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

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25 Mar 2006, 14:15

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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.

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

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27 Dec 2010, 15:30

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girindra 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

I think most people would agree that the answer lies in either E or C, at first glance some would propably pick C. However, C is wrong since we need the ratio between gross income and deductions.

Assume that my gross income is 100 and my deductions is 100 With 1+2) income +4% = 4$ and deductions up 15% = 15$ which equals a net decline

If we change my income to 500 and keep deductions at 100 With 1+2) Income +4% = 20$ and deductions up 15% = 15$ which equals a net increase.

Conclusion, we need to know ratio/fraction of gross income to deductions to find the answer.
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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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

I find it helps to write down the given relation:

Net Income = Gross Income - Deductions

Ques: By what % did Net Income increase if both Gross Income and Deductions increase? First up, what comes to mind is that if both Gross Income and Deductions increase by the same percentage, Net Income will increase by the same % too.

Say, both increase by 10%,

New Net Income = (110/100)Gross Income - (110/100)Deductions New Net Income = (110/100)(Gross Income - Deductions) = (110/100) Net Income

But here, even if we consider both statements together, we get New Net Income = (104/100)Gross Income - (115/100)Deductions There is no way we can find how New Net Income is related to Net Income. It will depend on the values of Gross Income and Deductions. (Take Gross Income as 100 and Deductions as 50 in one case and Deductions as 25 in another to see that Net Income changes by a different % in the two cases.)

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

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06 Feb 2011, 13:55

(n2-n1)/n1 is asked. n1=g1-d1 n2=g2-d2 1) g2=1.04g1 Not Suff. as we do not know anything abt d1/d2 2) d2=1.15d1 Not Suff. as we do not know anything abt n1/n2 Cobining, (1.04g1-1.15d1-g1+d1)/(g1-d1)=(0.04g1-0.15d1)/(g1-d1) Still Not Suff. to calculate exact %. So, E

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

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13 Jul 2014, 17:09

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b]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?[/b]

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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