is root[(x-3)^2] = 3-x ?
1. x not equal to 3
2. -x|x| > 0
OA B[/list]
GMAT Prep
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 118
- Joined: Mon May 21, 2012 10:07 pm
- Thanked: 23 times
- Followed by:4 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- 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
Target question: Is root[(x-3)^2] = 3-x ?das.ashmita wrote:Is root[(x-3)^2] = 3-x ?
1. x not equal to 3
2. -x|x| > 0
This question is a great candidate for rephrasing the target question.
To begin, notice that we have two nice rules:
- If k > 0, then root(k^2) = k
- If k < 0, then root(k^2) = -k
Now observe that (3-x) = -(x-3)
Given the above information, under what conditions will root[(x-3)^2] = 3-x?
In other words, under what conditions will root[(x-3)^2] = -(x-3)?
This will occur if x-3 is negative.
So, we can now rephrase the target question as: Is (x-3) negative?
Or we can write: Is x-3 < 0?
. . . or better yet: Is x < 3?
Now that we've rephrased the target question in much simpler terms, we can check the statements.
Statement 1: x not equal to 3
This doesn't give us a definitive answer to the rephrased target question (Is x < 3? )
As such, statement 1 is NOT SUFFICIENT
Statement 2: -x|x| > 0
First notice that this implies that x does not equal zero.
Next, notice that, if x does not equal zero, then |x| will always be positive.
So, -x|x| > 0 is the same as saying (-x)(positive) > 0
In other words, the product (-x)(positive) results in a positive number.
This tells us that (-x) must be positive, which means x must be negative.
If x is negative, then x is definitely less than 3.
As such, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sat Oct 06, 2012 7:14 am, edited 2 times in total.
GMAT/MBA Expert
- Brent@GMATPrepNow
- 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
If anyone is interested, we have a free video on the importance of rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Cheers,
Brent
Cheers,
Brent
-
- Master | Next Rank: 500 Posts
- Posts: 118
- Joined: Mon May 21, 2012 10:07 pm
- Thanked: 23 times
- Followed by:4 members
- sachin_yadav
- Master | Next Rank: 500 Posts
- Posts: 212
- Joined: Mon Dec 06, 2010 12:52 am
- Location: India
- Thanked: 5 times
- Followed by:1 members
After solving root[(x-3)^2] = 3-x, i got |x - 3| = 3 - x.
Now i can easily plug in few numbers according to the statement (1) & (2), and get the answer.
For example, (1) x not equal to 3.
I can use x = 0 and that satisfies the condition, but if i use x = 4, then definitely no.
Statement (2) simply gives that x < 0. So, Answer is B
Well this wasn't the first attempt that got me close to the answer. I wasted a lot of my time by solving absolute value equation further |x - 3| = 3 - x
(a). x - 3 = 3 - x
x + x = 3 + 3
2x = 6
x = 3
(b). x - 3 = -(3 - x)
x - 3 = -3 + x
x - x = -3 + 3
0 = 0
After solving all this i came to the conclusion that rephrase question is is x = 3 ?
Isn't this correct ?
Am i oversimplifying the equation ?
Please let me know your thoughts about this work.
Sachin
Now i can easily plug in few numbers according to the statement (1) & (2), and get the answer.
For example, (1) x not equal to 3.
I can use x = 0 and that satisfies the condition, but if i use x = 4, then definitely no.
Statement (2) simply gives that x < 0. So, Answer is B
Well this wasn't the first attempt that got me close to the answer. I wasted a lot of my time by solving absolute value equation further |x - 3| = 3 - x
(a). x - 3 = 3 - x
x + x = 3 + 3
2x = 6
x = 3
(b). x - 3 = -(3 - x)
x - 3 = -3 + x
x - x = -3 + 3
0 = 0
After solving all this i came to the conclusion that rephrase question is is x = 3 ?
Isn't this correct ?
Am i oversimplifying the equation ?
Please let me know your thoughts about this work.
Sachin
Never surrender
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
Hence, the rephrased question should be is x ≤ 3?sachin_yadav wrote:I wasted a lot of my time by solving absolute value equation further |x - 3| = 3 - x
(a). x - 3 = 3 - x [This is possible if (x - 3) ≥ 0]
x + x = 3 + 3
2x = 6
x = 3 [This means only one value of x satisfies the equation in the range (x - 3) ≥ 0]
(b). x - 3 = -(3 - x) [This is possible if (x - 3) ≤ 0]
x - 3 = -3 + x
x - x = -3 + 3
0 = 0 [This means all the value of x in the range (x - 3) ≤ 0 satisfy the equation ]
While solving absolute value problems do not forget the definition of absolute value.
Hope that helps.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
- sachin_yadav
- Master | Next Rank: 500 Posts
- Posts: 212
- Joined: Mon Dec 06, 2010 12:52 am
- Location: India
- Thanked: 5 times
- Followed by:1 members
Thank you so much and really appreciate it
Sachin
Sachin
Anju@Gurome wrote:Hence, the rephrased question should be is x ≤ 3?sachin_yadav wrote:I wasted a lot of my time by solving absolute value equation further |x - 3| = 3 - x
(a). x - 3 = 3 - x [This is possible if (x - 3) ≥ 0]
x + x = 3 + 3
2x = 6
x = 3 [This means only one value of x satisfies the equation in the range (x - 3) ≥ 0]
(b). x - 3 = -(3 - x) [This is possible if (x - 3) ≤ 0]
x - 3 = -3 + x
x - x = -3 + 3
0 = 0 [This means all the value of x in the range (x - 3) ≤ 0 satisfy the equation ]
While solving absolute value problems do not forget the definition of absolute value.
Hope that helps.
Never surrender