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M08-33

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M08-33 [#permalink]

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73% (00:43) correct 27% (01:23) wrong based on 112 sessions

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Re M08-33 [#permalink]

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Official Solution:

In what proportion should a 30%-solution and a 3%-solution be mixed to obtain a 12%-solution?

A. 1:3
B. 1:2
C. 2:3
D. 3:4
E. 4:5


Let \(X\) denote the volume of the 30%-solution and \(Y\) the volume of the 3%-solution.

\(\frac{(0.3X + 0.03Y)}{(X + Y)} = 12\%\) or \(30X + 3Y = 12X + 12Y\). From here \(18X = 9Y\) or \(X:Y = 1:2\).


Answer: B
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Re: M08-33 [#permalink]

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New post 18 Feb 2016, 05:35
Here, the trap is to confused with ratio and actual number. We need two equations for two unknowns but just one equation is enough to find out the ratio.
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Re: M08-33 [#permalink]

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New post 08 Jul 2017, 08:20
This can also be solved pretty quickly using Alligation. Let 30% Solution be A. And 3% Solution be B. Asked is A/B

From the snap shot we get \(B : A = 18 : 9 = 2 : 1 => A: B = 2:1\)
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Re: M08-33 [#permalink]

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New post 03 Sep 2017, 15:01
I did this (to me) more intuitively, as is possible with some ratio problems:

we need 12/100

we have 3/100 and 30/100

36/300 = 12/100, so 1x30+2x3 or 1:2

Time required <20 seconds, and another 10 seconds to verify answer just in case.
Re: M08-33   [#permalink] 03 Sep 2017, 15:01
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