GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 04 Aug 2020, 03:35 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the value of (2t + t - x)/(t - x)?

Author Message
TAGS:

### Hide Tags

Manager  Joined: 02 Dec 2012
Posts: 172
What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

4
1
52 00:00

Difficulty:   25% (medium)

Question Stats: 75% (01:13) correct 25% (01:42) wrong based on 2553 sessions

### HideShow timer Statistics

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

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

(2) t - x = 5
Math Expert V
Joined: 02 Sep 2009
Posts: 65785
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

6
11
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.

_________________
##### General Discussion
Retired Moderator B
Joined: 05 Jul 2006
Posts: 1317
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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
GMAT Club Legend  V
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A learner forever :)
Joined: 08 Jul 2010
Posts: 4512
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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

_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Senior Manager  B
Joined: 02 Dec 2014
Posts: 336
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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
_________________
"Are you gangsters?" - "No we are Russians!"
Manager  Joined: 21 Jan 2014
Posts: 93
GMAT 1: 500 Q32 V28
GPA: 4
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Aug 2009
Posts: 8792
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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..

_________________
CEO  G
Joined: 20 Mar 2014
Posts: 2525
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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.
_________________
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4987
GMAT 1: 770 Q49 V46
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

3
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

RELATED VIDEOS

_________________
If you enjoy my solutions, you'll love my GMAT prep course. Manager  B
Joined: 25 Jun 2016
Posts: 60
GMAT 1: 780 Q51 V46
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

1
A video solution to this question:

[you-tube][/you-tube]
Manager  P
Joined: 31 Jul 2017
Posts: 195
Location: Tajikistan
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

3
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)
Veritas Prep GMAT Instructor G
Joined: 01 Jul 2017
Posts: 83
Location: United States
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

1
2
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.
_________________
Aaron Pond
Veritas Prep Teacher of the Year

Visit me at https://www.veritasprep.com/gmat/aaron-pond/ if you would like to learn even more "GMAT Jujitsu"!
Intern  Joined: 15 May 2019
Posts: 8
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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?
Veritas Prep GMAT Instructor G
Joined: 01 Jul 2017
Posts: 83
Location: United States
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

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.
_________________
Aaron Pond
Veritas Prep Teacher of the Year

Visit me at https://www.veritasprep.com/gmat/aaron-pond/ if you would like to learn even more "GMAT Jujitsu"!
Intern  B
Joined: 09 Apr 2019
Posts: 5
GMAT 1: 690 Q47 V39
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

Hey guys, I don't understand why the second statement is insufficient. Why can't i solve for t: t=5+x and plug this into the original equation to get value of x? And then plug it back in and find value of t. What am i missing here? Thanks for the help!
Senior Manager  P
Joined: 17 Aug 2018
Posts: 387
Location: United States
GMAT 1: 610 Q43 V31
GMAT 2: 640 Q45 V32
GMAT 3: 640 Q47 V31
GRE 1: Q155 V155
WE: General Management (Other)
What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

pietro0000 wrote:
Hey guys, I don't understand why the second statement is insufficient. Why can't i solve for t: t=5+x and plug this into the original equation to get value of x? And then plug it back in and find value of t. What am i missing here? Thanks for the help!

Rewrite S2 and plug the value of (t-x) and see what you get. You cannot solve for t.
Intern  B
Joined: 24 Nov 2019
Posts: 4
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

Bunuel wrote:
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.

For a statement to be sufficient, does all the information have to exist on one side? I.e., how come we cannot use algebra to get the variable on one side with an integer on the other with statement 2?
Intern  Joined: 27 Mar 2020
Posts: 1
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

when we write it in the form of (2t/(t-x))+1 we are assuming that t is not equal to x, which is not provided anywhere, and we are canceling them out. i think the right option will be c.
Manager  G
Status: Done with one MBA, now aiming for something bigger!
Joined: 03 May 2020
Posts: 237
Location: India
Concentration: Marketing, Strategy
Re: What is the value of (2t + t - x)/(t - x)?  [#permalink]

### Show Tags

To find:
(2t + t - x)/(t - x) = 2t/(t-x) + 1

St. 1:
2t/(t - x) = 3
=> 2t/(t-x) + 1 = 3 + 1 = 4

=> St. 1 is sufficient

St. 2:
t - x = 5
=> 2t/(t-x) + 1 = 2t/5 + 1

=> St. 2 is insufficient

_________________
MBA - IB, IIFT | Class of 2018 - 20
Majors - Marketing | Minors - Finance, Strategy, and Trade
NMAT '17 - 99.xx percentile | IIFT '17 - 94.95 percentile | CAT '17 - 93.81 percentile Re: What is the value of (2t + t - x)/(t - x)?   [#permalink] 16 Jul 2020, 08:03

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