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# Which of the following fractions is closest to 1 given that a > b > 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
Which of the following fractions is closest to 1 given that a > b > 1?  [#permalink]

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21 Feb 2018, 23:18
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Difficulty:

35% (medium)

Question Stats:

68% (01:21) correct 32% (01:11) wrong based on 73 sessions

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Which of the following fractions is closest to 1 given that a > b > 1?

(A) a/b
(B) (a + 2)/(b + 2)
(C) (a + 1)/(b + 1)
(D) (a + 1)/b
(E) (a - 1)/(b - 1)

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Re: Which of the following fractions is closest to 1 given that a > b > 1?  [#permalink]

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21 Feb 2018, 23:26
Bunuel wrote:
Which of the following fractions is closest to 1 given that a > b > 1?

(A) a/b
(B) (a + 2)/(b + 2)
(C) (a + 1)/(b + 1)
(D) (a + 1)/b
(E) (a - 1)/(b - 1)

a= 3 b =2

(A) a/b = 1.5
(B) (a + 2)/(b + 2) = 1.25
(C) (a + 1)/(b + 1) = 1.33
(D) (a + 1)/b = 2
(E) (a - 1)/(b - 1) = 2

a = 100 b =10

(A) a/b = 10
(B) (a + 2)/(b + 2) 8.5
(C) (a + 1)/(b + 1) = 9.xx
(D) (a + 1)/b = 10.x
(E) (a - 1)/(b - 1) = 11

(B) Imo
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Re: Which of the following fractions is closest to 1 given that a > b > 1?  [#permalink]

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22 Feb 2018, 00:01
Bunuel wrote:
Which of the following fractions is closest to 1 given that a > b > 1?

(A) a/b
(B) (a + 2)/(b + 2)
(C) (a + 1)/(b + 1)
(D) (a + 1)/b
(E) (a - 1)/(b - 1)

In addition to the Alternative approach using numbers shown above, we'll show a Logical approach using fraction properties.

A fraction equals 1 when its numerator is equal to its denominator.
So, we're looking for the answer where the numerator is as close to the denominator as possible.
That is, we'd like to make b 'as close as possilbe' to a.
This happens when a and b become larger for the following reason:
The larger the numbers are, the less of an effect the difference between them makes.
For example, say the difference between a and b is 1.
This has a very large effect if a=3 and b=2 (because 1 is 50% of b), but only a small effect if a=101 and b=100 (because 1 is only 1% of b).
So we'll choose the answer choice that makes the numerator and deonminator as large as possible.
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Re: Which of the following fractions is closest to 1 given that a > b > 1?  [#permalink]

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22 Feb 2018, 10:17
1

as

a>b>1 => a/b >1

adding same positive number to numerator and denominator will reduce the value of a/b (i.e bring a/b close to 1)

hence

a/b > a+1/b+1 > a+2/b+2 >1 => a+2/b+2 is closest to 1
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Joined: 23 Sep 2016
Posts: 233
Which of the following fractions is closest to 1 given that a > b > 1?  [#permalink]

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23 Feb 2018, 01:01
Bunuel wrote:
Which of the following fractions is closest to 1 given that a > b > 1?

(A) a/b
(B) (a + 2)/(b + 2)
(C) (a + 1)/(b + 1)
(D) (a + 1)/b
(E) (a - 1)/(b - 1)

IMO B
i can eliminate D straight forward as numerator is increasing will take away from 1
lets take a=3 b=2 now reverse plugin
A 3/2= 1.5
B 5/4= 1.25 A eliminated
C 4/3= 1.3 eliminated
D eliminated before
E 2/1 eliminated
KUDOS please if you like my explanation.
Which of the following fractions is closest to 1 given that a > b > 1?   [#permalink] 23 Feb 2018, 01:01
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