DS Question Help - OG

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 54
Joined: Sat May 18, 2013 10:24 am
Thanked: 1 times
Followed by:1 members

DS Question Help - OG

by stevennu » Sat Oct 19, 2013 10:34 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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?

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sat Oct 19, 2013 10:56 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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]
R A H U L

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sat Oct 19, 2013 11:00 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
R A H U L

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Oct 20, 2013 7:07 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Senior | Next Rank: 100 Posts
Posts: 54
Joined: Sat May 18, 2013 10:24 am
Thanked: 1 times
Followed by:1 members

by stevennu » Sun Oct 20, 2013 7:53 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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!

Senior | Next Rank: 100 Posts
Posts: 54
Joined: Sat May 18, 2013 10:24 am
Thanked: 1 times
Followed by:1 members

by stevennu » Sun Oct 20, 2013 7:54 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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!

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Oct 20, 2013 8:00 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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 :)
R A H U L

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Oct 20, 2013 8:02 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Brent Hanneson - Creator of GMATPrepNow.com
Image

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Oct 20, 2013 8:20 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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!
R A H U L

Senior | Next Rank: 100 Posts
Posts: 54
Joined: Sat May 18, 2013 10:24 am
Thanked: 1 times
Followed by:1 members

by stevennu » Sun Oct 20, 2013 11:37 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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?

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Oct 20, 2013 5:44 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
R A H U L

User avatar
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Wed Jul 15, 2015 5:39 am

by Johnniewales » Fri Dec 18, 2015 10:45 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Fri Dec 18, 2015 1:54 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Brent Hanneson - Creator of GMATPrepNow.com
Image