Data Sufficiency

Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased?

(1) Guy's gross income increased by 4 percent on
January 1, 1989.
(2) Guy's deductions increased by 15 percent on
January 1, 1989.

What are the things required here to answer the question directly before getting into equations and blah!

my pick would E.


We would need to know his gross income in 1989 or in any of the years and deductions in one of the year..

A . we don't anything about the deduction

B, don't know anything about the income

Together say X id the income in 1989 then next income would be 1.04x
Say Y is the deduction then new deduction would be 1.15Y

Net income in 1989 = X-Y
next year it 1.04x- 1.15y;
change 1.04x -1.15y-(x-Y)

percent would be .04x -0.l15y/ x-y *100 == equation cannot be solved -- hence E

Hope it helps

Is there a way by plugging #s???

akahuja143 wrote:my pick would E.


We would need to know his gross income in 1989 or in any of the years and deductions in one of the year..

A . we don't anything about the deduction

B, don't know anyzthing about the income

Together say X id the income in 1989 then next income would be 1.04x
Say Y is the deduction then new deduction would be 1.15Y

Net income in 1989 = X-Y
next year it 1.04x- 1.15y;
change 1.04x -1.15y-(x-Y)

percent would be .04x -0.l15y/ x-y *100 == equation cannot be solved -- hence E

Hope it helps

bhumika.k.shah wrote:
What are the things required here to answer the question directly before getting into equations and blah!

Gross Income - Deductions = Net Income

Say 1000 Dollars is gross income 500 dollars deductions ; net income = 500 dollars

1. Insufficient
2. Insufficient

Both together is also not sufficient since we do not know what the Deductions/Gross Income ratio earlier.

ajith wrote: Both together is also not sufficient since we do not know what the Deductions/Gross Income ratio earlier.

Can someone please explain the above. What ratio is he talking about?

Gurpinder wrote:
Can someone please explain the above. What ratio is he talking about?

Consider 2 cases, Gross income was 100 and Net Deductions were 10 (Gross income to Deduction ratio =10)
Gross income was 200 and deductions were 10 ((Gross income to Deduction ratio = 20)

The net income increase in both cases are different even after using (1) and (2)together

Now, if the Gross income to Deduction ratio was constant, using (1) and (2) we could have found out the net income increase in percentage but, it is not indicated in the question, hence E

E is the answer.

Lets say I have 100 rupees and I give 20 rupees as donation . How much I am left out with ??? ANS : 80

Now lets assume .
100 increases by 10 % and my donation increases by 30% . we can still find out what I am left out with.

Now if we are unaware of figure 100 and donation 20 . will we be able to come to any conclusion?

IMO E

ajith wrote:

Gurpinder wrote:
Can someone please explain the above. What ratio is he talking about?

Consider 2 cases, Gross income was 100 and Net Deductions were 10 (Gross income to Deduction ratio =10)
Gross income was 200 and deductions were 10 ((Gross income to Deduction ratio = 20)

The net income increase in both cases are different even after using (1) and (2)together

Now, if the Gross income to Deduction ratio was constant, using (1) and (2) we could have found out the net income increase in percentage but, it is not indicated in the question, hence E

Thank you!

Makes sense.

Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased?

Given: Net Income = Gross Income - Deductions.

(1) Guy's gross income increased by 4 percent on January 1, 1989. No info about deductions. Not sufficient.
(2) Guy's deductions increased by 15 percent on January 1, 1989. No info about gross income. Not sufficient.

(1)+(2) If Gross Income=100 and Deductions=100, then Guy had decrease in Net Income (since Deductions increased by greater percent than Gross Income) BUT if Gross Income=1,000 and Deductions=100, then Guy had some increase in Net Income. So, we cannot get the percent by which Guy's net income changed on January 1, 1989. Not sufficient.