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.)-66, what is the value of x?

  1. 3
  2. 6
  3. 7
  4. 11

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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.)-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.) must be some form of 3a.
With little hit and trial, you may find = \\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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