Bodhee Prep-CAT Online Preparation

CAT 2019 Quant Question with Solution 1

Question:
If m and n are integers such that $(\sqrt{2})^{19} 3^{4} 4^{2} 9^{m} 8^{n}=3^{n} 16^{m}(\sqrt[4]{64})$ then m is

  1. $-20$
  2. $-12$
  3. $-24$
  4. $-16$
Show Answer

Correct Answer: Option: 2

$(\sqrt{2})^{19} 3^{4} 4^{2} 9^{m} 8^{n}=3^{n} 16^{m}(\sqrt[4]{64})$

$\Rightarrow 2^{19 / 2} \times 3^{4} \times 2^{4} \times 3^{2 m} \times 2^{3 n}=3^{n} \times 2^{4 m} \times 2^{3 / 2}$

$\Rightarrow {{2}^{(19/2+4+3n)}}\times {{3}^{(4+2m)}}={{2}^{(4m+3)}}\times {{3}^{n}}$

Comparing the powers of same bases we get

$\frac{19}{2}+4+3 n=4 m+\frac{3}{2} \cdots(1)$

$4+2 m=n \cdots(2)$

Substitute the value of n from (2) in (1) and solving for m, we get m = -12


CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2019 Slot-1


CAT 2019 Slot-2

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon