CAT 2017 Question Paper | Quants Slot 2

CAT Questions

Type in the answer or TITA type questions are a very common part of the CAT Question Paper. Not comfortable with questions that do not offer you 4 options to choose from ? Do you get confused and worried whether your TITA question is correct or incorrect ? Don't Worry! Incorporate CAT previous year paper in your online preparation strategy and ace these question types! Start right away with this beautiful question from Exponents and Logarithms! Make sure you try your hands on it before moving on to the solutions!

Question 26 : If log(2^a × 3^b × 5^c) is the arithmetic mean of log(2² × 3³ × 5), log(2⁶ × 3 × 5⁷), and log(2 × 3² × 5⁴), then a equals [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Exponents and Logarithms

3log(2^a × 3^b × 5^c) = log(2² × 3³ × 5) + log(2⁶ × 3 × 5⁷) + log(2 × 3² × 5⁴)
We have to find only the value of a
2^3a × 3^3b × 5^3c = (2² × 2⁶ × 2¹) × (3³ × 3 × 3²) × (5 × 5⁷ × 5⁴)
2^3a = 2⁹
3a = 9
a = 3

The question is "If log(2^a × 3^b × 5^c) is the arithmetic mean of log(2² × 3³ × 5), log(2⁶ × 3 × 5⁷), and log(2 × 3² × 5⁴), then a equals [TITA]"

Hence, the answer is 3