search
Log In
1 vote
142 views

Let $0.01^x+0.25^x=0.7$ . Then

  1. $x\geq1$
  2. $0\lt x\lt1$
  3. $x\leq0$
  4. no such real number $x$ is possible.
in Quantitative Aptitude
recategorized by
142 views
0
$\mathbf B$ should be the answer by simple substitution.

1 Answer

1 vote
$\underline{\mathbf{Answer:B}}\;$ $\bbox[orange,5px,border: 2px dotted red]{\color{blue}{\mathbf{0<x<1}}}$

$\underline{\mathbf{Explanation:}}$

Substitute $\mathbf {x = 0} \Rightarrow (0.001)^0 + (0.25)^0 = 1 + 1 = 2 \;\text{which is }\; \color{red}{> 0.7}$

Similarly, subsitute $\mathbf {x = 1} \Rightarrow (0.01)^1 + (0.25)^1 = 0.26\;\text{which is }\; \color{red}{< 0.7}$

$\therefore \mathbf x$ lies between $\mathbf 0$ and $\mathbf 1$.

$\therefore \mathbf B$ is the right option.

edited by
0

Can you please verify this answer, whether this method is correct or not?

@ankitgupta.1729

 

1

@`JEET

yeah, it is correct and the reason is, both functions $0.01^x$ and $0.25^x$ are strictly decreasing for interval $(-\infty,\infty)$.

So, if we consider $f(x)=0.01^x + 0.25^x$

then $f(1) = 0.26$  and since both functions are decreasing.So, value of sum of both functions for $x>1$ will also be decreasing. So, $f(>1)$  will always be less than $0.26$ and this way, we can't get $0.7$. So, option (A) is eliminated.

Now, $f(0) = 2$. Now, when $x<0$, both functions will be strictly increasing and so their sum will also be increasing. So, $f(<0)$ will always be $>2$ and so we will not get $0.7$ for $x\leq 0$. So, option (C) eliminated.

Now, since, $f(0) = 2$ and $f(1) = 0.26$ and $f(x)$ is decreasing in $(-\infty,\infty)$and continuous function, so there must be some value of $x$ which is between $0$ and $1$ for which $f(x)$ will be $0.7$.

1
Thanks.
1
How to find the functions are decreasing, monotonically decreasing?

By differentiation, right?
1

@`JEET Yeah, right.

Or we can simply remember that if $f(x) = a^x$

Then in case of $a > 1$ , $f(x)$ will be strictly increasing for all $x$

And in case of $0<a<1$, $f(x)$ will be strictly decreasing for all x.

It is quite intuitive also.

Related questions

2 votes
2 answers
1
192 views
The digit in the unit place of the number $7^{78}$ is $1$ $3$ $7$ $9$
asked Sep 18, 2019 in Quantitative Aptitude gatecse 192 views
1 vote
1 answer
2
97 views
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is $6$ $9$ $12$ $18$
asked Sep 18, 2019 in Quantitative Aptitude gatecse 97 views
3 votes
1 answer
3
165 views
If $P$ is an integer from $1$ to $50$, what is the probability that $P(P+1)$ is divisible by $4$? $0.25$ $0.50$ $0.48$ none of these
asked Sep 18, 2019 in Probability gatecse 165 views
0 votes
1 answer
4
170 views
If the co-efficient of $p^{th}, (p+1)^{th}$ and $(p+2)^{th}$ terms in the expansion of $(1+x)^n$ are in Arithmetic Progression (A.P.), then which one of the following is true? $n^2+4(4p+1)+4p^2-2=0$ $n^2+4(4p+1)+4p^2+2=0$ $(n-2p)^2=n+2$ $(n+2p)^2=n+2$
asked Sep 18, 2019 in Quantitative Aptitude gatecse 170 views
...