Question:

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

Options:
A.8.5
B.13
C.16
D.17.5
E.None of these
Answer: Option B

Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.

Then, \(\frac{(5^{2})^{7.5}\times (5)^{2.5}}{(5^{3})^{1.5}}\)  =5x

       \(\frac{5^{(2\times7.5)}\times 5^{2.5}}{5^{(3\times1.5)}}\) = 5x

      \(\frac{5^{15}\times5^{2.5}}{5^{4.5}}\)  =  5x

 5x = 5(15 + 2.5 - 4.5)

 5x = 513

Therefore x = 13.

 

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More Questions Related to Quantitative Aptitude > Surds & Indices :

Question 1.

\(\frac{1}{1+x^{(b-a)}+x^{(c-a)}} +\frac{1}{1+x^{(a-b)}+x^{(c-b)}} + \frac{1}{1+x^{(b-c)}+x^{(a-c)}} = ?\)

Options:
  1.    0
  2.    1
  3.    xa - b - c
  4.    None of these
Answer: Option B

Given Exp. =  \(\frac{1}{\left(1+\frac{x^{b}}{x^{a}}+\frac{x^{c}}{x^{a}}\right)} +\frac{1}{\left(1+\frac{x^{a}}{x^{b}}+\frac{x^{c}}{x^{b}}\right)}+\frac{1}{\left(1+\frac{x^{b}}{x^{c}}+\frac{x^{a}}{x^{c}}\right)}\)

= \(\frac{x^{a}}{(x^{a}+x^{b}+x^{c})}+\frac{x^{b}}{(x^{a}+x^{b}+x^{c})}+\frac{x^{c}}{(x^{a}+x^{b}+x^{c})}\)

= \(\frac{(x^{a}+x^{b}+x^{c})}{(x^{a}+x^{b}+x^{c})}\)

= 1

Question 2.

The value of [(10)150 ÷ (10)146]

Options:
  1.    1000
  2.    10000
  3.    100000
  4.    106
Answer: Option B

(10)150 ÷ (10)146 = \(\frac{10^{150}}{10^{146}}\)

= 10150 - 146

   = 104

   = 10000.

Question 3.

(256)0.16 x (256)0.09 = ?

Options:
  1.    4
  2.    16
  3.    64
  4.    256.25
Answer: Option A

(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)

   = (256)0.25

= \((256)^{\left(\frac{25}{100}\right)}\)

= \((256)^{\left(\frac{1}{4}\right)}\)

= \((4^{4})^{\left(\frac{1}{4}\right)}\)

= \(4^{4\left(\frac{1}{4}\right)}\)

= 41

   = 4

 

Question 4.

(0.04)-1.5 = ?

Options:
  1.    25
  2.    125
  3.    250
  4.    625
Answer: Option B

(0.04)-1.5 =  \(\left(\frac{4}{100}\right)^{-1.5}\)

\(\left(\frac{1}{25}\right)^{-(\frac{3}{2})}\)

= \(\left(25\right)^{\left(\frac{3}{2}\right)}\)

= \(\left(5^{2}\right)^{\left(\frac{3}{2}\right)}\)

= \(\left(5\right)^{2\times\left(\frac{3}{2}\right)}\)

= 53

= 125.

Question 5.

\(\frac{\left(243\right)^{\frac{n}{5}}\times3^{2n+1}}{9^{n}\times3^{n-1}}= ?\)

Options:
  1.    1
  2.    2
  3.    9
  4.    3n
Answer: Option C

Given Expression = \(\frac{\left(243\right)^{\frac{n}{5}}\times3^{2n+1}}{9^{n}\times3^{n-1}}\)

= \(\frac{\left(3^{5}\right)^{\left(\frac{n}{5}\right)} \times3^{2n+1}}{\left(3^{2}\right)^{n}\times3^{n-1}}\)

= \(\frac{\left(3^{5\times(\frac{n}{5})}\times3^{2n-1}\right)}{\left(3^{2n}\times3^{n-1}\right)}\)

= \(\frac{3^{n}\times3^{2n-+1}}{3^{2n}\times3^{n-1}}\)

= \(\frac{3^{(n+2n+1)}}{3^{(2n+n-1)}}\)

= \(\frac{3^{3n+1}}{3^{3n-1}}\)

= 3(3n + 1 - 3n + 1)   

= 32   = 9.

 

Question 6.

\(\frac{1}{1+a^{(n-m)}}+\frac{1}{1+a^{(m-n)}} = ?\)

Options:
  1.    0
  2.    \(\frac{1}{2}\)
  3.    1
  4.    am + n
Answer: Option C

\(\frac{1}{1+a^{(n-m)}}+\frac{1}{1+a^{(m-n)}} = \frac{1}{\left(1+\frac{a^{n}}{a^{m}}\right)} + \frac{1}{\left(1+\frac{a^{m}}{a^{n}}\right)}\)

\(\frac{a^{m}}{\left(a^{m}+a^{n}\right)}+\frac{a^{n}}{\left(a^{m}+a^{n}\right)}\)

= \(\frac{{\left(a^{m}+a^{n}\right)}}{{\left(a^{m}+a^{n}\right)}}\)

= 1.