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## DS Question Help - OG

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 9 member replies
stevennu Senior | Next Rank: 100 Posts
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#### DS Question Help - OG

Sat Oct 19, 2013 10:34 pm
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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stevennu Senior | Next Rank: 100 Posts
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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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Sun Oct 20, 2013 8:20 am
To reach from Statement 1 to what question is asking :

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

(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
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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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Sun Oct 20, 2013 8:20 am
To reach from Statement 1 to what question is asking :

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

(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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Brent@GMATPrepNow GMAT Instructor
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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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Johnniewales Newbie | Next Rank: 10 Posts
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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

theCodeToGMAT Legendary Member
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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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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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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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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

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stevennu Senior | Next Rank: 100 Posts
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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!

stevennu Senior | Next Rank: 100 Posts
Joined
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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!

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GMATGuruNY GMAT Instructor
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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.

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