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

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

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Okay, I am going to be blunt here. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full “GMAT Jujitsu” for this question:

First, let’s dissect the structure of this question. The two answer choices together comprise a perfect example of what I call a “C Trap” in my classes. It is part of human nature to want to make decisions using all the available information. The Testmaker knows this. If you encounter a problem where it is painfully obvious that the two statements together are sufficient, be careful. It should be very easy to see that if we were to use both statements together, we could solve this problem. We would have two equations and two variables. We could easily plug in Statement #2 into the Statement #1 and solve for $$t$$, then we could plug in our value for $$t$$ into Statement #2 and solve for $$x$$. Knowing both $$t$$ and $$x$$ would obviously give us the value for the expression in the question stem. But if it is that obvious that the two statements together work, what is this problem even doing on the GMAT? It seems too easy. When you encounter a problem structured like this, look closer for additional leverage.

Always look for large chunks of equations you can cancel or simplify all at once. Many questions creatively combine or eliminate large chunks so you can solve the question without needing to solve for each variable. In my classes, I call this strategy “Chunky-quations.” If you know how to dissect a question, these common “chunks” show up all over the place. This particular question asks us to solve for an expression – in other words, we don’t even have a full equation. In order to eliminate variables to get to a numerical solution for an expression, our options are very limited. One method is to substitute, thereby eliminating variables we don’t want to see. Another strategy is to “Divide and Conquer”, finding and cancelling chunks common to both the numerator and denominator of fractions. This can also eliminate variables.

Let’s begin by focusing on the easier of the two statements. (I call this strategy “Low-Hanging Fruit” in my classes. Looking at the easier statement first may help you to evaluate the problem and may even give you clues on how to evaluate the harder statement.) The question stem gives us the expression $$\frac{2t+t -x}{t -x}$$. It has a common chunk “$$t-x$$” in both the numerator and denominator, but the extra “$$2t$$” remains. If we were to substitute Statement #2 into this expression, we could either eliminate the “$$t-x$$” chunk, leaving the $$2t$$, or we could solve Statement #2 for one of the two variables, $$t$$ or $$x$$, and then substitute, eliminating that variable. But this would still leave the other variable. There is no way to eliminate both variables with Statement #2 alone. Eliminate it.

We could technically also solve Statement #1 for one of the two variables, $$t$$ or $$x$$, and then substitute, but that would cause the same problem. Don't do math for kicks and giggles. Do math because it helps you to get the answer to the question. We can easily rearrange Statement #1 so it reads “$$2t = 3(t-x)$$”. This contains the “$$t-x$$” chunk we were looking for. Thus, we can substitute “$$3(t-x)$$” for the “$$2t$$” in the original expression. This leaves:

$$\frac{2t+t -x}{t -x}=\frac{3(t-x)+(t -x)}{t -x}=\frac{4(t-x)}{t -x}$$

We have a common chunk in the top and bottom of the denominator, allow us to cancel both chunks, leaving only a numerical value remaining. Statement #1 is sufficient, and the answer is “A”.

Now, let’s look back at this problem through the lens of strategy. This question can teach us patterns seen throughout the GMAT. First, this problem highlights a common trap of the test where it baits you into picking an “obvious” answer without looking closer at the underlying structure. Be careful of obvious answers. There is almost always more going on. Next, you can see how we can use the structure of the problem to think about possible solutions. If you need to solve for an expression (instead of a full equation), you need to look for common “chunks", allowing you to eliminate entire pieces of the equation simultaneously. With expressions involving fractions, one of those ways of eliminating chunks is to find, factor, or create chunks that you can “Divide and Conquer.” And that is how you think like the GMAT.
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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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AaronPond wrote:
Okay, I am going to be blunt here. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full “GMAT Jujitsu” for this question:

First, let’s dissect the structure of this question. The two answer choices together comprise a perfect example of what I call a “C Trap” in my classes. It is part of human nature to want to make decisions using all the available information. The Testmaker knows this. If you encounter a problem where it is painfully obvious that the two statements together are sufficient, be careful. It should be very easy to see that if we were to use both statements together, we could solve this problem. We would have two equations and two variables. We could easily plug in Statement #2 into the Statement #1 and solve for $$t$$, then we could plug in our value for $$t$$ into Statement #2 and solve for $$x$$. Knowing both $$t$$ and $$x$$ would obviously give us the value for the expression in the question stem. But if it is that obvious that the two statements together work, what is this problem even doing on the GMAT? It seems too easy. When you encounter a problem structured like this, look closer for additional leverage.

