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If 0 < a < b is a < 10?

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Expert Post
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V
Joined: 02 Sep 2009
Posts: 41908

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

If 0 < a < b is a < 10? [#permalink]

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New post 21 Aug 2017, 06:41
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

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

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

Expert Post
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P
Joined: 02 Aug 2009
Posts: 4994

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

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

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New post 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

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Senior Manager
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G
Joined: 25 Feb 2013
Posts: 436

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

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

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New post 21 Aug 2017, 10:09
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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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