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DS OG 13th 105 problem

This topic has 2 expert replies and 2 member replies
sohailmbaprep Senior | Next Rank: 100 Posts Default Avatar
Joined
23 Feb 2012
Posted:
59 messages

DS OG 13th 105 problem

Post Sat Sep 15, 2012 12:06 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Material A costs $3 /kg ,and MAterial B costs $5/kg .If 10Kg of material K consists of X kilograms of Material A and y Kg of Material B,is x>y ?
    1) y>4
    2) the cost of the 10kg of material K is less than $40.

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    Post Sat Sep 15, 2012 12:26 am
    Quote:
    Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms
    of material K consists of x kilograms of material A and y kilograms of material B, is x >
    y?
    (1) y > 4
    (2) The cost of the 10 kilograms of material K is less than $40.
    Since statement 1 is in terms of y, we should rephrase the question stem in terms of y.

    x = the number of kilograms of A.
    y = the number of kilograms of B.
    Since a total of 10 kilograms are purchased:
    x + y = 10.
    x = 10-y.

    Substituting x=10-y into the question stem (Is x>y?), we get:
    10-y > y?
    10 > 2y?
    5 > y?

    Question rephrased: Is y < 5?

    Statement 1: y>4.
    Since it's possible that y=4.5 or that y=6, no way to determine whether y<5.
    INSUFFICIENT.

    Statement 2: The cost of the 10 kilograms of material K is less than $40.
    Since the cost of each of the x kilograms is $3 and the cost of each of the y kilograms is $5, we get:
    3x + 5y < 40.

    Substituting x=10-y into 3x+5y<40, we get:
    3(10-y) + 5y < 40
    30 - 3y + 5y < 40
    2y < 10
    y < 5.
    SUFFICIENT.

    The correct answer is B.

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    Post Sat Sep 15, 2012 2:54 am
    Quote:
    Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms
    of material K consists of x kilograms of material A and y kilograms of material B, is x > y?
    (1) y > 4
    (2) The cost of the 10 kilograms of material K is less than $40.
    One more approach.

    Since 10 kilograms are purchased, x+y = 10.

    Statement 1: y>4
    It's possible that y=5 and that x=5, in which case x=y.
    It's possible that y=4.5 and that x=5.5, in which case x>y.
    INSUFFICIENT.

    Statement 2: The cost of the 10 kilograms of material K is less than $40.
    If 10 kilograms are purchased at a total cost of $40, the average cost per kilogram = 40/10 = $4.
    Since the total cost here is actually LESS than $40, the average cost per kilogram is less than $4 -- LESS THAN HALFWAY between x ($3) and y ($5).
    For the average cost to be LESS THAN HALFWAY between x and y, more of x must be purchased, implying that x>y.
    SUFFICIENT.

    The correct answer is B.

    _________________
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    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

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    sarawutc Newbie | Next Rank: 10 Posts
    Joined
    31 Mar 2013
    Posted:
    5 messages
    Post Wed Jul 24, 2013 11:55 am
    Hi Experts,
    I have one question as for this question.
    The two statements are contradictory right ?
    I thought we wouldn't confront this situation in GMAT though.

    Post Wed Jul 24, 2013 7:41 pm
    Hi sarawutc,

    The two Facts/statements in DS questions will NOT be contradictory, but one of them may contain "options" that the other does not.

    In this question:

    Fact 1 tells us that y > 4
    Fact 2 tells us that y < 5

    While your first reaction might be to call these two Facts contradictory, they're not....

    IF you were dealing with a DS question that required you to Combine Facts, then there will be at least one possible answer (it's just that sometimes there's more than 1 answer and you're responsible to find those possibilities).

    In this case, y could = 4.01, 4.5, 4.999999, etc.

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

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