Always look for large chunks of equations you can cancel or simplify all at once. Many questions creatively combine or eliminate large chunks so you can solve the question without needing to solve for each variable. In my classes, I call this strategy “Chunky-quations.” If you know how to dissect a question, these common “chunks” show up all over the place. This particular question asks us to solve for an expression – in other words, we don’t even have a full equation. In order to eliminate variables to get to a numerical solution for an expression, our options are very limited. One method is to substitute, thereby eliminating variables we don’t want to see. Another strategy is to “Divide and Conquer”, finding and cancelling chunks common to both the numerator and denominator of fractions. This can also eliminate variables.

Let’s begin by focusing on the easier of the two statements. (I call this strategy “Low-Hanging Fruit” in my classes. Looking at the easier statement first may help you to evaluate the problem and may even give you clues on how to evaluate the harder statement.) The question stem gives us the expression $$\frac{2t+t -x}{t -x}$$. It has a common chunk “$$t-x$$” in both the numerator and denominator, but the extra “$$2t$$” remains. If we were to substitute Statement #2 into this expression, we could either eliminate the “$$t-x$$” chunk, leaving the $$2t$$, or we could solve Statement #2 for one of the two variables, $$t$$ or $$x$$, and then substitute, eliminating that variable. But this would still leave the other variable. There is no way to eliminate both variables with Statement #2 alone. Eliminate it.

We could technically also solve Statement #1 for one of the two variables, $$t$$ or $$x$$, and then substitute, but that would cause the same problem. Don't do math for kicks and giggles. Do math because it helps you to get the answer to the question. We can easily rearrange Statement #1 so it reads “$$2t = 3(t-x)$$”. This contains the “$$t-x$$” chunk we were looking for. Thus, we can substitute “$$3(t-x)$$” for the “$$2t$$” in the original expression. This leaves:

$$\frac{2t+t -x}{t -x}=\frac{3(t-x)+(t -x)}{t -x}=\frac{4(t-x)}{t -x}$$

We have a common chunk in the top and bottom of the denominator, allow us to cancel both chunks, leaving only a numerical value remaining. Statement #1 is sufficient, and the answer is “A”.

Now, let’s look back at this problem through the lens of strategy. This question can teach us patterns seen throughout the GMAT. First, this problem highlights a common trap of the test where it baits you into picking an “obvious” answer without looking closer at the underlying structure. Be careful of obvious answers. There is almost always more going on. Next, you can see how we can use the structure of the problem to think about possible solutions. If you need to solve for an expression (instead of a full equation), you need to look for common “chunks", allowing you to eliminate entire pieces of the equation simultaneously. With expressions involving fractions, one of those ways of eliminating chunks is to find, factor, or create chunks that you can “Divide and Conquer.” And that is how you think like the GMAT.

How to analyze so much thing under 2 mins?
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Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

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barcelona123 wrote:
How to analyze so much thing under 2 mins?

Reread my post. The majority of the post is a thorough explanation of common patterns of the GMAT, not just an analysis of the question. As I mentioned in my post, "The tactics I will show you here will be useful for numerous questions, not just this one." I figured if I am going to give an explanation, I am going to show how to apply overarching principles to a whole category of questions. (After all, while you will never see this exact problem on the GMAT, you will likely see problems that test critical-thinking skills in a similar way!) Once you understand the common patterns that define how the GMAT thinks, the analysis can happen pretty quickly.
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Hit "+1 Kudos" if my post helped you understand the GMAT better.
Look me up at https://www.veritasprep.com/gmat/aaron-pond/ if you want to learn more GMAT Jujitsu. Re: What is the value of (2t + t - x)/(t - x)?   [#permalink] 17 Aug 2019, 14:44
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