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# If a > 0 and b > 0, is 1/(a + b) < 1? (1) a/b = 2 (2) a + b > 1

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
If a > 0 and b > 0, is 1/(a + b) < 1? (1) a/b = 2 (2) a + b > 1  [#permalink]

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31 Oct 2018, 23:24
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:00) correct 34% (01:42) wrong based on 29 sessions

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If a > 0 and b > 0, is 1/(a + b) < 1?

(1) a/b = 2

(2) a + b > 1

_________________
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 668
Re: If a > 0 and b > 0, is 1/(a + b) < 1? (1) a/b = 2 (2) a + b > 1  [#permalink]

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31 Oct 2018, 23:36
Bunuel wrote:
If a > 0 and b > 0, is 1/(a + b) < 1?

(1) a/b = 2

(2) a + b > 1

Lets try to simplify the question stem further.
1/(a+b) <1 ?

since, a > 0 & b > 0 , a+b>0... so we can cross-multiply by (a+b) without affecting the inequality question.

$$\frac{1}{(a+b)} * (a+b) < 1* (a+b)$$?
Or,
$$(a+b) >1$$?

This is our new question stem.

St 1. a/b = 2

a = 2b
Is a+b>1?
Is 2b+b>1?
Is 3b>1?
Is b>1/3 ? We do not know. Hence not sufficient.

St 2. a + b > 1 This is exactly our simplified question stem. Hence sufficient!

Hence Option (B) is our choice.

Best,
_________________

Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

Re: If a > 0 and b > 0, is 1/(a + b) < 1? (1) a/b = 2 (2) a + b > 1 &nbs [#permalink] 31 Oct 2018, 23:36
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