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Register now and save up to $200 Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Reach higher with Artificial Intelligence. Guaranteed Now free for 30 days Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code ## OG2016 - Q69 tagged by: ceilidh.erickson This topic has 4 expert replies and 0 member replies amina.shaikh309 Senior | Next Rank: 100 Posts Joined 23 Apr 2016 Posted: 31 messages #### OG2016 - Q69 Mon May 02, 2016 6:37 am Guy's net income equals his gross income minus his deductions. By what % did Guy's net income change on Jan 1,1989, when both his gross income and his deductions increased? 1. Guy's gross income increased by 4% on Jan 1, 1989 2. Guy's deductions increased by 15% on Jan 1, 1989 ### GMAT/MBA Expert DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 120 members Upvotes: 1153 GMAT Score: 770 Mon May 02, 2016 8:03 am amina.shaikh309 wrote: Guy's net income equals his gross income minus his deductions. By what % did Guy's net income change on Jan 1,1989, when both his gross income and his deductions increased? 1. Guy's gross income increased by 4% on Jan 1, 1989 2. Guy's deductions increased by 15% on Jan 1, 1989 You can see pretty quickly when you pick numbers that the answer will have to be E. Say that initially Guy has$100 in gross income and $100 in deductions. His net income is 0. That's the old net income. Percent Change = [(New - Old)/Old] * 100. If the Old is 0, we can't calculate a percent change, as we'll have a 0 in the denominator! (Tweak the numbers, and, of course, you could get a non-zero denominator. So the percent change could be undefined or not.) _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
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Mon May 02, 2016 8:01 am
The third possibility - circumventing algebra and picking numbers - is to THINK CONCEPTUALLY about the relationships given.

Because net income is defined as a difference between gross and deductions, we don't know anything about the proportional relationship of gross to deductions. If gross is HUGE but deductions are tiny, the 4% increase in gross will be bigger than a 15% increase in deductions. If those numbers are much closer to each other, though, the 15% increase in deductions will weigh more heavily than the 4% increase in gross, and the net income could actually decrease.

To have sufficient information here, we'd also need a PROPORTION of gross income to net income.

Consider the difference between this situation and the following:

Simple income is defined as wage times number of hours works. By how much did Guy's simple income increase when his wage went up 20% and his hours worked went up 10%?

Here, the relationship is multiplicative: S = (w)(h)
Multiplicative relationships are proportional.

We can express the change as:
(1.2w)(1.1h)
= 1.32wh
Since we know that wh = S, there must have been a 32% increase in S.

So, if you know the percent change in each term in a multiplicative relationship (a product or ratio), you'll know the percent change in the total. If it's an additive relationship (a difference or sum), just knowing the percent change in each term is not enough to know the percent change in the total.

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### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
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Mon May 02, 2016 7:42 am
This question can be solved either algebraically or by picking numbers.

ALGEBRA:

let N = net income, G = gross income, D = deductions
N = G - D

let x = change in net income, y = change in gross income, and z = change in deductions
N(1 + x/100) = G(1 + y/100) - D(1 + z/100)

If we want to know the value of x, we need information about G, D, y, and z. (You could solve for x algebraically here, but that would make things needlessly complicated).

1. Guy's gross income increased by 4% on Jan 1, 1989

This tells us that y = 4, but tells us nothing about z, G, or D. Insufficient.

2. Guy's deductions increased by 15% on Jan 1, 1989

This tells us that z = 15, but tells us nothing about y, G, or D. Insufficient.

1 & 2 together:

We can now express the new net income as:

N(1 + x/100) = 1.04G - 1.15D

substitute G - D for N:
(G - D)(1 + x/100) = 1.04G - 1.15D
1 + x/100 = (1.04G - 1.15D)/(G - D)

Since we cannot simplify the righthand side of the equation and cancel G and D, we cannot solve for x. Insufficient.

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### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
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Mon May 02, 2016 7:50 am
If you found the algebra confusing or weren't sure how to interpret it, picking numbers is a good option.

PICKING NUMBERS:

It's easy to see that the statements are insufficient on their own, as they each give only partial information. Therefore, let's start with the 2 statements together:

1 & 2 together:

If Net = Gross - Deductions, let:
original Gross = 100
original Deductions = 10

thus, original Net = 90

After a 4% increase to Gross and a 15% increase to deductions,
new Gross = 104
new Deductions = 11.5

thus, new Net = 92.5
the percent change in the Net is a little more than a 2.5% increase

Now, let's see if we get the same result with different values.

To keep things simple, keep the same Gross, but pick a much larger number for deductions:
original Gross = 100
original Deductions = 80

thus, original Net = 20

After a 4% increase to Gross and a 15% increase to deductions,
new Gross = 104
new Deductions = 92

thus, new Net = 12
the percent change in the Net is now a 40% decrease!

We got vastly different results in different cases, so the answer must be E.

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