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# If 1/5 of the larger of two positive numbers is greater than 6 times

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Math Expert
Joined: 02 Sep 2009
Posts: 58429
If 1/5 of the larger of two positive numbers is greater than 6 times  [#permalink]

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01 Nov 2018, 00:13
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Difficulty:

55% (hard)

Question Stats:

70% (02:08) correct 30% (02:08) wrong based on 48 sessions

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If 1/5 of the larger of two positive numbers is greater than 6 times the smaller of the same two numbers, is the smaller number less than 5?

(1) The larger number is greater than 120.
(2) The larger number is less than 150.

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Re: If 1/5 of the larger of two positive numbers is greater than 6 times  [#permalink]

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01 Nov 2018, 12:46
Let a be the smaller number and b be the larger number. So, b>a>0.
Also, as per question, (1/5)*b > 6*a, which gives, b>30a ...... (A)

Stmt 1: b>120
Let b be 144, then 144>30a which gives a<4.8
Let b be 153, then 153>30a which gives a<5.1, which means a can be 5.05 too.
Hence Insufficient. Eliminate A,D

Stmt 2: b<150
b<150 and b>30a, hence, 30a<150 or a<5
Hence sufficient.

Option B
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Re: If 1/5 of the larger of two positive numbers is greater than 6 times   [#permalink] 01 Nov 2018, 12:46
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