Target Test Prep 20% Off Flash Sale is on! Code: FLASH20

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

GMAT Prep Prac 1 - Q19

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Wed Apr 08, 2009 9:22 pm
Location: Canada

GMAT Prep Prac 1 - Q19

by mayuran23 » Tue Apr 14, 2009 3:32 pm
In the xy-plane, does the line with equation y = 3x + 2 contain the point (r,s)?

(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0

Since, when plugging (r,s) into y = 3x + 2 gives you s = 3r + 2, i'm assuming that this makes one of the terms in stmt 1 and 2 = 0 (3r + 2 - s = 0, since 3r + 2 = s).

Any suggestions please?
Top
User avatar
MBA Student
Posts: 1194
Joined: Sat Aug 16, 2008 9:42 pm
Location: Paris, France
Thanked: 71 times
Followed by:17 members
GMAT Score:710

by gmat740 » Tue Apr 14, 2009 7:36 pm
OA is D


I. (3r + 2 - s)(4r + 9 - s) = 0
so
(3r + 2 - s) = 0
(4r + 9 - s) = 0

solve both these eqn's
s= -19
r = -7

now our equation is

y = 3x +2

so for a point to lie on the lie, it must satisfy the equation of line

s = 3r + 2

Put the values of r and s

-19 = 3(-7)+2
-19= -19

Hence (r,s) lie on the line.


II. (4r - 6 - s)(3r + 2 - s) = 0

(4r - 6 - s) = 0

(3r + 2 - s) = 0

proceed just like the steps above and you will get two different values of r and s

put those values of r and s back into the eqn of the line and check whether they satisfy or not


So both statements are suff

So answer D


Hope this Helps

Karan
Top
Senior | Next Rank: 100 Posts
Posts: 72
Joined: Sat Mar 28, 2009 10:05 pm
Thanked: 2 times

by nasa » Tue Apr 14, 2009 8:27 pm
IMO C
In the xy-plane, does the line with equation y = 3x + 2 contain the point (r,s)?

(1) (3r + 2 - s)(4r + 9 - s) = 0 => 3r+2 = s or 4r+9 = s
i.e. (1) is true either if (r,s) falls on line 3x+2=y
or if (r,s) falls on line 4r+9=y
(2) (4r - 6 - s)(3r + 2 - s) = 0 => 4r-6 = s or 3r+2 = s

Now we have 3 different lines
3x+2=y, 4x+9=y, 4x-6=y
and 1 and 2 becomes true only if (r,s) is contained in line 3x+2=y
So, C
Top
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Sat Mar 07, 2009 9:34 am

by shkusira » Tue Apr 14, 2009 11:24 pm
I agree with Nasa. Got C. what is the OA?
Top
Legendary Member
Posts: 876
Joined: Thu Apr 10, 2008 8:14 am
Thanked: 13 times

by ketkoag » Wed Apr 15, 2009 4:14 am
IMO D, now lets rewrite the equation..
i.e. 3x + 2-y=0.
By statement 1, (3r + 2 - s)(4r + 9 - s) = 0
i.e. either (3r + 2 - s)=0 or (4r + 9 - s) = 0 or both are 0.
by this we can conclude that the equation y = 3x + 2 contains the point (r,s).

Similarly,by statement 2, (4r - 6 - s)(3r + 2 - s) = 0
again (3r + 2 - s)=0 i.e. equation y = 3x + 2 contains the point (r,s).

Hence D.
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Wed Jun 11, 2008 5:29 am
Thanked: 65 times

by bluementor » Wed Apr 15, 2009 4:19 am
If point (r,s) is contained within y=3x + 2, then the following must be true:

y =3x + 2
s = 3r + 2 (by susbstituting values for x and y with r and s, respectively)
3r + 2 -s = 0

Statement 1:
(3r + 2 - s)(4r + 9 - s) = 0

It could be that (3r + 2 - s) or (4r + 9 - s) or both are equal to zero. insufficient to conclude that (3r + 2 - s) is definitely equal to zero.

