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

by vinni.k » Thu Oct 12, 2017 9:39 am
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

OA is D

Can you please give 2 or 3 approaches on how to handle this question ? My approach is taking about 3.5 to 4 mins on this question.

Thanks
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by DavidG@VeritasPrep » Thu Oct 12, 2017 10:38 am
vinni.k 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

OA is D

Can you please give 2 or 3 approaches on how to handle this question ? My approach is taking about 3.5 to 4 mins on this question.

Thanks
Say the initial consumption was 0. We can find the initial national income by solving 0 = 90 + 9y/11; and y = -110
If the new consumption is 99, we can find the new national income by solving 99 = 90 + 9y/11; now y = 11

So the national income increased from -110 to 11, for a net increase of 121. The answer is D
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by [email protected] » Thu Oct 12, 2017 12:15 pm
Hi vinni.k,

We're given the equation C = 90 + 9Y/11. With this relationship, if we increase/decrease one of the variables, then we will have to also increase/decrease the other variable to properly 'compensate' for the change. This question can be solved rather easily by TESTing VALUES (the approach David used). You can also solve it with a bit of arithmetic and some logic.

If the consumption (C) increases by 99, then we to increase the 'right side' of the equation 99 also. We can't change the "90", so we have to increase the value of Y so that 9Y/11 becomes '99 more' than it used to be. You can do this math in 2 small steps:

First, to cancel out the denominator, we can make Y=11. this gives us 99/11 = 9. Second, since we're dealing with multiplication, to raise 9 to 99, we need to multiply by 11. Thus, we're increasing Y by 11 and then multiplying by 11. This is the equivalent of (11)(11) = 121.

Final Answer: D

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by vinni.k » Fri Oct 13, 2017 11:50 am
Thanks David for your approach.

Rich,
thanks for your approach too, but this is what i was able to make from the first few statements
9y/11 = 99 . After solving this gives me 121; however, i am not able to understand the following explanation.
[email protected] wrote:
First, to cancel out the denominator, we can make Y=11. this gives us 99/11 = 9. Second, since we're dealing with multiplication, to raise 9 to 99, we need to multiply by 11. Thus, we're increasing Y by 11 and then multiplying by 11. This is the equivalent of (11)(11) = 121.
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by [email protected] » Sat Oct 14, 2017 11:39 am
Hi vinni.k,

Here's a bit more explanation on the approach that I used:

9Y/11 will equal some value. To increase that value, we clearly have to increase the value of Y.

Regardless of what the 'starting value' is for Y, IF we increase Y by 11, then the INCREASE to 9Y/11 will be.... 9(11)/11 = 9

For example. IF Y = 0, then 9(0)/11 = 0
Increasing Y by 11 gives us 9(11)/11 = 9

Based on the wording of the prompt, we need to increase the value of 9Y/11 by 99... and that is '11 times' more than the example that we just dealt with. Thus, we have to increase Y by 11 and THEN multiply that number by 11.... (+11)(11) = 121.

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by Scott@TargetTestPrep » Wed Nov 27, 2019 10:48 am
vinni.k 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

OA is D

Can you please give 2 or 3 approaches on how to handle this question ? My approach is taking about 3.5 to 4 mins on this question.

Thanks
Let x be the increase in the total national income. We can create the equation:

C + 99 = 90 + 9(Y + x)/11

However, since C = 90 + 9Y/11, we have:

90 + 9Y/11 + 99 = 90 + 9(Y + x)/11

9Y/11 + 99 = 9Y/11 + 9x/11

99 = 9x/11

11 = x/11

121 = x

Alternate Solution:

Let's begin by expressing Y in terms of C:

C = 90 + (9/11)Y

11C = 990 + 9Y

9Y = 11C - 990

Y = (11/9)C - 110

Now, suppose C increases by 99, i.e., C becomes C + 99. Then,

(11/9)(C + 99) - 110 = (11/9)C + 121 - 110 = (11/9)C - 110 + 121

Since (11/9)C - 110 = Y; we have:

(11/9)C - 110 + 121 = Y + 121

Thus, we see that when C increases to C + 99, Y increases to Y + 121.

Answer: D

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