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# 31/125 =

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
31/125 =  [#permalink]

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24 Jan 2014, 02:55
1
6
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:56) correct 12% (01:08) wrong based on 781 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

Problem Solving
Question: 58
Category: Arithmetic Operations on rational numbers
Page: 69
Difficulty: 500

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Math Expert
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Re: 31/125 =  [#permalink]

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24 Jan 2014, 02:55
16
7
SOLUTION

$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

$$\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248$$.

Answer: A.
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Re: 31/125 =  [#permalink]

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24 Jan 2014, 04:50
2
4
For the sake of time, we approximate 31 to 30. 30/125 = 6/25.
We multiply the fraction by 4 to get the denominator to 100 -> 24/100 = 24% = 0.24.

Since we rounded numerator down, the answer is a bit undervalued so the closest answer is (A). 0.248.
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Re: 31/125 =  [#permalink]

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24 Jan 2014, 22:51
1
1
$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

$$\frac{31}{125} = \frac{31*8}{125*8} = \frac{248}{1000} = 0.248$$

Answer: (A)
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Re: 31/125 =  [#permalink]

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27 Jun 2015, 09:30
125 can simply be written as 1000/8
multiply 8 with 31 to get 248
divide it by 1000 to get .248
answer is A
simple one
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Joined: 26 Feb 2016
Posts: 12
Re: 31/125 =  [#permalink]

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20 Apr 2016, 07:54
Bunuel wrote:
SOLUTION

$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

$$\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248$$.

Answer: A.

why do you choose to times by 8?
Math Expert
Joined: 02 Sep 2009
Posts: 52906
Re: 31/125 =  [#permalink]

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20 Apr 2016, 07:56
sabxu1 wrote:
Bunuel wrote:
SOLUTION

$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

$$\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248$$.

Answer: A.

why do you choose to times by 8?

The options are in decimals. To transform a fraction to decimal the denominator must be some power of 10. 125*8 = 1000.
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31/125 =  [#permalink]

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20 Apr 2016, 23:03
Bunuel wrote:
sabxu1 wrote:
Bunuel wrote:
SOLUTION

$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

$$\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248$$.

Answer: A.

why do you choose to times by 8?

The options are in decimals. To transform a fraction to decimal the denominator must be some power of 10. 125*8 = 1000.

do you times i by 8 because you want to get to an easy number such as 1000?
Math Expert
Joined: 02 Sep 2009
Posts: 52906
Re: 31/125 =  [#permalink]

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20 Apr 2016, 23:11
sabxu1 wrote:
Bunuel wrote:
sabxu1 wrote:
why do you choose to times by 8?

The options are in decimals. To transform a fraction to decimal the denominator must be some power of 10. 125*8 = 1000.

do you times i by 8 because you want to get to an easy number such as 1000?

As I said, we multiply by 8 to get in the denominator some power of 10 to transform the fraction into the decimal easily.
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Re: 31/125 =  [#permalink]

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21 Apr 2016, 00:50
1
sabxu1 wrote:
Bunuel wrote:
SOLUTION

$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

$$\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248$$.

Answer: A.

why do you choose to times by 8?

Since the options are all in the decimal forms, we need to divide the numerator by denominator.
If we have a calculator, we can directly divide it. But since we are not allowed a calculator, we need to make our lives simpler.

Hence we try to bring denominator in a form by which the division becomes easier.
125 = 5^3
If we multiply 5^3 by 2^3, we get 10^3 or 1000 and then we can easily divide.

Hope this clarifies your doubt.
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Re: 31/125 =  [#permalink]

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09 Jun 2017, 22:40
1
Bunuel wrote:
$$\frac{31}{125} =$$

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

$$\frac{31}{125}$$

$$~ \frac{31}{124}$$

$$=\frac{1}{4}$$

$$=0.25$$

Thus, answer will be (A) 0.248
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Re: 31/125 =  [#permalink]

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21 Jun 2017, 07:17
In case someone is interested in a more detailed approach.

$$\frac{31}{125} = \frac{30}{125}+\frac{1}{125} = \frac{6}{25}+\frac{1}{125} = \frac{5}{25} + \frac{1}{25} + \frac{1}{125} = \frac{1}{5}+ \frac{1}{25} + \frac{1}{125}$$

$$= 0.2 + \frac{0.2}{5}+ \frac{1}{125} = 0.2 +0.04 + \frac{1}{125} = 0.24 + \frac{1}{125}$$

= a little over 0.24

= Option A
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Re: 31/125 =  [#permalink]

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06 Sep 2018, 12:18
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Re: 31/125 =   [#permalink] 06 Sep 2018, 12:18
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