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In the country of XYZ, the I-score of a politician is computed

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In the country of XYZ, the I-score of a politician is computed [#permalink] New post   10 Aug 2021, 05:42
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In the country of XYZ, the I-score of a politician is computed from the following formula:

\(I = \frac{41ab^2c^3}{d^2}\), in which the variables \(a, b, c,\) and \(d\) represent various perceived attributes of the politician, all of which are measured with positive numbers.

Mayor Flower’s I-score is 150% higher than that of Councilor Plant; moreover, the values of \(a, b,\) and \(c\) are 60% higher, 40% higher, and 20% lower, respectively, for Mayor Flower than for Councilor Plant. The value of \(d\) for Councilor Plant is \(x\)% higher or lower than the corresponding value for Mayor Flower.

Quantity A
Quantity B
\(x\)
14.50%


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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A
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motion2020
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In the country of XYZ, the I-score of a politician is computed [#permalink] New post   Updated on: 14 Aug 2021, 09:08
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revised..

let's check change in \(ab^2c^3\)
\((1+3/5)*(1+2/5)^2*(1-1/5)^3=8/5 * 49/5^2 * 64/5^3 = (8*49*64)/5^6 = 1.6\)
Since I is inversely related with \(d^2\), every increase in I will result in decrease of \(d^2\), unless changes of \(a, b, c\) are outweighing the change in I. Change in I is 150% higher for Flower. Change in I is 2.5 vs changes of \(a, b, c\) equal to 1.6. Change requested is lower or higher, hence sq.root(2.5/1.6)=sq.root(25/10 * 10/16)=5/4=1.25 or 25%

Answer must be A

Originally posted by motion2020 on 10 Aug 2021, 17:16.
Last edited by motion2020 on 14 Aug 2021, 09:08, edited 1 time in total.
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Re: In the country of XYZ, the I-score of a politician is computed [#permalink] New post   14 Aug 2021, 05:58
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[quote="motion2020"]revised..

let's check change in \(ab^2c^3\)
\((1+3/5)*(1+2/5)^2*(1-1/5)^3=8/5 * 49/5^2 * 64/5^3 = (8*49*64)/5^6 = 1.6\)
Since I is inversely related with \(d^2\), every increase in I will result in decrease of \(d^2\), unless changes of \(a, b, c\) are outweighing the change in I. Change in I is 150% higher for Flower. Change in I is 2.5 vs changes of \(a, b, c\) equal to 1.6. Change requested is lower or higher, hence sq.root(2.5/1.6)=sq.root(25/10 * 10/16)=sq.root(5/4)=1.25 or 25%

Answer must be A[/It also says that x% is higher or lower what do we conclude from that do we take higher or lower ]
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Re: In the country of XYZ, the I-score of a politician is computed [#permalink] New post   14 Aug 2021, 06:03
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Jayz007 wrote:
motion2020 wrote:
revised..

let's check change in \(ab^2c^3\)
\((1+3/5)*(1+2/5)^2*(1-1/5)^3=8/5 * 49/5^2 * 64/5^3 = (8*49*64)/5^6 = 1.6\)
Since I is inversely related with \(d^2\), every increase in I will result in decrease of \(d^2\), unless changes of \(a, b, c\) are outweighing the change in I. Change in I is 150% higher for Flower. Change in I is 2.5 vs changes of \(a, b, c\) equal to 1.6. Change requested is lower or higher, hence sq.root(2.5/1.6)=sq.root(25/10 * 10/16)=sq.root(5/4)=1.25 or 25%

Answer must be A[/It also says that x% is higher or lower what do we conclude from that do we take higher or lower ]


It also says that x% is higher or lower what do we conclude from that do we take higher or lower than the corresponding value of Mayor Flower
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Re: In the country of XYZ, the I-score of a politician is computed [#permalink] New post   14 Aug 2021, 09:10
ok, in my previous post there was sq.root left over, though the value was not under sq.root - revised

IMO, higher/lower means ignore the direction of change (increase or decrease) and focus on the percentage value

Jayz007 wrote:
motion2020 wrote:
revised..

let's check change in \(ab^2c^3\)
\((1+3/5)*(1+2/5)^2*(1-1/5)^3=8/5 * 49/5^2 * 64/5^3 = (8*49*64)/5^6 = 1.6\)
Since I is inversely related with \(d^2\), every increase in I will result in decrease of \(d^2\), unless changes of \(a, b, c\) are outweighing the change in I. Change in I is 150% higher for Flower. Change in I is 2.5 vs changes of \(a, b, c\) equal to 1.6. Change requested is lower or higher, hence sq.root(2.5/1.6)=sq.root(25/10 * 10/16)=sq.root(5/4)=1.25 or 25%

Answer must be A[/It also says that x% is higher or lower what do we conclude from that do we take higher or lower ]
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Re: In the country of XYZ, the I-score of a politician is computed [#permalink] New post   27 Nov 2021, 21:30
motion2020 wrote:
revised..

let's check change in \(ab^2c^3\)
\((1+3/5)*(1+2/5)^2*(1-1/5)^3=8/5 * 49/5^2 * 64/5^3 = (8*49*64)/5^6 = 1.6\)
Since I is inversely related with \(d^2\), every increase in I will result in decrease of \(d^2\), unless changes of \(a, b, c\) are outweighing the change in I. Change in I is 150% higher for Flower. Change in I is 2.5 vs changes of \(a, b, c\) equal to 1.6. Change requested is lower or higher, hence sq.root(2.5/1.6)=sq.root(25/10 * 10/16)=5/4=1.25 or 25%

Answer must be A
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In the country of XYZ, the I-score of a politician is computed [#permalink] New post   17 Oct 2023, 07:13
motion2020 wrote:
revised..

let's check change in \(ab^2c^3\)
\((1+3/5)*(1+2/5)^2*(1-1/5)^3=8/5 * 49/5^2 * 64/5^3 = (8*49*64)/5^6 = 1.6\)
Since I is inversely related with \(d^2\), every increase in I will result in decrease of \(d^2\), unless changes of \(a, b, c\) are outweighing the change in I. Change in I is 150% higher for Flower. Change in I is 2.5 vs changes of \(a, b, c\) equal to 1.6. Change requested is lower or higher, hence sq.root(2.5/1.6)=sq.root(25/10 * 10/16)=5/4=1.25 or 25%

Answer must be A


motion2020 can you please explain why are we dividing the 2 numbers? Also, how are you getting 64/5^3? Isn't it supposed to be 512/5^3 ??
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Re: In the country of XYZ, the I-score of a politician is computed [#permalink] New post   17 Oct 2023, 10:27
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he simply put into formula the decrease pf 20%

\((1-1/5)^3\)

or you can simply write instead of fractions which is more complicated, the direct % decrease

0.80

As for the fraction

4/5^3=64/5. I believe he disregarded to raise to the power of three the 5 because all the fractions are with a denominator of 5. we care about the numerator
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Re: In the country of XYZ, the I-score of a politician is computed [#permalink]
17 Oct 2023, 10:27
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