Guy's net income equals his gross income minus his deductions. By what

SOLUTION

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.

Answer: E.
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I like those kind of questions because are almost pure logic without to stay too much thinking about numbers.

\(NI = net income\)

\(GI = gross income\)

\(Ded= deduction\)

\(NI = GI - Ded\)

1) we have only GI

2) we have only Ded

Both are insuff

Now is the most abstract part that you have to understand very carefully: if GI increase by 4% and Ded by 15% if we do not have a clear anchor point: GI even with a small variation could be larger than Ded so we could have a NI BUT if we have the reverse situation we would not have NI because the Ded could be larger than GI and the latter would disappear without to establish with security NI

E is the answer
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N.Income = G.Income - Deductions

lets say ni= gi -d

from 1 gi => 1.04 gi doesnot take abt Deductions so not sufficient

from 2 d => 1.15 d doesnot take abt Gross income so not sufficient

from 1 and 2

new net income = 1.04 gi - 1.15 d

Using thsi we still cant find the % change in Net income so E

1) No info about Deduction - Insufficient
2) No info about Gross income - Insufficient
1+2) New Income = 1.04 G + 1.15 D
New Income will vary for different relative values of Gross Income & Deductions - Insufficient

Answer E

I have a question:

If the problem provided with a Gross and Deduction ratio, then the correct answer would have been be C?

Since we are looking for a percent change, it doesn't matter actual values, right?

Yes, you are right.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.


When you modify the original condition and the question, it is frequently given in the Gmat Math test, which is “2 by 2” question like the table below.

In the above, there are 4 variables(a,b,c,d) and you also need 4 equations, which is likely to make E the answer.
When 1) & 2), you come up with Percent increase=(After-Before)* 100/Before=[1.04a-1.15c-(a-c)]* 100/(a-c) but you cannot find out the relations between a and c. So, you cannot find the answer. In other words, there can be more than one answer, which is not sufficient. Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Given: Guy's net income equals his gross income minus his deductions.

Target question: By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased?

When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Statement 1 tells us that Guy's gross income increased by 4 percent on January 1, 1989
Statement 2 tells us that Guy's deductions increased by 15 percent on January 1, 1989.
Let's examine two possible cases:

Case a: Guy's gross income WAS $200 and his deductions WERE $100.
So, his PREVIOUS net income = $200 - $100 = $100

AFTER the increases, Guy's gross income is $208 and his deductions are $115.
So, his CURRENT net income = $208 - $115 = $93

Guy's net income went from $100 to $93, which represents a 7% DECREASE in net income


Case b: Guy's gross income WAS $1000 and his deductions WERE $20.
So, his PREVIOUS net income = $1000 - $20 = $980

AFTER the increases, Guy's gross income is $1040 and his deductions are $23
So, his CURRENT net income = $1040 - $23 = $1017

Guy's net income went from $980 to $1017, which represents some INCREASE in net income

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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Bunuel I am bit concerned about percentage. I just solved 1 scenario and didn't thought about the other one.

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.

I just solved the first scenario and marked the answer as c. Can you tell me what are the safe values to play with percentage, As I could see sometimes the value gets change below 50 and sometimes it could to to 1000 and still value don't change. Please help.

himgkp1989, it's important to realise that the Gross Income and Deductions may have different weights and it is impossible to figure out the percentage change unless you know the their weights (the only exception is if they change by the same percentage).

Great thanks BrentGMATPrepNow. So will it be C if exact value of Gross income & deduction have been given? Thanks

That's correct.
If we were given those values, the correct answer would be C

Great thanks BrentGMATPrepNow for confirmation and your great help always.

Plugging in two pairs of numbers for N and D on this type of question ("testing cases") might have been too messy of a method on the GMAT Classic—but now that the Data Insights section of the GMAT Focus (which includes the Data Sufficiency question type!) allows the use of the on-screen calculator, I would say that this method is again clearly on the table.

1st example of testing C vs. E: N = 100, D = 10, NET = 90

new N = 104, new D = 11.5, NET = 92.5, % change = (2.5/90) x 100 = +2.77%

2nd example of testing C vs E: N = 100, D = 50, NET = 50

new N = 104, new D = 57.5, NET = 46.5, % change = (-3.5/50) x 100 = -7%

Clearly these are two different answers to the question as phrased—which is the definition of NOT SUFFICIENT.­­

You could also argue that given the pairs of numbers I have chosen (notice that for simplicity's sake, I only changed one of the numbers—and that for estimation's sake, I changed it significantly), a calculator is unnecessary, and estimation is sufficient.

Why? The first percent change is clearly positive, and the second is clearly negative.­­­­­­­