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Quantitative Aptitude > Number System

DECIMAL FRACTION MCQs

Decimals, Fractions, Decimals And Fractions

Total Questions : 871 | Page 6 of 88 pages
Question 51.

he expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for xequal to:

  1.    0.02
  2.    0.2
  3.    0.04
  4.    0.4
 Discuss Question
Answer: Option C. -> 0.04

Given expression = (11.98)2 + (0.02)2 + 11.98 x x.


For the given expression to be a perfect square, we must have


11.98 x x = 2 x 11.98 x 0.02 or x   = 0.04

Question 52.

 \(\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}\) is approximately equal to:

  1.    2
  2.    2.40
  3.    2.43
  4.    2.50
 Discuss Question
Answer: Option D. -> 2.50

Given expression =  \(\frac{(0.3333)}{(0.2222)}\times\frac{(0.1667)(0.8333)}{(0.6667)(0.1250)}\)


= \(\frac{3333}{2222}\times\frac{\frac{1}{6}\times\frac{5}{6}}{\frac{2}{3}\times\frac{125}{1000}}\)


=\(\left(\frac{2}{3}\times\frac{1}{6}\times\frac{5}{6}\times\frac{3}{2}\times8\right)\)


= \(\frac{5}{2}\)


= 2.50

The given expression is (0.1667)(0.8333)(0.3333)/(0.2222)(0.6667)(0.1250)

We can simplify the expression by first dividing the numerator and denominator by their respective common factors:

= [(1/6)(5/6)(1/3)] / [(2/9)(2/3)(1/8)]

= (5/6) / (1/27)

= (5/6) x 27

= 45/2

= 22.5

Therefore, the answer is option D, 2.50.

To understand this solution, let's break down the steps:

Step 1: Divide numerator and denominator by their respective common factors.

In the numerator, we can see that all three numbers have a factor of 3. By dividing each number by 3, we get:

(0.1667/3) x (0.8333/3) x (0.3333/3)

Simplifying each term, we get:

(1/6) x (5/6) x (1/3)

Similarly, in the denominator, we can see that all three numbers have a factor of 2. By dividing each number by 2, we get:

(0.2222/2) x (0.6667/2) x (0.1250/2)

Simplifying each term, we get:

(2/9) x (2/3) x (1/8)

Now, we can substitute these simplified expressions into the original expression:

[(1/6)(5/6)(1/3)] / [(2/9)(2/3)(1/8)]

Step 2: Simplify the expression.

To simplify the expression, we can multiply the numerator and denominator by the reciprocal of the denominator:

[(1/6)(5/6)(1/3)] x [(8/2)(9/2)(3/3)]

Simplifying each term, we get:

(5/6) x 27

This gives us the simplified expression, which we can evaluate to get the answer.

Step 3: Evaluate the expression.

Evaluating the expression, we get:

(5/6) x 27 = 45/2 = 22.5

Therefore, the answer is option D, 2.50.

In summary, to solve the given expression, we simplified it by dividing both the numerator and denominator by their respective common factors. Then, we evaluated the simplified expression to get the answer.

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 53.

3889 + 12.952 - ? = 3854.002

  1.    47.095
  2.    47.752
  3.    47.932
  4.    47.95
 Discuss Question
Answer: Option D. -> 47.95

Let 3889 + 12.952 - x = 3854.002.


Then x = (3889 + 12.952) - 3854.002


   = 3901.952 - 3854.002


   = 47.95.

Question 54.

0.04 x 0.0162 is equal to:

  1.    6.48 x 10-3
  2.    6.48 x 10-4
  3.    6.48 x 10-5
  4.    6.48 x 10-6
 Discuss Question
Answer: Option B. -> 6.48 x 10-4

4 x 162 = 648. Sum of decimal places = 6.
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10-4

To solve this problem, we can simply multiply the two numbers together using a calculator or longhand multiplication. However, it's important to understand the scientific notation or standard form of numbers and how to convert between them to select the correct answer.

