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Register now and save up to $200 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 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 Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2457 messages Followed by: 115 members Upvotes: 1153 GMAT Score: 770 Top Reply 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
Joined
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Posted:
1706 messages
Followed by:
224 members
Upvotes:
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Top Reply
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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Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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### GMAT/MBA Expert

DavidG@VeritasPrep Legendary Member
Joined
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Posted:
2457 messages
Followed by:
115 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

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
Joined
04 Dec 2012
Posted:
1706 messages
Followed by:
224 members
Upvotes:
1443
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.

_________________

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

Thanked by: gmatdestroyer13, Anitochka
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

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