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DS Question Help - OG

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stevennu Senior | Next Rank: 100 Posts Default Avatar
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DS Question Help - OG

Post Sat Oct 19, 2013 10:34 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Question 171 in the DS section of the OG

    What is the value of (2T+T-X)/(T-X)

    (1) (2T)/(T-X)=3
    (2) (T-X)=5

    The answer key simplifies statement 1 to (2T)/(T-X) + (T-X)/(T-X)

    How is it that the equation is simplified to the equation above? I simplified it as (2T)/(T-X) + (T)/(T-X) - (X)/(T-X)

    What am I missing?

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    theCodeToGMAT Legendary Member
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    Post Sat Oct 19, 2013 10:56 pm
    To find value of: ( 2T + T - X ) / ( T - X)

    Rephrase: To find value of 2T/(T-X) + 1

    Statement 1:
    2T/(T-X) = 3
    3 + 1 = 4
    SUFFICIENT


    Statement 2:
    T-X = 5
    INSUFFICIENT

    Answer {A}

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    theCodeToGMAT Legendary Member
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    Post Sat Oct 19, 2013 11:00 pm
    stevennu wrote:
    Question 171 in the DS section of the OG

    What is the value of (2T+T-X)/(T-X)

    (1) (2T)/(T-X)=3
    (2) (T-X)=5

    The answer key simplifies statement 1 to (2T)/(T-X) + (T-X)/(T-X)

    How is it that the equation is simplified to the equation above? I simplified it as (2T)/(T-X) + (T)/(T-X) - (X)/(T-X)

    What am I missing?
    Steven, you over simplied the question, making it more complex.

    Rather than writing, (T-X)/(T-X) as T/(T-X) - X/(T-X

    you could have simply written "1"

    However, you din't make any mistake though.. If you simplify statement 1, then you will get some relation between T & X and most probably you will end up getting a definite numerical value

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    Post Sun Oct 20, 2013 7:07 am
    stevennu wrote:
    What is the value of (2t+t-x)/(t-x)?

    (1) (2t)/(t-x) = 3
    (2) t-x = 5
    An alternate approach is to simplify the statements and TEST TWO CASES.

    Statement 1: (2t)/(t-x) = 3
    2t = 3t - 3x
    3x = t.
    If x=1 and t=3, then (2t+t-x)/(t-x) = (2*3 + 3 - 1)/(3-1) = 8/2 = 4.
    If x=2 and t=6, then (2t+t-x)/(t-x) = (2*6 + 6 - 2)/(6-2) = 16/4 = 4.
    Since (2t+t-x)/(t-x) = 4 in each case, SUFFICIENT.

    Statement 2: t-x = 5
    t = x+5.
    If x=1 and t=6, then (2t+t-x)/(t-x) = (2*6 + 6 - 1)/(6-1) = 17/5.
    If x=2 and t=7, then (2t+t-x)/(t-x) = (2*7 + 7 - 2)/(7-2) = 19/5.
    Since (2t+t-x)/(t-x) can be equal to different values, INSUFFICIENT.

    The correct answer is A.

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    stevennu Senior | Next Rank: 100 Posts Default Avatar
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    Post Sun Oct 20, 2013 7:53 am
    theCodeToGMAT wrote:
    stevennu wrote:
    Question 171 in the DS section of the OG

    What is the value of (2T+T-X)/(T-X)

    (1) (2T)/(T-X)=3
    (2) (T-X)=5

    The answer key simplifies statement 1 to (2T)/(T-X) + (T-X)/(T-X)

    How is it that the equation is simplified to the equation above? I simplified it as (2T)/(T-X) + (T)/(T-X) - (X)/(T-X)

    What am I missing?
    Steven, you over simplied the question, making it more complex.

    Rather than writing, (T-X)/(T-X) as T/(T-X) - X/(T-X

    you could have simply written "1"

    However, you din't make any mistake though.. If you simplify statement 1, then you will get some relation between T & X and most probably you will end up getting a definite numerical value
    I'm having trouble understanding why Statement 1 simplifies to (2T)/(T-X) + (T-X)/(T-X). Wouldn't you take each individual term and then write it above a common denominator? That's what I did when I simplified Statement 1 to (2T)/(T-X) + (T)/(T-X) - (X)/(T-X). I took each of the terms in the numerator and wrote them above the common denominator of (T-X). What rule or further simplification allows us to go from Statement 1 to (2T)/(T-X) + (T-X)/(T-X)? Why aren't the T and -X broken out?

    I understand the T-X / T-X is great because you can simplify it to 1, however I'm not sure how they arrived at that statement.

    Thanks for the replies!

    stevennu Senior | Next Rank: 100 Posts Default Avatar
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    Post Sun Oct 20, 2013 7:54 am
    theCodeToGMAT wrote:
    stevennu wrote:
    Question 171 in the DS section of the OG

    What is the value of (2T+T-X)/(T-X)

    (1) (2T)/(T-X)=3
    (2) (T-X)=5

    The answer key simplifies statement 1 to (2T)/(T-X) + (T-X)/(T-X)

    How is it that the equation is simplified to the equation above? I simplified it as (2T)/(T-X) + (T)/(T-X) - (X)/(T-X)

    What am I missing?
    Steven, you over simplied the question, making it more complex.

