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Math Expert V
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Guy's net income equals his gross income minus his deduction  [#permalink]

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Question Stats: 69% (01:32) correct 31% (01:28) wrong based on 1781 sessions

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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.

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Math Expert V
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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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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.

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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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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

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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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1
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
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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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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

Math Expert V
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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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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?
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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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marcovg4 wrote:
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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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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Bunuel wrote:
marcovg4 wrote:
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.

Hi Bunuel,

I came here to ask the same question, although I was expecting a different answer.

If we have an original ratio of Gross/Deduc, and they gave us the adjusted Gross/Deduc -- that would just mean that we have a new ratio for Gross/Deduc, correct?

If we compare the two ratios, don't we just get a old net/new net? Without knowing the anchor points, how can we still classify that as a change, wouldn't it instead just be a ratio? Meaning, a ratio of new/old could be 5/4, so the new net could be 100 and the old could be 80. Using the same theory, it could also be 200/160. The dollar amount has a much bigger change in the second example?
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Guy's net income equals his gross income minus his deduction  [#permalink]

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russ9 wrote:
Bunuel wrote:
marcovg4 wrote:
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.

Hi Bunuel,

I came here to ask the same question, although I was expecting a different answer.

If we have an original ratio of Gross/Deduc, and they gave us the adjusted Gross/Deduc -- that would just mean that we have a new ratio for Gross/Deduc, correct?

If we compare the two ratios, don't we just get a old net/new net? Without knowing the anchor points, how can we still classify that as a change, wouldn't it instead just be a ratio? Meaning, a ratio of new/old could be 5/4, so the new net could be 100 and the old could be 80. Using the same theory, it could also be 200/160. The dollar amount has a much bigger change in the second example?

BUMP.

Suppose, original ratio is given as Gr:De = 100 : 80 .....[Also, assuming it as smart number]
Then, 1+2) New Gr : De = 1.04*100 : 1.15*80 => 104 : 92
New NI = 12
Old NI = 20
We get (12-20)/20 = -8/20 = 40 percent decrease.
The NI is supposed to increase and but due to the higher De percentage, NI decreased. Is it sufficient or not?

...or am I lost?

Update 1: NI can increase/decrease because the questions says what percent NI change.
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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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1
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.
Attachment: GCDS Bunuel Guy's net income equals his gross (20160106).jpg [ 31.45 KiB | Viewed 20725 times ]

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.
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Re: Guy's net income equals his gross income minus his deduction  [#permalink]

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Bunuel wrote:
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.[/quote]

Hi Bunuel,

I came here to ask the same question, although I was expecting a different answer.

If we have an original ratio of Gross/Deduc, and they gave us the adjusted Gross/Deduc -- that would just mean that we have a new ratio for Gross/Deduc, correct?

If we compare the two ratios, don't we just get a old net/new net? Without knowing the anchor points, how can we still classify that as a change, wouldn't it instead just be a ratio? Meaning, a ratio of new/old could be 5/4, so the new net could be 100 and the old could be 80. Using the same theory, it could also be 200/160. The dollar amount has a much bigger change in the second example?[/quote]

BUMP.

Suppose, original ratio is given as Gr:De = 100 : 80 .....[Also, assuming it as smart number]
Then, 1+2) New Gr : De = 1.04*100 : 1.15*80 => 104 : 92
New NI = 12
Old NI = 20
We get (12-20)/20 = -8/20 = 40 percent decrease.
The NI is supposed to increase and but due to the higher De percentage, NI decreased. Is it sufficient or not?

...or am I lost?

Update 1: NI can increase/decrease because the questions says what percent NI change.[/quote]

Hi VeritasKarishma or any other experts,

Could you guys please comment on this ?

Thanks a lot
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Guy's net income equals his gross income minus his deduction  [#permalink]

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Bunuel wrote:
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.

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

Cheers,
Brent
_________________ Guy's net income equals his gross income minus his deduction   [#permalink] 13 Dec 2019, 13:58
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