expression
46+12+18+24+…+6x = 46(1+2+3+4+x)
= 46 * 4(1+2+3+4+x)
= 46 * 4$\frac{x(x+1)}{2}$ (using the formula for sum of natural numbers from 1 to x)

Equating left and right side expresssions, we get 46 * 4$\frac{x(x+1)}{2}$ = 4168
Or 46 * 4$\frac{x(x+1)}{2}$ = 46*28
==> $\frac{x(x+1)}{2}$ = 28
or x(x+1) = 56

Solving for x we get, x = 7

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