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# What is the value of (2t + t - x)/(t - x)?

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Manager
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What is the value of (2t + t - x)/(t - x)?  [#permalink]

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05 Feb 2013, 05:38
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25% (medium)

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73% (00:58) correct 27% (01:19) wrong based on 1556 sessions

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What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5
Math Expert
Joined: 02 Sep 2009
Posts: 49206
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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05 Feb 2013, 05:41
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What is the value of (2t + t - x)/(t - x)?

$$\frac{2t + t - x}{t - x}=\frac{2t}{t - x}+\frac{t - x}{t - x}=\frac{2t}{t - x}+1=?$$

(1) 2t/(t - x) = 3 --> $$\frac{2t}{t - x}+1=3+1=4$$. Sufficient.

(2) t - x = 5 --> $$\frac{2t + (t - x)}{(t - x)}=\frac{2t + 5}{5}$$ --> different values of t will give different values ofr this expression. Not sufficient.

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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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07 Feb 2013, 16:13
1
What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5

2t/(t-x) + t/(t-x) - x(t-x) = ??

from 1

3/2= t/(t-x) , and x = t-2/3t , thus suff

from 2

t-x = 5 obviously not suff

i d say A
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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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05 Feb 2016, 07:20
What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5

Question : (2t + t - x)/(t - x) = ?

Question : [(2t)/(t - x)] + (t - x)/(t - x) = ?

Question : [(2t)/(t - x)] + 1 = ?

Statement 1: 2t/(t - x) = 3
i.e. [(2t)/(t - x)] + 1 = 3+1 = 4
SUFFICIENT

Statement 2: t - x = 5
we can't get the value 2t/(t - x) by the given information, Hence
NOT SUFFICIENT

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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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06 Feb 2016, 12:56
1
What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5

Statement 1. Multiply both sides by (t-x) ==> 2t=3t-3x Hence t=3x Plug in original equation to get (6x+9x-x)/2x = 7
Statement 2. x=t-5 Plug in original expression to get (2t-5)/5 Clearly not sufficient
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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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05 Mar 2016, 08:46
Could you please explain why is not possibile to solve the question with the following method?

Plug a value for "t", like t=2.
In this way the equation is now 2(2)+2-x/2-x
So now the question asks only the value of x.

1) SUFFICIENT - 2(2)/2-x -> x=2/3
2) SUFFICIENT – 2-x=5 -> x=-3

Correct AC is D

thanks
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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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05 Mar 2016, 09:53
1
pepo wrote:
Could you please explain why is not possibile to solve the question with the following method?

Plug a value for "t", like t=2.
In this way the equation is now 2(2)+2-x/2-x
So now the question asks only the value of x.

1) SUFFICIENT - 2(2)/2-x -> x=2/3
2) SUFFICIENT – 2-x=5 -> x=-3

Correct AC is D

thanks

hi,
you are to find the value of an equation which consists of two variables...
when nothing is given, you cannot assume one value to be some integer and work for second...
If there was a statement given that t=3, what would you do then..
someone can take values of both t and x and will not require any statement..
The main point is that you cannot do it this way..

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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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05 Mar 2016, 10:12
1
pepo wrote:
Could you please explain why is not possibile to solve the question with the following method?

Plug a value for "t", like t=2.
In this way the equation is now 2(2)+2-x/2-x
So now the question asks only the value of x.

1) SUFFICIENT - 2(2)/2-x -> x=2/3
2) SUFFICIENT – 2-x=5 -> x=-3

Correct AC is D

thanks

This is the beauty of DS questions. You are assuming the very thing that you need to show is sufficient. To evaluate options in a DS question, you need to be absolutely sure that you get a unique value for the question asked. In this case, statement 1 clearly is sufficient as you can see in the solutions posted above.

Question for you. How do you know that 't' is the ONLY variable ? I can assume both t and x to be constants while at the same time someone else can assume both of these or one of these to be constants. This is the very reason why you can not assume values in a DS question if it is not mentioned clearly in the question or the given statements.

FYI, t=5 and x=2 also satisfy the given conditions.

Your approach might have worked in a PS question but do not adopt this strategy for DS questions.
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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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21 Jul 2016, 15:46
2
Top Contributor
What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5

Target question: What is the value of (2t + t - x)/(t - x)?
This is a good candidate for REPHRASING the target questions.
We'll use the fact that (a + b)/c = a/c + b/c
Likewise, (2t + t - x)/(t - x) = 2t/(t - x) + (t - x)/(t - x)
= 2t/(t - x) + 1
At this point, we can see that we really just need to find the value of 2t/(t - x)
REPHRASED target question: What is the value of 2t/(t - x)?

Statement 1: 2t/(t - x) = 3
Perfect! This is EXACTLY the information we need!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: t - x = 5
There are several values of t and x that satisfy statement 2. Here are two:
Case a: t = 5 and x= 0, in which case 2t/(t - x) = 5
Case b: t = 6 and x= 1, in which case 2t/(t - x) = 12/5
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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06 Jan 2017, 17:31
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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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28 Jun 2018, 04:08
2
2t+t-x/t-x=?
St1, 2t/t-x=3, so we are left with t-x/t-x=1, so 3+1=4, st is suff
St 2 is not suff because we have no clue what 2t equals to, so (A)
Re: What is the value of (2t + t - x)/(t - x)? &nbs [#permalink] 28 Jun 2018, 04:08
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