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OG 13: DS Q#77

This topic has 1 expert reply and 3 member replies
ProGMAT Senior | Next Rank: 100 Posts
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OG 13: DS Q#77

Post Fri Aug 16, 2013 8:34 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A total of $60,000 was invested for 1 year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4080, what is the value of x?

    (1) x=3y/4
    (2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

    OA: C

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    Post Sat Aug 17, 2013 4:32 am
    Quote:
    A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

    (1) x = 3y / 4
    (2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
    Since 4080 is between 5% and 10% of 60,000, it is likely that x and y are between 5 and 10.

    Statement 1: x = (3/4)y
    It's possible that x=6 and y=8 or that x=6.6 and that y=8.8.
    To accommodate the desired combination of percentages, we could simply adjust the amount invested at each percentage so that the total amount of interest earned = 4080.
    Since x can be different values, INSUFFICIENT.

    Statement 2: The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3/2.

    Sum of the parts of the ratio = 3+2 = 5.
    Since the actual amount invested = 60,000, and 60,000/5 = 12000, the two parts of the ratio must be multiplied by 12,000:
    12,000(3:2) = 36,000:24,000.
    Thus, 36,000 earns x% interest and 24,000 earns y% interest.
    It's possible that x=6 or that x=6.6.
    To accommodate each value for x, we could simply adjust the value of y so that the total amount of interest earned = 4080.
    Since x can be different values, INSUFFICIENT.

    Statements 1 and 2 combined:
    32,000 earns x% interest and 24,000 earns y% interest.
    Since x=(3/4)y, for every 4% of interest earned by the $24,000, 3% interest is earned by the $36,000.
    If x=3 and y=4:
    (.03)(36,000) + (.04)(24,000) = 1080+960 = 2040.
    Since 2040 is half the amount of interest needed, the percentages must be doubled to 6% and 8%.
    Thus, x=6.
    SUFFICIENT.

    The correct answer is C.

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    Thanked by: ProGMAT, faraz_jeddah
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    faraz_jeddah Master | Next Rank: 500 Posts
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    Post Wed Sep 25, 2013 4:43 am
    Is there a shortcut to this problem?
    Maybe structuring it in the "x Equations x variables" format?

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    theCodeToGMAT Legendary Member
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    Post Wed Sep 25, 2013 5:08 am
    faraz_jeddah wrote:
    Is there a shortcut to this problem?
    Maybe structuring it in the "x Equations x variables" format?
    We don't have to solve for values.. remember it's Data Sufficiency..

    My steps:
    Total Interest = Interest in First Slot + Interest in Second Slot
    4080 = (A*x*1 + (60000-A)*y*1)/100


    Statement 1: We have no information about "A" hence we will not be able to deduce a proper numerical answer
    INSUFFICIENT

    Statement 2:
    First Slot is countable
    Second Slot is 2/5*60000
    here, we don't have info about the X & y relation.. hence we would be able to deduce numerical answer.
    INSUFFICIENT

    Combining..
    we have all values required..

    Answer {C}

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    R A H U L

    Post Wed Sep 25, 2013 11:31 pm
    Hi faraz_jeddah,

    Yes, there is a way to use a "system math" rule to answer this question, but you have to be careful about how you deal with the variables in the initial prompt.

    You can clearly see the variables X and Y, which represent the 2 unknown interest rates. You only need 1 more variable to account for the invested money.

    M = amount invested at X%
    (60,000 - M) = amount invested at Y%

    We're told that M(X/100) + (60,000 - M)(Y/100) = $4080. This is 1 equation with 3 variables

    We're asked to solve for X.

    Fact 1: X = 3Y/4

    Here we have another equation, but this 1 equation isn't enough for us to figure out what X is.
    Fact 1 is INSUFFICIENT

    Fact 2: This sentence translates into this: M/(60,000 - M) = 3/2

    Here we can figure out the value of M, but we don't have enough to figure out what X is.
    Fact 2 is INSUFFICIENT

    Combining Facts, we have 3 variables and 3 unique equations. You CAN solve this system and get the value of X.

    Final Answer: C

    GMAT assassins aren't born, they're made,
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