BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

explanation please

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

Re: explanation please

by Ian Stewart » Thu Mar 19, 2009 3:50 am
kaf wrote:Can some please explain to me why

sq root(x) = x-2

solving we get x=4 and x=1

thanks
If you square both sides, you have

x = (x-2)^2
x = x^2 - 4x + 4

We can solve this by factoring if we get zero on one side:

0 = x^2 - 5x + 4
0 = (x-4)(x-1)

If the product of those factors is zero, one of them must equal zero, so either x - 4 = 0 and x = 4, or x - 1 = 0 and x = 1.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Senior | Next Rank: 100 Posts
Posts: 53
Joined: Mon Feb 09, 2009 12:18 am
Thanked: 1 times

by kaf » Thu Mar 19, 2009 8:20 am
Thanks a lot Ian

I saw this this DS question and i have been trying to figure it out.If you can please help with a little explanation i will be grateful
Are lines p (with slope m) and q (with slope n) perpendicular to each other?

1. m + 2 = n
2. m + n = 0

I don't know the answer to this question. I feel both the statements are required to answer the question (when combined the values of m & n are -1 & 1 respectively, which satisfies the perpendicular slope concept). Any contentions?
thanks
Top
Senior | Next Rank: 100 Posts
Posts: 88
Joined: Tue Mar 03, 2009 8:10 am
Thanked: 3 times

by quocbao » Thu Mar 19, 2009 8:31 am
I think it should be x = 4

x = 1 is not possible, because square root x > 0, so x - 2 > 0, so x > 2
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Thu Mar 19, 2009 8:40 am
Yes, quocbao is correct - you need to make sure that the solutions both make sense in the original equation. Since root(x) can't be negative, the solution x = 1 doesn't make sense here.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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 » Thu Mar 19, 2009 8:58 am
Are lines p (with slope m) and q (with slope n) perpendicular to each other?

1. m + 2 = n
2. m + n = 0

I don't know the answer to this question. I feel both the statements are required to answer the question (when combined the values of m & n are -1 & 1 respectively, which satisfies the perpendicular slope concept). Any contentions?
Well I am not an Expert like Ian but yes I do have a solution for this statement

Since its given that m and n are slopes and not the line
so m+2=n does not really gives a solution


However,
m+n=0
this gives m=-n
so slopes, m and n are equal and of opposite sign
Thus the condition of Perpendicularity is m*n=-1

But over here it's not given whether the value of m or n is 1

Untill its not given,then both answers are insuff(E)

Else B

Hope this helps
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 » Thu Mar 19, 2009 12:17 pm
Image
[/img]
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Thu Mar 19, 2009 4:15 pm
gmat740 wrote: However,
m+n=0
this gives m=-n
so slopes, m and n are equal and of opposite sign
Thus the condition of Perpendicularity is m*n=-1
This question has been recently discussed here: https://www.beatthegmat.com/slope-t33092.html, but I wanted to address a small math error.

If m + n = 0

then:

m = -n

as you stated, BUT to get -1 on the right side we must DIVIDE both sides by n, leaving us with:

m/n = -1,

which is NOT the condition of perpendicularity (which is why statement (2) is insufficient by itself).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
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 » Thu Mar 19, 2009 5:12 pm
Thanks a lot Stuart, I got it.I mised out a point over here.
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 » Tue Mar 24, 2009 3:36 am
Quote:
Are lines p (with slope m) and q (with slope n) perpendicular to each other?

1. m + 2 = n
2. m + n = 0

I don't know the answer to this question. I feel both the statements are required to answer the question (when combined the values of m & n are -1 & 1 respectively, which satisfies the perpendicular slope concept). Any contentions?
Statement 1 by itself is not sufficient to make us check whether or not m n = -1.

Same with statement 2.

Combining the two enables us to have m + 2 = -m or m = -1 and hence n = 1 and so m n = -1 is found to be yes, true! So how about C?
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
Post new topic Post Reply
• Page 1 of 1