Scientific notation or standard form is a way of representing numbers as a coefficient multiplied by a power of 10. For example, the number 325 in scientific notation would be 3.25 x 10^2. The coefficient is always greater than or equal to 1 and less than 10, and the exponent represents the number of places the decimal point must be moved to get the original number. Here are some relevant formulas and definitions:

  • Scientific notation: a number expressed as a coefficient times 10 raised to a power
  • Coefficient: the part of a number in scientific notation that is greater than or equal to 1 and less than 10
  • Exponent: the part of a number in scientific notation that represents the power of 10
  • Multiplication: when multiplying numbers in scientific notation, you multiply the coefficients and add the exponents

Now, let's solve the problem. We have:

0.04 x 0.0162

To convert these numbers to scientific notation, we move the decimal point to the right until we have a coefficient between 1 and 10. We get:

4 x 10^-2 x 1.62 x 10^-2

To multiply these two numbers, we simply multiply the coefficients and add the exponents:

4 x 1.62 x 10^-2+(-2) = 6.48 x 10^-4

Therefore, the correct answer is B, 6.48 x 10^-4.

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 55.

  . \(\frac{4.2\times4.2-1.9\times1.9}{2.3\times6.1}\)is equal to:

  1.    0.5
  2.    1.0
  3.    20
  4.    22
 Discuss Question
Answer: Option B. -> 1.0

Given Expression =  \(\frac{(a^{2}-b^{2})}{(a+b)(a-b)} = \frac{(a^{2}-b^{2})}{(a^{2}-b^{2})} = 1\)

Question 56.

\(If \frac{144}{0.144} = \frac{14.4}{x}\)  , then the value of x is:

  1.    0.0144
  2.    1.44
  3.    14.4
  4.    144
 Discuss Question
Answer: Option A. -> 0.0144

\(If \frac{144}{0.144} = \frac{14.4}{x}\)


 


\(\Rightarrow\frac{144\times1000}{144}= \frac{14.4}{x}\)


\(\Rightarrow x= \frac{14.4}{1000} = 0.0144\)

Question 57.

The price of commodity X increases by 40 paise every year, while the price of commodityY increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?

  1.    2010
  2.    2011
  3.    2012
  4.    2013
 Discuss Question
Answer: Option B. -> 2011

Suppose commodity X will cost 40 paise more than Y after z years.


Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40


 0.25z = 0.40 + 2.10


\(\Rightarrow z = \frac{2.50}{0.25} = \frac{250}{25}= 10\)


Therefore X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.

Question 58.

Which of the following are in descending order of their value ?

 Discuss Question
Answer: Option B. -> 2011
Question 59.

Which of the following fractions is greater than \(\frac{3}{4}\) and less than \(\frac{5}{6}\) ?

  1.    \(\frac{1}{2}\)
  2.    \(\frac{ 2}{3}\)
  3.    \( \frac{4}{5}\)
  4.    \(\frac{9}{10}\)
 Discuss Question
Answer: Option C. -> \( \frac{4}{5}\)

\(\frac{3}{4}=0.75,\frac{5}{6}=0.883,\frac{1}{2}=0.5,\frac{2}{3}=0.66,\frac{4}{5}=0.8,\frac{8}{10}=0.9,\)


Clearly, 0.8 lies between 0.75 and 0.833.


So, \(\frac{4}{5}\) lies between \(\frac{3}{4}\)  and  \(\frac{5}{6}\) .

Question 60.

The rational number for recurring decimal 0.125125.... is:

  1.    \(\frac{63}{487}\)
  2.    \(\frac{119}{993}\)
  3.    \(\frac{125}{999} \)
  4.    None of these
 Discuss Question
Answer: Option C. -> \(\frac{125}{999} \)

0.125125... = 0.125 = \(\frac{125}{999} \)

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