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# Of the following, which best approximates:

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Of the following, which best approximates: [#permalink]
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HKD1710 wrote:
Of the following, which best approximates:

$$\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$$ ?

(A) 2.00
(8) 2.40
(C) 2.43
(D) 2.50
(E) 3.43

rounded 0.16 to 0.2 --> 1/5

80/100 = 4/5

30/100 = 3/10

= 1/5*4/5*3/10 = 12/ 250

0.2222 = 2/10 = 1/5

0.6667 = 7/10

0.125 = 1/8

1/5*7/10*1/8 = 7/400

12/250 *400/7 = 96/35 = 2.7

Closest to 2.7 is Option D 2.5
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Re: Of the following, which best approximates: [#permalink]
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HKD1710 wrote:
Of the following, which best approximates:

$$\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$$ ?

(A) 2.00
(8) 2.40
(C) 2.43
(D) 2.50
(E) 3.43

I ball parked the given values to 0.16 * 0.8 * 0.3 / ( 0.2 * 0.6 * 0.12)

When divided will give 8/3

Nearest to D
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Re: Of the following, which best approximates: [#permalink]
nkin wrote:
We can see that,

0.16667 = 1/6 , 0.3333 = 1/3 , 0.2222 = 2/9, 0.6667 = 2/3 , 0.125 = 1/8 , 0.8333 = 5/6

Side note: If one does not remember, quick way to find these out would be as follows: Let x = 0.22222, 10*x = 2.22222, so 10*x - x = 2
Hence 9x = 2, or x = 2/9

If we substitute back we get 2.5 as the answer.

Hope that helps.

How do we do the same for 0.125 or where digits are not repeating?
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Of the following, which best approximates: [#permalink]
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HKD1710 wrote:
Of the following, which best approximates:

$$\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$$ ?

(A) 2.00
(8) 2.40
(C) 2.43
(D) 2.50
(E) 3.43

$$(0.1667)=1/6$$
$$(0.8333)=5/6$$
$$(0.3333)=1/3$$
$$(0.2222)=2/9$$
$$(0.6667)=2/3$$
$$(0.1250)=1/8$$

Therefore we have, Numerator $$= 1/6*5/6*1/3 = 5/108$$
Denominator $$= 2/9*2/3*1/8 = 1/54$$

Fraction = $$(5/108)/(1/54) = (5/2) = 2.5$$

Hence, D.
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Re: Of the following, which best approximates: [#permalink]
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HKD1710 wrote:
Of the following, which best approximates:

$$\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$$ ?

(A) 2.00
(8) 2.40
(C) 2.43
(D) 2.50
(E) 3.43

Strategy: Since the answer choices are tightly packed, approximation won't help us here. Instead, it looks like we need to convert each decimal to a fraction.

Let's simplify the numerator and denominator independently

NUMERATOR
$$(0.1667)(0.8333)(0.3333) ≈ (\frac{1}{6})(\frac{5}{6})(\frac{1}{3}) ≈ \frac{5}{108}$$

DENOMINATOR
$$(0.2222)(0.6667)(0.1250) ≈ (\frac{2}{9})(\frac{2}{3})(\frac{1}{8}) ≈ \frac{4}{216} ≈ \frac{1}{54}$$

So.....
$$\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)} = \frac{\frac{5}{108}}{\frac{1}{54}}$$

$$= \frac{5}{108} \times \frac{54}{1}$$

$$=\frac{5}{2 }$$

$$= 2.5$$

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Re: Of the following, which best approximates: [#permalink]
is there any quick tip to remember how 0.1667 is 1/6 and 0.8333 is 5/6?

For other combinations where denominator is 3,9 or 5 is very redundant in other problems hence gets memorised easily.
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Re: Of the following, which best approximates: [#permalink]
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x=0.1667
10x=1.667
10x-x=1.667-0.1667
9x=1.5
90x=15
x=1/6

Similarly x=0.8333
10x=8.333
10x-x=8.333-0.8333
9x=7.5
90x=75
x=5/6

Hope it helps

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Re: Of the following, which best approximates: [#permalink]
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