Statement 1:
(4r - 6 - s)(3r + 2 - s) = 0

It could be that (3r + 2 - s) or (4r - 6 - s) or both are equal to zero. insufficient to conclude that (3r + 2 - s) is definitely equal to zero.

Both statements together:

Either

(3r + 2 - s)

OR

Both (4r - 6 - s) AND (4r + 9 - s)

must equal to zero.


If (4r - 6 - s) and (4r + 9 - s) are equal to zero, then:

4r - s = 6
4r - s = -9, both of these contradict each other.

Hence, (4r - 6 - s) and (4r + 9 - s) are NOT equal to zero, and (3r + 2 - s) must be equal to zero. So line y= 3x+2 must contain point (r,s) Sufficient.

Choose C.

-BM-
Top
Master | Next Rank: 500 Posts
Posts: 107
Joined: Wed Mar 04, 2009 4:39 am
Location: Vancouver
Thanked: 9 times
GMAT Score:750

by pakaskwa » Wed Apr 15, 2009 2:29 pm
The OA is C. I just did the question yesterday on GMATPrep. I chose D, and I was wrong.
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Sat Apr 18, 2009 2:54 am
Great explanation -BoMb-
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Tue Mar 24, 2009 5:48 pm
GMAT Score:710

by sunnyd283 » Sun May 24, 2009 2:00 pm
'Gmat740', you really should make sure you don't put wrong official answers onto your posts. I use this forum for my own revision and it's annoying when people state wrong official answers as a matter of fact rather than their own misinformed opinion. Please take care not to do this again.

The official answer is C. You need both statements to see that r=(s-2)/3.
Top
User avatar
MBA Student
Posts: 1194
Joined: Sat Aug 16, 2008 9:42 pm
Location: Paris, France
Thanked: 71 times
Followed by:17 members
GMAT Score:710

by gmat740 » Sun May 24, 2009 6:41 pm
Gmat740', you really should make sure you don't put wrong official answers onto your posts. I use this forum for my own revision and it's annoying when people state wrong official answers as a matter of fact rather than their own misinformed opinion. Please take care not to do this again.

The official answer is C. You need both statements to see that r=(s-2)/3.
Well to my best knowledge at that time, the OA was D as I came across the same question in some of the book( I don't remember since it has been a long time!)

I did not put intentionally the wrong answer. It was after my post I came across other answers and realize that MY OA is wrong.

We are here to learn from mistakes and I learned from mine. Until and unless we don't try, how are we going to learn??

I should have used IMO instead of OA, I will take care about that.

Cheers
Top
Legendary Member
Posts: 1169
Joined: Sun Jul 06, 2008 2:34 am
Thanked: 25 times
Followed by:1 members

by aj5105 » Wed May 27, 2009 3:32 am
BOMBAT!!
bluementor wrote:If point (r,s) is contained within y=3x + 2, then the following must be true:

y =3x + 2
s = 3r + 2 (by susbstituting values for x and y with r and s, respectively)
3r + 2 -s = 0

Statement 1:
(3r + 2 - s)(4r + 9 - s) = 0

It could be that (3r + 2 - s) or (4r + 9 - s) or both are equal to zero. insufficient to conclude that (3r + 2 - s) is definitely equal to zero.

Statement 1:
(4r - 6 - s)(3r + 2 - s) = 0

It could be that (3r + 2 - s) or (4r - 6 - s) or both are equal to zero. insufficient to conclude that (3r + 2 - s) is definitely equal to zero.

Both statements together:

Either

(3r + 2 - s)

OR

Both (4r - 6 - s) AND (4r + 9 - s)

must equal to zero.


If (4r - 6 - s) and (4r + 9 - s) are equal to zero, then:

4r - s = 6
4r - s = -9, both of these contradict each other.

Hence, (4r - 6 - s) and (4r + 9 - s) are NOT equal to zero, and (3r + 2 - s) must be equal to zero. So line y= 3x+2 must contain point (r,s) Sufficient.

Choose C.

-BM-
Top

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 » Thu May 12, 2011 7:25 am
mayuran23 wrote:In the xy-plane, does the line with equation y = 3x + 2 contain the point (r,s)?

