Problem Solving

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

GMAT assassins aren't born, they're made,
Rich

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