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# M09#12

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Re: M09#12 [#permalink]  14 Jun 2013, 05:56
is it not as simple as 0.9/1.2?
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Re: M09#12 [#permalink]  15 Jun 2013, 02:36
santas wrote:
is it not as simple as 0.9/1.2?

No. We shouldn't consider like that. We cannot simply add 0.1 for every cylinder. Actually we need to do add 10% of the sum.
Consider Power of one cylinder engine is 1. For every cylinder increase, power increases by 10%. So then

2 Cylinder Engine power = 1+(10% of 1) = 1.1
3 Cylinder Engine power = 1.1+(10% of 1.1) = 1.21
4 Cylinder Engine power = 1.21+(10% of 1.21) = 1.33
5 Cylinder Engine power = 1.33+(10% of 1.33) = 1.46
6 Cylinder Engine power = 1.46+(10% of 1.46) = 1.61
7 Cylinder Engine power = 1.61+(10% of 1.61) = 1.77
8 Cylinder Engine power = 1.77+(10% of 1.77) = 1.95
9 Cylinder Engine power = 1.95+(10% of 1.95) = 2.15
10 Cylinder Engine power = 2.15+(10% of 2.15) = 2.37
11 Cylinder Engine power = 2.37+(10% of 2.37) = 2.61
12 Cylinder Engine power = 2.61+(10% of 2.61) = 2.87

So $$\frac{2.15}{2.87}=0.75$$

Hope this helps !
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Re: M09#12 [#permalink]  15 Jun 2013, 02:38
very simple...

each time a cylinder is added it increases by 1.1

So the required ans is
= (1.1)^9/(1.1)^12

= 1/(1.1)^3

= 1000/11*11*11

= 1000/1331(lol more simpler)

= 0.75 ...which is D
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Re: M09#12 [#permalink]  16 Jun 2013, 04:09
Ratio= (1/1.333)=3/4=0.75
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Re: M09#12 [#permalink]  19 Jun 2013, 00:33
1
KUDOS
Power of 9 cylinder = X
Power of 10 cylinder = 1.1X
Power of 11 cylinder = 1.1^2 X
Power of 12 cylinder = 1.1^3 X

==> Power of 9 cylinder / Power of 12 cylinder = X / 1.1^3X = 1/1.33
Tip:
when you see 0.333 or 1.3333 or 2.3333 ==> Think about "3 times of them" because 0.3333 x 3 = 1; 1.333 x 3 = 4

We time both numerator and denominator by 3
==> [1 x 3] / [1.33 x 3] = 3/4 = 0.75

Hope it helps.
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Re: M09#12 [#permalink]  23 Jun 2013, 17:06

This problem would use the percentage increase or percentage decrease formula. As we know the increase in one cylinder means 10% increase, hence an increase from 9 to 12 cylinders is (1.1)^3 times. To get that, an increase by 10% is

P(1+i%) or
P(1+0.1)
= P(1.1)

Doing that 3 times
= P(1.1)(1.1)(1.1)

Take a simple value of P, or 9 cylinder power as 100 = Percentage increase from 9 to 12 = 100 (1.1)^3

As we need the ratio here:
= 100/ (100(1.1)^3) = approx. .75

Hope this helps!
Current Student
Joined: 30 May 2013
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Re: M09#12 [#permalink]  26 Jun 2013, 13:49
I used 10 as my base and eventually got to 10/13.31.
But how would you put this in decimal form and get .75 without a calculator?
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Re: M09#12 [#permalink]  28 Jun 2013, 19:27
Quote:
If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?

(A) 0.69
(B) 0.71
(C) 0.72
(D) 0.75
(E) 0.78

this worked best for me
Assume that 9 cylinders has a power output of 100%, then...

9 cylinders: 100
10 cylinders: 100 + 10 = 110
11 cylinders: 110 + 11 = 121
12 cylinders: 121 + 12 = 133

Thus, the ratio of 9 cylinders : 12 cylinders is...
100/133 = 0.75
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Re: M09#12 [#permalink]  02 Jun 2014, 20:50
If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?

(A) 0.69
(B) 0.71
(C) 0.72
(D) 0.75
(E) 0.78

The power of engine decreases by 9.09% when the number of its cylinders is decreased by one.
Hence, power of engine decreases by (9+9-0.81)% or 17.37% when the number of its cylinders is decreased by two
Likewise, power power of engine decreases by (17.37+9.09-0.15)% or 24.89% when the number of cylinders is decreased by three.
Let the power of 12-cylinder engine be 100.
So, the ratio of power of a 9 cylinder engine to that of 12 cylinder engine is (100-24.89)/100=0.75 (approximated)

The question can be solved quickly by approximating 9.09 as 9.

Re: M09#12   [#permalink] 02 Jun 2014, 20:50

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# M09#12

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