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

Redeem

No properties - Modulus

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Sun May 24, 2009 4:51 am

No properties - Modulus

by rahcool4u » Fri Jun 26, 2009 6:57 am
Can anyone explain how to solve the below modulus questions (from gmat prep).

Q1) Is √(x-3)^2 = 3 –x ?

1) x ≠ 3
2) –x│x│ > 0

Q2) Is │x│ = y – z ?

1) x +y =z
2) x < 0


Answers:
Q1) B
Q2) C
Top
Source: — Data Sufficiency |
User avatar
Senior | Next Rank: 100 Posts
Posts: 91
Joined: Wed Apr 01, 2009 9:53 pm
Thanked: 11 times

by Robinmrtha » Fri Jun 26, 2009 7:33 am
Q1) Is &#8730;(x-3)^2 = 3 –x ?

&#8730;(x-3)^2 = 3 –x
For this condition to be true...x should always be less than 3
So, the question is asking if x is greater than or less than 3

statement 1
x &#8800; 3
So insufficient as x can be both greater than or less than 3

statement 2
–x&#9474;x&#9474; > 0
for the left hand side to be true x should be negative...
so x is negative hence it is less than 3
sufficient...
Answer B
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 91
Joined: Wed Apr 01, 2009 9:53 pm
Thanked: 11 times

by Robinmrtha » Fri Jun 26, 2009 7:39 am
Q2) Is &#9474;x&#9474; = y – z ?

1) x +y =z
2) x < 0

The question is asking whether y is greater than z???
statement 1
x+y=z
or y =z-x
y is greater than z if x is positive and less than z if x is negative...
so insufficient

statement 2
x is negative but does not say anything about y or z
insufficient

when combined since x is negative y is less than z
sufficient
hence answer is C
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Sun May 24, 2009 4:51 am

by rahcool4u » Sat Jun 27, 2009 2:22 am
Thanks Robinmrtha :)
Q1 is still not clear to me.

Why the condition &#8730;(x-3)^2 = 3 –x , is true only for -ve values of x.
eg:

Take x =5, &#8730;(5-3)^2 = 3 –5 -> 2 = -2 -> condition 1 fails for +ve values
Take X =-5, &#8730;(-5-3)^2 = 3 +5 -> -8 = 8 -> condition 1 fails for -ve values
Take X =0, &#8730;(0-3)^2 = 3 -0 -> -3 = 3 -> condition 1 fails for 0

According to me, the answer should be D.
Did I miss something ?
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 91
Joined: Wed Apr 01, 2009 9:53 pm
Thanked: 11 times

by Robinmrtha » Sat Jun 27, 2009 7:25 am
Fren when you take
Take X =-5, &#8730;(-5-3)^2 = 3 +5 -> &#8730;64 = 8
you are doing the same mistake when you are taking x=0

Hope this helps
Top
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Wed Oct 29, 2008 8:26 am
Thanked: 1 times

by carpe_diem » Sat Jun 27, 2009 7:40 am
rahcool4u wrote:Thanks Robinmrtha :)
Q1 is still not clear to me.

Why the condition &#8730;(x-3)^2 = 3 –x , is true only for -ve values of x.
eg:

Take x =5, &#8730;(5-3)^2 = 3 –5 -> 2 = -2 -> condition 1 fails for +ve values
Take X =-5, &#8730;(-5-3)^2 = 3 +5 -> -8 = 8 -> condition 1 fails for -ve values
Take X =0, &#8730;(0-3)^2 = 3 -0 -> -3 = 3 -> condition 1 fails for 0

According to me, the answer should be D.
Did I miss something ?
When you take X = -5 and do &#8730;(-5-3)^2 then this would be &#8730;64 = 8 and not -8. This is because in GMAT &#8730;X will always be positive. So you need to first square the number 8 which is 64 and then take square root which in this case will always be + ve. Hence 8 = 8. Sufficient.
Top
Legendary Member
Posts: 1161
Joined: Mon May 12, 2008 2:52 am
Location: Sydney
Thanked: 23 times
Followed by:1 members

by mehravikas » Sat Jun 27, 2009 4:57 pm
Please correct me if I am wrong - Can I simplify the question to be:

&#8730;(x-3)^2 = 3 -x

x - 3 = 3 - x
i.e. 2x = 6
Is x = 3???

Robinmrtha wrote:Fren when you take
Take X =-5, &#8730;(-5-3)^2 = 3 +5 -> &#8730;64 = 8
you are doing the same mistake when you are taking x=0

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

by aj5105 » Mon Jun 29, 2009 4:25 am
IMO, No.

Sqrt(x^2) = |x| . So, simplify the question on those terms.

mehravikas wrote:Please correct me if I am wrong - Can I simplify the question to be:

&#8730;(x-3)^2 = 3 -x

x - 3 = 3 - x
i.e. 2x = 6
Is x = 3???

Robinmrtha wrote:Fren when you take
Take X =-5, &#8730;(-5-3)^2 = 3 +5 -> &#8730;64 = 8
you are doing the same mistake when you are taking x=0

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

by aj5105 » Mon Jun 29, 2009 4:50 am
Is &#8730;(x-3)^2 = 3 –x ?

1) x &#8800; 3
2) –x&#9474;x&#9474; > 0


IMO, the stem statement is asking if x = 3 or x is greater than 3.

Statement 1 : We cannot say. Insufficient.

Statement 2 : We know x < 0. Definite No. So (B)

Please correct me if I am wrong.
Top
Legendary Member
Posts: 1161
Joined: Mon May 12, 2008 2:52 am
Location: Sydney
Thanked: 23 times
Followed by:1 members

by mehravikas » Mon Jun 29, 2009 12:23 pm
Can you elaborate further by giving another example please?
aj5105 wrote:IMO, No.

Sqrt(x^2) = |x| . So, simplify the question on those terms.

mehravikas wrote:Please correct me if I am wrong - Can I simplify the question to be:

&#8730;(x-3)^2 = 3 -x

x - 3 = 3 - x
i.e. 2x = 6
Is x = 3???

Robinmrtha wrote:Fren when you take
Take X =-5, &#8730;(-5-3)^2 = 3 +5 -> &#8730;64 = 8
you are doing the same mistake when you are taking x=0

Hope this helps
Top
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pm
Thanked: 331 times
Followed by:11 members

by cramya » Mon Jun 29, 2009 3:38 pm
IMO, the stem statement is asking if x = 3 or x is greater than 3.

Statement 1 : We cannot say. Insufficient.

Statement 2 : We know x < 0. Definite No. So (B)

Please correct me if I am wrong.
Replying to PM and building upon the explanation:


sqrt(X^2) = |x| as u pointed out rightly Similarly in this prob sqrt[(x-3)^2] = |x-3| here our X = x-3

The question is asking Is |x-3| = 3-x True when x<=0 False when x>0

Stmt I

x &#8800; 3

Cant say for sure if x <=0 or x>0

INSUFF

Stmt II

-x |x| > 0

|x| cannot be 0 since -x |x| >0

By defnition |x| is x when x>=0 and |x| = -x when x<0

You can either apply the defnition or pick a negative and positive number and see what happens

Picking numbers is easy here rather than getting tangled with the theory(IMO):

Let x = 2

- (2) |2| > 0 NO

Let x=-2

- (-2) * |-2|

2 * 2 >0 TRUE


-x |x| > 0 only when x<0 in this prob so x is neagtive therefore
&#8730;(x-3)^2 = 3 –x

B

Hope this helps!

Regards,
CR
Top
Post new topic Post Reply
• Page 1 of 1