CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

The question is from Log and Exponents. This is about Quadratic Equations. Our task is to find out the correct statements. 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 3: If 2^2x+4 – 17 × 2^x+1 = –4, then which of the following is true?

1. x is a positive value
2. x is a negative value
3. x can be either a positive value or a negative value
4. None of these

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: Carving a quadratic equations from an Exponents question is very useful.

2^x+4 – 17 * 2^x+1 = – 4
=> 2^x+1 = y
2^2x+2 = y²
2²(2^2x+2) – 17 * 2^x+1 = –4
4y² – 17y + 4 = 0
4y² – 16y – y + 4 = 0
4y (y – 4) – 1 (y – 4) = 0
y = \\frac{1}{4}\\) or 4
2^x+1 = \\frac{1}{4}\\) or 4
=> x + 1 = 2 or – 2
x = 1 or – 3

The question is "which of the following is true?"

Hence, the answer is "x can be either a positive value or a negative value".

Choice C is the correct answer.