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# Which of the following fractions is the greatest ?

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Retired Moderator
Joined: 12 Aug 2015
Posts: 2428
GRE 1: 323 Q169 V154
Which of the following fractions is the greatest ? [#permalink]

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06 Nov 2016, 09:19
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64% (00:39) correct 36% (00:34) wrong based on 114 sessions

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Which of the following fractions is the greatest ?

A) -3/2
B) -23/22
C) -100/99
D) -999/998
E) -9999/9998
[Reveal] Spoiler: OA

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Re: Which of the following fractions is the greatest ? [#permalink]

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06 Nov 2016, 15:47
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E) because numerator is greater than denominator by 1, now consider 1 with the denominator. The value of 1 devided by the denominator will be the greatest for option a if it was a positive term since all options are negative we need to select the least negative term that is option e

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Joined: 28 Jun 2016
Posts: 207
Concentration: Operations, Entrepreneurship
Re: Which of the following fractions is the greatest ? [#permalink]

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06 Nov 2016, 18:37
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stonecold wrote:
Which of the following fractions is the greatest ?
A)-3/2
B)-23/22
C)-100/99
D)-999/998
E)-9999/9998

A) -1-1/2

B) -1-1/22

C) -1-1/99

D) -1-1/998

E) -1-1/9998

IMO E

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Joined: 22 Jan 2015
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Re: Which of the following fractions is the greatest ? [#permalink]

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09 Feb 2018, 23:48
stonecold wrote:
Which of the following fractions is the greatest ?

A) -3/2
B) -23/22
C) -100/99
D) -999/998
E) -9999/9998

Ans) Rule: If you add a constant to numerator and denominator of an improper fraction(a fraction greater than 1), the fraction becomes smaller.
Hence, we want the number that is the smallest in absolute value(as we have a negative number). So 9999/9998 has the smallest absolute value, and -9999/9998 is the greatest.
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Re: Which of the following fractions is the greatest ? [#permalink]

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10 Feb 2018, 09:04
stonecold wrote:
Which of the following fractions is the greatest ?

A) -3/2
B) -23/22
C) -100/99
D) -999/998
E) -9999/9998

Hi stonecold, how to approach this question kinda confused how to solve it ? thanks!
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Re: Which of the following fractions is the greatest ? [#permalink]

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11 Feb 2018, 00:27
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stonecold wrote:
Which of the following fractions is the greatest ?

A) -3/2
B) -23/22
C) -100/99
D) -999/998
E) -9999/9998

If one fails to see the logical angle of the question, then you can use below method as well to arrive at the greatest fraction. Note all the fractions are negative, hence the smallest absolute value will be the greatest

A) let, $$\frac{-3}{2}=a$$, add $$1$$ to both sides, we get

$$\frac{-3}{2}+1=a+1=>\frac{2-3}{2}=a+1=> \frac{-1}{2}=a+1$$

B) $$\frac{-23}{22}=b$$, using the above approach you will get $$\frac{-1}{22}=b+1$$

C) $$\frac{-100}{99}=c$$, using the above approach you will get $$\frac{-1}{99}=c+1$$

D) $$\frac{-999}{998}=d$$, using the above approach you will get $$\frac{-1}{998}=d+1$$

E) $$-\frac{9999}{9998}=e$$, using the above approach you will get $$\frac{-1}{9998}=e+1$$

clearly $$e+1$$ is the greatest value. Hence Option E
Re: Which of the following fractions is the greatest ?   [#permalink] 11 Feb 2018, 00:27
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