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# If 0 < a < b is a < 10?

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Math Expert
Joined: 02 Sep 2009
Posts: 41908

Kudos [?]: 129394 [0], given: 12197

If 0 < a < b is a < 10? [#permalink]

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21 Aug 2017, 06:41
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Difficulty:

55% (hard)

Question Stats:

56% (01:41) correct 44% (01:11) wrong based on 41 sessions

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If 0 < a < b is a < 10?

(1) 1/a + 1/b = 5

(2) 1/a > 1/10
[Reveal] Spoiler: OA

_________________

Kudos [?]: 129394 [0], given: 12197

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4994

Kudos [?]: 5525 [0], given: 112

Re: If 0 < a < b is a < 10? [#permalink]

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21 Aug 2017, 09:40
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Bunuel wrote:
If 0 < a < b is a < 10?

(1) 1/a + 1/b = 5

(2) 1/a > 1/10

hi...
0<a<b

statement I
$$\frac{1}{a} + \frac{1}{b} = 5$$....
both a and b are positive and a<b, so $$\frac{1}{a}>\frac{1}{b}$$..
lets find slightly MORE than the MAX possible value of a... let a=b
so $$\frac{1}{a} + \frac{1}{a}=\frac{2}{a} = 5......a=\frac{2}{5}$$
now when b increase from 2/5, a has to decrease from 2/5 to get the SUM as 5
so a<10
sufficient
statement II
1/a>1/10
cross multiply..
a<10
sufficient

D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5525 [0], given: 112

Senior Manager
Joined: 25 Feb 2013
Posts: 436

Kudos [?]: 198 [1], given: 31

Location: India
GPA: 3.82
If 0 < a < b is a < 10? [#permalink]

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21 Aug 2017, 10:09
1
KUDOS
Bunuel wrote:
If 0 < a < b is a < 10?

(1) 1/a + 1/b = 5

(2) 1/a > 1/10

Statement 1: as $$a$$ & $$b$$ are positive and $$a<b$$, so reciprocal of $$a$$ & $$b$$ will be $$\frac{1}{a}>\frac{1}{b}$$ ------(1)
Now adding $$\frac{1}{a}$$ to both sides of eq.1

therefore $$\frac{1}{a}$$ $$+$$ $$\frac{1}{a}$$$$>$$$$\frac{1}{b}$$ $$+$$ $$\frac{1}{a}$$, or

$$\frac{2}{a}>5$$ (as $$\frac{1}{a} +\frac{1}{b} =5$$). Hence $$a<\frac{2}{5}$$
Therefore $$a<10$$. Sufficient

Statement 2: $$\frac{1}{a}>\frac{1}{10}$$, cross multiplying
$$a<10$$. Sufficient

Option $$D$$

Kudos [?]: 198 [1], given: 31

If 0 < a < b is a < 10?   [#permalink] 21 Aug 2017, 10:09
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