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# M08-33

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Math Expert
Joined: 02 Sep 2009
Posts: 54544

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16 Sep 2014, 00:38
2
2
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:43) correct 27% (01:27) wrong based on 117 sessions

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 54544

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16 Sep 2014, 00:38
1
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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 $$X:Y = 1:2$$.

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Intern
Joined: 22 Aug 2014
Posts: 41

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18 Feb 2016, 06:35
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.
Manager
Joined: 12 Jun 2016
Posts: 214
Location: India
WE: Sales (Telecommunications)

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08 Jul 2017, 09:20
1
1
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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My Best is yet to come!
Intern
Joined: 02 Aug 2017
Posts: 6
GMAT 1: 710 Q46 V41
GMAT 2: 600 Q39 V33

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03 Sep 2017, 16:01
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, 16:01
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# M08-33

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