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 [spoiler]{A}[/spoiler]

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

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.

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 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!

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

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!

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?

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

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