(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0

Since, when plugging (r,s) into y = 3x + 2 gives you s = 3r + 2, i'm assuming that this makes one of the terms in stmt 1 and 2 = 0 (3r + 2 - s = 0, since 3r + 2 = s).

Any suggestions please?
If (r,s) is on the line defined by the equation y=3x+2, then (r,s) must satisfy the equation y=3x+2. In other words, it must be true that s=3r+2
For example: We know that the point (5, 17) is on the line y=3x+2, because when we plug x=5 and y=17 into the equation, we get 17 = 3(5)+2 and the equation holds true.

So, we can reword the target question to be "Does s = 3r + 2?"

1. (3r+2-s)(4r+9-s) = 0
From this, we know that either (3r+2-s) = 0 or (4r+9-s) = 0
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our new target question is no
Since we get two different answers to the target question, statement 1 is NOT SUFFICIENT

2. (4r-6-s)(3r+2-s) = 0
From this, we know that either (4r-6-s) = 0 or (3r+2-s) = 0
If (4r-6-s)) = 0 then s = 4r-6, in which case the answer to our new target question is no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
Since we get two different answers to the target question, statement 2 is NOT SUFFICIENT

Statements 1&2 combined: Since (3r+2-s) is the only expression common to both statements, it must be true that 3r+2-s = 0, in which case y MUST equal 3r+2
As such the answer is C
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Legendary Member
Posts: 516
Joined: Fri Jul 31, 2009 3:22 pm
Thanked: 112 times
Followed by:13 members

by smackmartine » Thu May 12, 2011 6:05 pm
I found that there is a variation in these type of questions. If the same question comes as problem solving , it would be :

In the xy-plane, if the line with equation y = 3x + 2 contain the point (r,s), which of the following must be true?

1) (3r + 2 - s)(4r + 9 - s) = 0
2) (4r - 6 - s)(3r + 2 - s) = 0
3) (3r + 2 - s)=0

A) 1 only
B) 2 only
C) 3 only
D) ALL
E) None

In this case [spoiler]D) ALL[/spoiler] would be correct answer because we can neglect the other solutions (4r + 9 - s)=0 and (4r - 6 - s)=0 in statement 1 and 2 respectively.

Experts please comment, if there are any discrepancies.
Top
Master | Next Rank: 500 Posts
Posts: 152
Joined: Wed Mar 12, 2008 4:36 pm
Thanked: 8 times
Followed by:2 members

by artistocrat » Fri May 13, 2011 4:02 pm
In the xy-plane, does the line with equation y = 3x + 2 contain the point (r,s)?

(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0

(1)either 3r+2=s (contains r,s) and/or 4r+9=s
INSUFF

(2)either 3r+2=s (contains r,s) and/or 4r-6=s
INSUFF

(1)&(2) 3r+2=s (contains r,s), because you can't have both 4r+9=s and 4r-6=s
SUFF

Answer: C
Top

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 » Sat May 14, 2011 6:34 am
smackmartine wrote:I found that there is a variation in these type of questions. If the same question comes as problem solving , it would be :

In the xy-plane, if the line with equation y = 3x + 2 contain the point (r,s), which of the following must be true?

1) (3r + 2 - s)(4r + 9 - s) = 0
2) (4r - 6 - s)(3r + 2 - s) = 0
3) (3r + 2 - s)=0

A) 1 only
B) 2 only
C) 3 only
D) ALL
E) None

In this case [spoiler]D) ALL[/spoiler] would be correct answer because we can neglect the other solutions (4r + 9 - s)=0 and (4r - 6 - s)=0 in statement 1 and 2 respectively.

Experts please comment, if there are any discrepancies.
You're 100% correct, smackmartine,

If we know that the line with equation y = 3x + 2 contains the point (r,s), then is must be true that s=3r+2
If s=3r+2 when we can also conclude that 3r + 2 - s = 0

1) If 3r + 2 - s = 0, then (3r + 2 - s)(4r + 9 - s) = 0
2) If 3r + 2 - s = 0, then (4r - 6 - s)(3r + 2 - s) = 0
3) If 3r + 2 - s = 0, then (3r + 2 - s) = 0

So, the answer is D
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply