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# In a certain economy, C represents the total amount of

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In a certain economy, C represents the total amount of [#permalink]

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14 Dec 2012, 12:27
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In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?
[Reveal] Spoiler: OA

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Re: In a certain economy, C represents the total amount of [#permalink]

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14 Dec 2012, 20:00
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roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?

$$C_{old} = 90 + \frac{9Y_{old}}{11}$$

$$Y_{old} = \frac{(C_{old} - 90)*11}{9}$$

$$Y_{new} = \frac{(C_{old} + 99 - 90)*11}{9} = \frac{(C_{old} + 9)*11}{9}$$

$$Increase = Y_{new} - Y_{old} = \frac{(C_{old} + 9)*11}{9} - \frac{(C_{old} - 90)*11}{9} = \frac{99*11}{9}$$

= 121

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Re: In a certain economy, C represents the total amount of [#permalink]

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15 Dec 2012, 02:07
MacFauz wrote:
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?

$$C_{old} = 90 + \frac{9Y_{old}}{11}$$

$$Y_{old} = \frac{(C_{old} - 90)*11}{9}$$

$$Y_{new} = \frac{(C_{old} + 99 - 90)*11}{9} = \frac{(C_{old} + 9)*11}{9}$$

$$Increase = Y_{new} - Y_{old} = \frac{(C_{old} + 9)*11}{9} - \frac{(C_{old} - 90)*11}{9} = \frac{99*11}{9}$$

= 121

Ok so your thinking process was - i need to find an increase hence subtract Yold and Ynew.
I did isolated Y and then instead of C i put C+99 but wasnt aware that i should treat them as Old and New.
interesting...
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Re: In a certain economy, C represents the total amount of [#permalink]

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15 Dec 2012, 04:54
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?

$$C=90+\frac{9Y}{11}$$ --> $$Y=\frac{11C}{9}-9*11$$.

$$Y_1=\frac{11C}{9}-9*11$$;
$$Y_2=\frac{11(C+99)}{9}-9*11=\frac{11C}{9}+11*11-9*11=(\frac{11C}{9}-9*11)+121$$.

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Re: In a certain economy, C represents the total amount of [#permalink]

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15 Dec 2012, 06:14
MacFauz wrote:
roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?

$$C_{old} = 90 + \frac{9Y_{old}}{11}$$

$$Y_{old} = \frac{(C_{old} - 90)*11}{9}$$

$$Y_{new} = \frac{(C_{old} + 99 - 90)*11}{9} = \frac{(C_{old} + 9)*11}{9}$$

$$Increase = Y_{new} - Y_{old} = \frac{(C_{old} + 9)*11}{9} - \frac{(C_{old} - 90)*11}{9} = \frac{99*11}{9}$$

= 121

I like your approach step by step, is fine.

But also if we do :C = 90 + 9y/11 ------> adding 99 we have 11 (C - 90 +99)/9= y -------> 11C + 99/9 = Y clearly the only value that fits is 11 * 2 + 99/9 = y. $$That is, 121$$
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Re: In a certain economy, C represents the total amount of [#permalink]

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16 Dec 2012, 03:18
Ans:
C = 90 + 9y/11 , adding 99 we have 11 (C - 90 +99)/9= y , (11C + 99)/9 = Y , so the increase is Y-y=121 the answer is (D).
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Re: In a certain economy, C represents the total amount of [#permalink]

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30 Jan 2014, 06:41
Just assume y=11 and C=99

Then C=198 and Y=132

So Y increases by 121

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Re: In a certain economy, C represents the total amount of [#permalink]

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30 Jan 2014, 20:20
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roygush wrote:
In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars?

A.11
B.22
C.99
D.121
E.171

I tried several different approaches any tried to input numbers to see how it reacts but nothing worked...
can someone care to explain?

Given $$C = 90 + \frac{9Y}{11}$$
Note that C changes whenever Y changes. So if C increases by 99, it's because Y increased from Y1 to Y2.

$$\frac{9}{11}(Y2 - Y1) = 99$$
$$Y2 - Y1 = 121$$
Y increased by 121 which led to an increase of 99 in C.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 12906 Followers: 563 Kudos [?]: 158 [0], given: 0 Re: In a certain economy, C represents the total amount of [#permalink] ### Show Tags 27 Jan 2016, 22:54 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 06 Apr 2010 Posts: 17 Followers: 0 Kudos [?]: 2 [0], given: 7 In a certain economy, C represents the total amount of consumption in [#permalink] ### Show Tags 09 Mar 2016, 10:17 In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation $$C= 90+\frac{9}{11}y$$ . If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars? A) 11 B) 22 C) 99 D) 121 E) 171 Math Expert Joined: 02 Sep 2009 Posts: 35950 Followers: 6863 Kudos [?]: 90115 [0], given: 10418 Re: In a certain economy, C represents the total amount of [#permalink] ### Show Tags 09 Mar 2016, 10:21 ninayeyen wrote: In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation $$C= 90+\frac{9}{11}y$$ . If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars? A) 11 B) 22 C) 99 D) 121 E) 171 Merging topics. Please refer to the discussion above. _________________ Verbal Forum Moderator Joined: 02 Aug 2009 Posts: 4148 Followers: 308 Kudos [?]: 3265 [0], given: 100 Re: In a certain economy, C represents the total amount of [#permalink] ### Show Tags 10 Mar 2016, 06:48 ninayeyen wrote: In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation $$C= 90+\frac{9}{11}y$$ . If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income, in millions of dollars? A) 11 B) 22 C) 99 D) 121 E) 171 hi, lets see the equation- $$C= 90+\frac{9}{11}y$$ .. here 90 is a constant term, so ANY increase / decrease in C will be COMPENSATED by y.. so an increase of 99 will be taken care by y.. $$99= \frac{9}{11}y$$ or y=121.. D _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html Re: In a certain economy, C represents the total amount of [#permalink] 10 Mar 2016, 06:48 Similar topics Replies Last post Similar Topics: 3 Of the total amount that Jill spent on a shopping trip, excluding taxe 3 10 Jan 2016, 06:41 6 A couple spent$264 in total while dining out and paid this amount usi 8 02 Dec 2014, 08:12
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