In a certain economy, C represents the total amount of

Question

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?

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?

MacFauz · Accepted Answer

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

Answer is D

roygush · Answer

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...

Bunuel · Answer

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 .

Answer: D

Carcass · Answer

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

priyamne · Answer

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).

jlgdr · Answer

Just assume y=11 and C=99

Then C=198 and Y=132

So Y increases by 121

D

KarishmaB · Answer

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.

ninayeyen · Answer

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

Bunuel · Answer

Merging topics. Please refer to the discussion above.

chetan2u · Answer

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

ScottTargetTestPrep · Answer

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

AldrinAntonyPJ · Answer

Step 1: Understand the Given Equation
We are given the relationship between consumption ( C ) and national income ($ Y $) in the form of the equation:

\

This equation indicates how consumption is dependent on national income.

### Step 2: Identify the Change in Consumption
The problem states that the total amount of consumption increases by 99 million dollars. We need to find the corresponding increase in national income.

### Step 3: Set Up the Equation for the Initial and Final States
Let's denote the initial consumption as $ C_1 $ and the final consumption as $ C_2 $. The change in consumption ($ \Delta C $) is given as 99 million dollars.

So, we can write:

\

### Step 4: Use the Given Relationship to Express the Change
Using the given equation for consumption, we can write the initial and final consumption in terms of the national income:

Initial consumption:
\

Final consumption:
\

### Step 5: Express the Change in Terms of Income
Since the change in consumption is 99 million dollars, we can write:

\

Substituting the equations for $ C_1 $ and $ C_2 $:

\

### Step 6: Simplify the Equation
Subtract 90 from both sides of the equation to simplify:

\

### Step 7: Solve for the Change in National Income
To isolate the terms involving $ Y $, we subtract $ \frac{9Y_1}{11} $ from both sides:

\

Factor out $ \frac{9}{11} $ on the left-hand side:

\

Solve for $ Y_2 - Y_1 $:

\

### Step 8: Conclusion
The increase in the total national income, $ \Delta Y $, is 121 million dollars.

So, the increase in the total national income is 121 million dollars.

mcrea · Answer

My way:

C(old) = 90 + 9*Y(old)/11
C(new) = 90 + 9*Y(new)/11

subtract new from old:

C(new)-C(old) = 90 + 9*Y(new)/11 - 90 - 9*Y(old)/11 
99 = 9/11 * (Y(old)-Y(new))

Y(new)-Y(old) = (99*11)/9 = 121

IMO D

GMATinsight · Answer

C=90+9Y/11

i.e. Y = (C-90)*11/9

Now, C increases by 99

i.e. Y' = (C +99 -90)*11/9
i.e. Y' = (C-90)*11/9 +  99*11/9 
i.e. Y' = (C-90)*11/9 +  11*11 
i.e. Y' = (C-90)*11/9 +  121

i.e. Y' = Y + 121

Answer: Option D

In a certain economy, C represents the total amount of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a certain economy, C represents the total amount of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards