I would like to use approximation of numbers as below:

\(\frac{(0.513)(0.488)(0.942)}{(0.684)(0.314)(0.183)}\)
=\(\frac{(513)(488)(942)}{(684)(314)(183)}\)
apx=\(\frac{(500)(500)(950)}{(700)(300)(190)}\)
apx=\(\frac{(5)(5)(5)}{(7)(3)}\)
apx=\(\frac{(5)(5)(5)}{(7)(3)}\)
apx=\(\frac{(125)}{(21)}\)
apx=6....................(21*6=126)................................Thus Answer c
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\(\frac{(0.513)(0.488)(0.942)}{(0.684)(0.314)(0.183)}\) \(=\) \(\frac{(3*0,171)(8*0,061)(3*0,314)}{(4*0,171)(0.314)(3*0,061)}\) \(=\) 6

Answer: C
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Take approximate values and solve

0.5*0.5*1/(0.7*0.3*0.2)
=125/21
Approx 6
as 21*6=216

Posted from my mobile device

1) Remove all the decimals
2) 942/314 = 3
3) If you can't see other obvious big factors, then just try to use smaller factors to reduce.
4) You'll get reduced fraction as 6.

ANSWER: C

The fraction has to be simplified
=>(3*0.171*8*0.061*3*0.314)/4*0.171*0.314*3*0.061

=>3*8*3/4*1*3
=>6
Therefore IMO C

you can also try to do the following

(1/2*1/2*1)/(7/10*3/10*2/10)

leading to approx (1/4)/(42/1000) (do not reduce denominator before last passage)

then 1/4*1000/42 which leads up to 250/42 that is approx 6

bottom line: i'd try to get rid of decimals as soon as possible, therefore managing to get to the correct answer in under 2 min. you can approximate here since the answers are pretty spread apart

hope it is useful

Useful concept: \(\frac{A \times B \times C}{D \times E \times F} = \frac{A}{D} \times \frac{B}{E} \times \frac{C}{F}\)

Strategy: As you can imagine, we certainly don't want to actually find the product in the numerator and the product in the denominator and then divide the results. Instead, let's invest a little bit of time identifying any pairs of values that might simplify today " nice" fraction.

First off, I recognize that \(0.942\) is exactly \(3 \times 0.314\).

So, let's rewrite our expression as follows: \(\frac{(0.513)(0.488)(0.942)}{(0.684)(0.314)(0.183)} = \frac{0.942}{0.314} \times \frac{(0.513)(0.488)}{(0.684)(0.183)}= 3 \times \frac{(0.513)(0.488)}{(0.684)(0.183)}\)

Next, I know that \(3 \times 0.18 = 0.54\), which means \(\frac{0.54}{0.18} = 3\)

The fraction \(\frac{0.513}{0.183}\) kind of resembles \(\frac{0.54}{0.18} = 3\).
However, since \(0.513\) is a bit smaller than \(0.54\), and since \(0.183\) is a teeny bit bigger than \(0.18\), we know that \(\frac{0.513}{0.183}\) will be a little bit smaller than \(3\).

So, we can rewrite our expression as follows: \(3 \times \frac{(0.513)(0.488)}{(0.684)(0.183)} = 3 \times \frac{0.513}{0.183} \times \frac{0.488}{0.684} = 3 \times little less than3 \times \frac{0.488}{0.684} \)

Finally, we know that \(\frac{4}{6} = \frac{2}{3}\), and \(\frac{440}{660} = \frac{2}{3}\), and \(\frac{460}{690} = \frac{2}{3}\)

Since \(0.488\) is a bit bigger than \(460\), we can conclude that \(\frac{0.488}{0.684}\) is a little bit bigger than \(\frac{2}{3}\).

So, our expression becomes:
\(3 \times little less than3 \times \frac{0.488}{0.684} = 3 \times (little less than3) \times (a little more than \frac{2}{3})\)

The "little more than part" some What cancels out with the " little less than" part to get: \(3 \times 3 \times \frac{2}{3}\), which evaluates to be \(6\)

Answer: C
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