    Rather than writing, (T-X)/(T-X) as T/(T-X) - X/(T-X

    you could have simply written "1"

    However, you din't make any mistake though.. If you simplify statement 1, then you will get some relation between T & X and most probably you will end up getting a definite numerical value
    I'm having trouble understanding why Statement 1 simplifies to (2T)/(T-X) + (T-X)/(T-X). Wouldn't you take each individual term and then write it above a common denominator? That's what I did when I simplified Statement 1 to (2T)/(T-X) + (T)/(T-X) - (X)/(T-X). I took each of the terms in the numerator and wrote them above the common denominator of (T-X). What rule or further simplification allows us to go from Statement 1 to (2T)/(T-X) + (T-X)/(T-X)? Why aren't the T and -X broken out?

    I understand the T-X / T-X is great because you can simplify it to 1, however I'm not sure how they arrived at that statement.

    Thanks for the replies!

    theCodeToGMAT Legendary Member
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    Post Sun Oct 20, 2013 8:00 am
    Well Steven... that depends upon how you break a question.

    For instance: recently a question was posted in which we had to find whether r^5s^3t^4 <0

    Now, there are two(or more) ways of looking this problem.

    Some solved using what has to be found i.e. r^5s^3t^4
    Some simplified to rs < 0 .. since even power of -ve is +ve.

    So, there is no such rule for Simplification.. maybe one tick works well for one .. may not work well for other Smile

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    Post Sun Oct 20, 2013 8:02 am
    stevennu wrote:
    theCodeToGMAT wrote:
    stevennu wrote:
    Question 171 in the DS section of the OG

    What is the value of (2T+T-X)/(T-X)

    (1) (2T)/(T-X)=3
    (2) (T-X)=5

    The answer key simplifies statement 1 to (2T)/(T-X) + (T-X)/(T-X)

    How is it that the equation is simplified to the equation above? I simplified it as (2T)/(T-X) + (T)/(T-X) - (X)/(T-X)

    What am I missing?
    Steven, you over simplied the question, making it more complex.

    Rather than writing, (T-X)/(T-X) as T/(T-X) - X/(T-X

    you could have simply written "1"

    However, you din't make any mistake though.. If you simplify statement 1, then you will get some relation between T & X and most probably you will end up getting a definite numerical value
    I'm having trouble understanding why Statement 1 simplifies to (2T)/(T-X) + (T-X)/(T-X). Wouldn't you take each individual term and then write it above a common denominator? That's what I did when I simplified Statement 1 to (2T)/(T-X) + (T)/(T-X) - (X)/(T-X). I took each of the terms in the numerator and wrote them above the common denominator of (T-X). What rule or further simplification allows us to go from Statement 1 to (2T)/(T-X) + (T-X)/(T-X)? Why aren't the T and -X broken out?

    I understand the T-X / T-X is great because you can simplify it to 1, however I'm not sure how they arrived at that statement.

    Thanks for the replies!
    I think stevennu meant to say that the expression in the target question (not statement 1) simplifies to be (2T)/(T-X) + (T-X)/(T-X)

    There's a nice rule that says (a+b)/c = a/c + b/c

    So, (2T+T-X)/(T-X) = 2T/(T-X) + (T-X)/(T-X)
    = 2T/(T-X) + 1

    Cheers,
    Brent

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    theCodeToGMAT Legendary Member
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    Post Sun Oct 20, 2013 8:20 am
    To reach from Statement 1 to what question is asking :

    (2T)/(T-X)=3

    Add 1 both sides


    (2T)/(T-X) + 1 = 3 + 1 --(1)

    Since, "1" can be re-written as (T-X)/(T-X) --(2)

    replace "1" in LHS of (1) with (2)

    (2T)/(T-X) + (T-X)/(T-X) = 4

    Hope this clears!

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    stevennu Senior | Next Rank: 100 Posts Default Avatar
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    Post Sun Oct 20, 2013 11:37 am
    I think I was making an error with the simplification. After breaking up the terms of the numerator to 2T/T-X + T/T-X - X/T-X, I started to cancel the T/T in each of the equations. I just realized that since the two terms T/T-X and X/T-X have the same common denominator, I should have just simplified to T-X/T-X. However, my question is why couldn't we simplify T/T-X to 1/-X and -X/T-X to 1/T? Don't the T's and X's cancel?

    theCodeToGMAT Legendary Member
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    Post Sun Oct 20, 2013 5:44 pm
    Steven, you cannot do that..

    That property works fine when performing such operation with numerator but not with denominator

    For instance:

    If the question were: 2T/T-X + (T-X)/T - (T-X)/T

    then you could have simplified to: 2T/T-X + T/T - X/T - T/T + X/T

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    Johnniewales Newbie | Next Rank: 10 Posts
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    Post Fri Dec 18, 2015 10:45 am
    Why can't we say t=5+x and substitute for T in the equation
    . Please can someone tell me why because if I choose to go that route
    Statement 2 also seems sufficient

    Post Fri Dec 18, 2015 1:54 pm
    Johnniewales wrote:
    Why can't we say t=5+x and substitute for T in the equation
    . Please can someone tell me why because if I choose to go that route
    Statement 2 also seems sufficient
    \

    Show us your work when you replaced t with 5+x

    Cheers,
    Brent

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