# CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

###### CAT Questions | Logarithms and Exponents | Logarithm - Identities

The question is from Log and Exponents. We can solve this easily using log identities. We need to find out the value of x from the given equation. With every extra hour you log in for this topic, it becomes exponentially simpler. CAT Logarithms and Exponents is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 10: If 33 + 6 + 9 + ……… 3x = (0.$$overline{037}$)-66, what is the value of x? 1. 3 2. 6 3. 7 4. 11 ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Logs and Exponents: Application of Basic Identities of Logarithms! First of all, let us define the xth term. 33+6+9+……….3x =$0.$$overline{037}$)-66 Whenever you encounter a distinctive number such as one given in R.H.S of above equation, always try to find its significance in the context of question. In this case L.H.S has 3a, so$0.$$overline{037}$) must be some form of 3a. With little hit and trial, you may find $0.$overline{037}$ = \\frac{1}{27}\\$ = $\frac{1}{3^3}\\$ = 3-3 33$1 + 2 + 3 + ...X) = 3 -3 * -66
=> 33 * 3x(x+1)/2 = 33*66
$$frac{x$x+1$}{2}$ = 66 x$x+1) = 132
Solving this equation for x > 0, we get x = 11.
You should directly be able to see that 132 = 11 * 12 => x= 11
And avoid wasting time solving the complete equation.

The question is "what is the value of x?"

##### Hence, the answer is "11".

Choice D is the correct answer.

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