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Of the following, which best approximates:

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HKD1710
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Of the following, which best approximates: [#permalink] New post  11 Nov 2018, 09:07
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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
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nkin
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Re: Of the following, which best approximates: [#permalink] New post  11 Nov 2018, 09:15
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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.
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Chethan92
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Re: Of the following, which best approximates: [#permalink] New post  11 Nov 2018, 09:12
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0.16667 = 1/6
0.3333 = 1/3
0.2222 = 2/9
0.6667 = 2/3
0.125 = 1/8
0.8333 = 5/6

Substituting this,

9*3*8*5/6*3*6*2*2 = 5/2 = 2.5

D is the answer.
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dave13
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Of the following, which best approximates: [#permalink] New post  11 Nov 2018, 10:35
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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] New post  03 Feb 2019, 09:27
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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] New post  15 Mar 2021, 06:35
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] New post  18 Feb 2022, 08:17
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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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BrentGMATPrepNow
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Re: Of the following, which best approximates: [#permalink] New post  23 May 2022, 08:30
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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.....
\(\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)} = \frac{\frac{5}{108}}{\frac{1}{54}}\)

\(= \frac{5}{108} \times \frac{54}{1}\)

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

\(= 2.5\)

Answer: D
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Re: Of the following, which best approximates: [#permalink]
23 May 2022, 08:30
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