Is (sqrt) x-5^2 = 5-x? : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 07:20

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is (sqrt) x-5^2 = 5-x?

Author Message
Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 117 [0], given: 1

Is (sqrt) x-5^2 = 5-x? [#permalink]

### Show Tags

10 Jun 2007, 15:07
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is (sqrt) x-5^2 = 5-x?

1) -x|x| > 0
2) 5-x > 0

Please solve and explain stmnt. 1 in detail.

Does ((sqrt) x-5^2) * ((sqrt) x-5^2) = x-5^2?
Manager
Joined: 07 May 2007
Posts: 178
Followers: 2

Kudos [?]: 49 [0], given: 0

### Show Tags

10 Jun 2007, 16:07
Are you taking the root of only x or the entire expression x-25?
Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 117 [0], given: 1

### Show Tags

11 Jun 2007, 10:17
Hi,

It's the square root of the entire left hand side expression. In other words, the entire left side of the equation is under the radical sign.
Manager
Joined: 07 May 2007
Posts: 178
Followers: 2

Kudos [?]: 49 [0], given: 0

### Show Tags

11 Jun 2007, 17:13
1) -x|x| > 0 means x must be negative because |x| is always positive
So x-25 is negative and sqrt(x-25) is imaginary. On the otherhand
5-x is positive.

We can conclude sqrt(x-25) is not equal to 5-x.

1 alone is suff

2) 5-x>0 means x<5
So x-25 is negative and sqrt(x-25) is imaginary. On the otherhand
5-x is positive.
We can conclude sqrt(x-25) is not equal to 5-x.

2 alone is suff
VP
Joined: 10 Jun 2007
Posts: 1459
Followers: 7

Kudos [?]: 255 [0], given: 0

### Show Tags

11 Jun 2007, 17:53
You know, this is a strange one...because GMAT NEVER deals with imaginary number. If we try to solve your equation:
sqrt(x-5^2) = 5-x
=> sqrt(x-25) = 5-x
square both sides
=> x-25 = (5-x)*(5-x)
=> (x+5)*(x-5) = x^2-10x+25
=> (x+5)*(x-5) = (x-5)*(x-5)
=> (x+5) = (x-5)
=> x = x+10
We know that there is no valid solution to this problem other than imaginary number; thus, I'll go with D.
Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 117 [0], given: 1

### Show Tags

11 Jun 2007, 20:08
The OG guide offers this explanation for stmnt 1:
|x| > 0 and, since the product of -x and |x| is positive, -x>0.

Does this make sense to any of you? What am I missing? How is -x * |x| positive. Isn't |x| always +ve? That said, wouldn't:
-x * |x| = -x(x)
Manager
Joined: 23 Dec 2006
Posts: 136
Followers: 1

Kudos [?]: 26 [0], given: 0

### Show Tags

11 Jun 2007, 20:25
Are you sure the left hand side is correct, and not sqrt[(x-5)^2]? It's more symmetrical than x-5^2 = x-25, so i wonder.
VP
Joined: 10 Jun 2007
Posts: 1459
Followers: 7

Kudos [?]: 255 [0], given: 0

### Show Tags

11 Jun 2007, 20:27
ggarr wrote:
The OG guide offers this explanation for stmnt 1:
|x| > 0 and, since the product of -x and |x| is positive, -x>0.

Does this make sense to any of you? What am I missing? How is -x * |x| positive. Isn't |x| always +ve? That said, wouldn't:
-x * |x| = -x(x)

-x|x|>0 only when x<0. For example, if x=-2, then -x|x| = 2|2| = 4. This is the same as -x>0. If you multiply -1 to -x>0, you would get x<0.
Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 117 [0], given: 1

### Show Tags

11 Jun 2007, 20:36
sludge wrote:
Are you sure the left hand side is correct, and not sqrt[(x-5)^2]? It's more symmetrical than x-5^2 = x-25, so i wonder.

hi sludge, yes, the entire expression, (x-5)^2 is underneath the radical sign.
11 Jun 2007, 20:36
Display posts from previous: Sort by