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A grocery store sells two varieties of jelly bean jars, and

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A grocery store sells two varieties of jelly bean jars, and [#permalink]  06 Aug 2011, 03:44
A grocery store sells two varieties of jelly bean jars, and each type of jellybean jar contains only red and yellow jellybeans. If jar B contains 20% more red jellybeans than jar A , but 10% fewer yellow jellybeans, and jar A contains twice as many red jellybeans as yellow jellybeans, by what percent is the number of jellybeans in jar B larger than the number of jellybeans in jar A?

Method 1:

Jar B contains 20% more red jellybeans than jar A but 10% fewer yellow jellybeans

120Rb = 100Ra
90Yb = 100Ya

Jar A contains twice as many red jellybeans as yellow jellybeans

100Ra must be doubled so must be Rb: 240Rb = 200Ra

By what percent is the number of jellybeans in jar B larger than the number of jellybeans in jar A?

Rb + Yb / Ra + Ya = 120 + 90 / 100 + 100 = 210 / 200 = 2.1

Jar B contains 10% more jellybeans than jar A.

Method 2:

Thoughts on the reasoning? Any faster method? Algebra?

Last edited by LGOdream on 06 Aug 2011, 05:22, edited 1 time in total.
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Re: A grocery store sells two varieties of jellybean jars... [#permalink]  06 Aug 2011, 05:17
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LGOdream wrote:
A grocery store sells two varieties of jelly bean jars, and each type of jellybean jar contains only red and yellow jellybeans. If jar B contains 20% more red jellybeans than jar A , but 10% fewer yellow jellybeans, and jar A contains twice as many red jellybeans as yellow jellybeans, by what percent is the number of jellybeans in jar B larger than the number of jellybeans in jar A?

$$R_b=1.2R_a$$

$$Y_b=0.9Y_a$$

$$R_a=2Y_a$$

Total in Jar B: $$R_b+Y_b$$

Total in Jar A: $$R_a+Y_a$$

%More in Jar B: $$\frac{Total_{(JarB)}-Total_{(JarA)}}{Total_{(JarA)}}*100$$

%More in Jar B: $$\frac{R_b+Y_b-R_a-Y_a}{R_a+Y_a}*100$$

%More in Jar B: $$\frac{1.2R_a+0.9Y_a-2Y_a-Y_a}{2Y_a+Y_a}*100$$

%More in Jar B: $$\frac{1.2*2*Y_a+0.9Y_a-2Y_a-Y_a}{2Y_a+Y_a}*100=10%$$
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Re: A grocery store sells two varieties of jellybean jars... [#permalink]  06 Aug 2011, 05:21
Oh yeah, that was one silly error on my part. I translated fast to algebra and completely missed the ratios.

Thank you!
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Re: A grocery store sells two varieties of jellybean jars... [#permalink]  20 Jan 2012, 03:13
Expert's post
In this kind of problem I'm more comfortable with the chart as suggested in MGMAT Guide 2.....

What I would ask: in this problem we have Jar A Difference and then Jar B if we use the chart. Ok

In other weighted average % change we have for example 2007 and 2008, and then the Total.

But sometimes I put, as in the Jar problem, only Jar A and B and the TOTAL. This is a mistake, because we havve a difference.

How to recognize when we have to use the first or the second. In other words HOW to set a chart in the right way ??' For instance an hint or a word, or a shift in the question stem.

I hope is clear what I 'm trying to say.

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Re: A grocery store sells two varieties of jellybean jars... [#permalink]  20 Jan 2012, 03:46
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carcass wrote:
In this kind of problem I'm more comfortable with the chart as suggested in MGMAT Guide 2.....

What I would ask: in this problem we have Jar A Difference and then Jar B if we use the chart. Ok

In other weighted average % change we have for example 2007 and 2008, and then the Total.

But sometimes I put, as in the Jar problem, only Jar A and B and the TOTAL. This is a mistake, because we havve a difference.

How to recognize when we have to use the first or the second. In other words HOW to set a chart in the right way ??' For instance an hint or a word, or a shift in the question stem.

I hope is clear what I 'm trying to say.

I'm not sure I understand your question. So can you please give an example (maybe with a chart you are talking about).

As for the question itself:
A grocery store sells two varieties of jelly bean jars, and each type of jellybean jar contains only red and yellow jellybeans. If jar B contains 20% more red jellybeans than jar A , but 10% fewer yellow jellybeans, and jar A contains twice as many red jellybeans as yellow jellybeans, by what percent is the number of jellybeans in jar B larger than the number of jellybeans in jar A?

Probably the easiest way would be to pick some smart numbers. As we have fraction of Red/Yellow=2/1 (3 parts) for jar A, then let the number of jellybean in A be 60 (multiple of 3). Then:

Jar A: Red=40 and Yellow=20 --> Total=60;
Jar B: Red=40*1.2=48 and Yellow=20*0.9=18 --> Total=66;

Percent=Difference/Original*100=(66-60)/60*100=10% (as we are comparing to Jar A put in denominator total for A).

Hope it's clear.
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Re: A grocery store sells two varieties of jelly bean jars, and [#permalink]  20 Jan 2012, 04:24
Expert's post
Attachment:

shot1.jpg [ 29.07 KiB | Viewed 1809 times ]
Ok what I mean is this

In the first one I did: Jar A Jar B and then Total NOT Difference. I handle it as the second one (the chart of voters). It is wrong.

How to recognize in a problem to set a chart as the first one or the second one. I do not see difference but indeed there is difference.

Thanks
Attachments

shot2.jpg [ 30.57 KiB | Viewed 1805 times ]

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Re: A grocery store sells two varieties of jelly bean jars, and [#permalink]  20 Jan 2012, 05:03
Expert's post
carcass wrote:
Ok what I mean is this

the first chart is this

The following problem, that is again a weighted average % change problem is this

In the first one I did: Jar A Jar B and then Total NOT Difference. I handle it as the second one. is wrong.

How to recognize in a problem to set a chart as the first one or the second one. I do not see difference but indeed there is difference.

Thanks

The original question asks: "by what percent is the number of jellybeans in B larger than the number of jellybeans in jar A?" Thus we are interested in Difference/Original=Difference/Jar A.

For example by what percent is 14 more than 10: general formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$ --> $$Percent=\frac{14-10}{10}*100=40%$$ --> 14 is 40% more than 10.

The second question:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

Now, this question asks about the ratio of (This year's Revolutionary voters) to (This year's total voters). So, no percent increase (decrease) involved.

Solution
Set the equation for the number of total voters this year: $$1.1R+1.05S=1.08(R+S)$$ --> $$2R=3S$$

The question is $$\frac{1.1R}{1.1R+1.05S}=?$$ --> $$\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}$$. Now, as $$2R=3S$$ then $$70R=105S$$ (multiplying by 35) --> substitute 105S by 70R: $$\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}$$

Hope it's clear.
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Re: A grocery store sells two varieties of jelly bean jars, and [#permalink]  20 Jan 2012, 05:46
Expert's post
Thanks for the help.

Now is CLEAR.

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Re: A grocery store sells two varieties of jelly bean jars, and [#permalink]  30 Oct 2014, 05:40
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Re: A grocery store sells two varieties of jelly bean jars, and   [#permalink] 30 Oct 2014, 05:40
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