search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
2 votes
149 views

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. $-16$
in Quantitative Aptitude 11.6k points 221 1489 2361
edited by
149 views

1 Answer

1 vote

Given that,

$\left ( \sqrt{2} \right )^{19}3^{4}4^{2}g^{m}\cdot g^{n} = 3^{n}\cdot 16^{m} \left ( 4\sqrt{64} \right )$

$\implies 2^{19/2}\cdot 3^{4}\cdot \left ( 2^{2} \right )^{2} \left ( 3^{2} \right )^{m} \left ( 2^{3} \right )^{n} = 3^{n} \left ( 2^{4} \right )^{m} \left ( 2^{6} \right )^{1/4}$

$\implies 2^{19/2}\cdot 3^{4}\cdot 2^{4}\cdot 3^{2m} \cdot 2^{3n} = 3^{n}\cdot 2^{4m}\cdot 2^{6/4}$

$\implies 2^{\left ( 19/2 + 4 + 3n \right )}\cdot 3^{\left ( 4 + 2m \right )} = 3^{n} \:2^{\left ( 4m + \frac{6}{4} \right )}$

Comparing both sides, we get

  • $4 + 2m = n \qquad \qquad \to (i)$
  • $\frac{19}{2} + 4 + 3n = 4m + \frac{3}{2} \qquad \to (ii)$

$(ii) \implies 3n+ \frac{19}{2}-\frac{3}{2}+4-4m=0$

$\implies 3n+ \frac{16}{2}+4-4m=0$

$\implies 3n+ 12-4m=0$

Putting the value of $n$ from equation $(i),$ we get

$3\left ( 4+2m \right )+12-4m=0$

$\implies 12+6m+12-4m=0$

$\implies 2m + 24 =0$

$\implies 2m = -24$

$\implies m = -\frac{24}{2}$

$\boxed{m = -12}$

Correct Answer: B

364 points 1 1 4
edited ago by

Related questions

1 vote
1 answer
1
138 views
The income of Amala is $20$% more than that of Bimala and $20$% less than that of Kamala. If kamala’s income goes down by $4$% and Bimala’s goes up by $10$%, then the percentage by which kamala’s income would exceed Bimala’s is nearest to $31$ $28$ $32$ $29$
asked Mar 8, 2020 in Quantitative Aptitude jothee 11.6k points 221 1489 2361 138 views
0 votes
1 answer
2
88 views
In a class, $60$% of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68$% of the students, including $30$ boys, pass an examination, the percentage of the girls who do not pass is____
asked Mar 8, 2020 in Quantitative Aptitude jothee 11.6k points 221 1489 2361 88 views
1 vote
1 answer
3
85 views
On selling a pen at $5$% loss and a book at $15$% gain, Karim gains Rs. $7$. If he sells the pen at $5$% gain and the book at $10$% gain, he gains Rs. $13$. What is the cost price of the book in Rupees? $80$ $85$ $95$ $100$
asked Mar 8, 2020 in Quantitative Aptitude jothee 11.6k points 221 1489 2361 85 views
1 vote
2 answers
4
117 views
Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is $5:6$ $4:5$ $3:4$ $2:3$
asked Mar 8, 2020 in Quantitative Aptitude jothee 11.6k points 221 1489 2361 117 views
0 votes
0 answers
5
65 views
Let $S$ be the set of all points $(x,y)$ in the $x-y$ plane such that $|x|+|y|\leq 2$ and $|x|\geq 1$. Then, the area, in square units, of the region represented by $S$ equals _____
asked Mar 8, 2020 in Quantitative Aptitude jothee 11.6k points 221 1489 2361 65 views
...