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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
Joined
23 Apr 2016
Posted:
31 messages

OG2016 - Q69

Post Mon May 02, 2016 6:37 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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 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.

    The answer is E.

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    Post 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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    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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