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OG2016 - Q69

This topic has 4 expert replies and 0 member replies
amina.shaikh309 Senior | Next Rank: 100 Posts Default Avatar
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OG2016 - Q69

Post 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

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Post 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.)

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Post 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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Post 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.)

_________________
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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!
Post 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!

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Thanked by: gmatdestroyer13, Anitochka
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