ds:is x^2>5^2?

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arjunshn: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Wed Apr 06, 2011 11:50 pm

by arjunshn » Wed Apr 13, 2011 3:42 am

Is X^2 > 5^2 ?
1) |X -5| = 3 |X + 5|
2) |X| > 3

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Source: Beat The GMAT — Data Sufficiency | Wed Apr 13, 2011 3:42 am

HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Wed Apr 13, 2011 3:46 am

Using A : magnitude of x is either 10 or 2.5 [insufficient]
using B : magnitude of x can be 4,5 or more [insufficeitn]

Combining:
magnitude of x is 10

IMO C

First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.

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arjunshn: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Wed Apr 06, 2011 11:50 pm

by arjunshn » Wed Apr 13, 2011 4:02 am

from 1st we get to know that x<5
from second we know that x>3 and x<-3

when we combine we get to know the range of x i.e -5<x<-3 and 3<x<5
thus NO
imo c

is this correct?

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Wed Apr 13, 2011 4:04 am

It should be C.

Regards,

Pranay

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arjunshn: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Wed Apr 06, 2011 11:50 pm

by arjunshn » Wed Apr 13, 2011 4:10 am

can you please explain how is it c?

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Wed Apr 13, 2011 4:16 am

HSPA wrote:using B : magnitude of x can be 4,5 or more [insufficeitn]

Just to add to it, x can also be -4, -5, -6 ..

@Arjunshn, HSPA has describe it nice.

Hope it helps.

Regards,

Pranay

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arjunshn: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Wed Apr 06, 2011 11:50 pm

by arjunshn » Wed Apr 13, 2011 4:23 am

what abt the first option..is my explanation right?

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Wed Apr 13, 2011 4:30 am

I am not sure how you concluded x<5 from option 1.

My approach was to square on both sides to obtain a qudratic equation of x.

Then solve for x to get 5/2 and -10.

Regards,

Pranay

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arjunshn: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Wed Apr 06, 2011 11:50 pm

by arjunshn » Wed Apr 13, 2011 4:33 am

i took three intervals for the 1st equation x<-5, -5<x<5 and x>5
when u put the values on the number line only first two satisfy thus x<5

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Wed Apr 13, 2011 4:34 am

arjunshn wrote:from 1st we get to know that x<5
from second we know that x>3 and x<-3

when we combine we get to know the range of x i.e -5<x<-3 and 3<x<5
thus NO
imo c

is this correct?

The two scenario approach is useful for equations using absolute values.
The equation has two solutions, which can be found using the two scenarios:

scenario 1: Copy the equation as is, without the absolute value. Solve.
X -5 = 3(X + 5)
x-5 = 3x+15
-5-15 = 3x-x
-20 = 2x
-10=x

Scenario 2: copy the equation without the absolute value sign, but put a (-) minus sign on one the right side.
X -5 = -3(X + 5)
x-5 = -3x-15
2x = -10
x=-2.5

As a final step for the two scenario approach, check your work by plugging in both values into the original equation |X -5| = 3 |X + 5| to see that the equation is indeed satisfied for both values:

x=-10 |-10 -5| = 3 |-10 + 5|
|-15| = 3|-5|
15 is indeed equal to 3*5.

x=-2.5 |-2.5 -5| = 3 |-2.5 + 5|
|-7.5| = 3|-2.5|
7.5 is indeed equal to 3*2.5.

So both of these values satisfy the equation, and are thus the solutions of x.

Alone, this is insufficient to answer the question: For x^2 to be greater than 5^2, x must be either >5 or smaller than -5.
-10 is smaller than -5, so the answer here is YES.
-2.5 is greater than -5, so the answer is NO.

Stat. (2) is insufficient for the same reasoning: it is possible to find examples that are both within and outside the required ranges.

combined, only x=-10 satisfies Stat. (2)'s requirements, so the answer to the question is a definite YES. Answer is C.

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

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arjunshn: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Wed Apr 06, 2011 11:50 pm

by arjunshn » Wed Apr 13, 2011 4:43 am

thank you

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Fri Apr 15, 2011 10:19 am

arjunshn wrote:Is X^2 > 5^2 ?
1) |X -5| = 3 |X + 5|
2) |X| > 3

Taking into account that |a-b| = dist(a,b) for any two real numbers a and b (where dist means the distance in the real number line), please note that:

The question may be rephrased as: |x| > 5, that is, is dist(x, origin) greater than 5?

(1) dist(x,5) = 3*dist(x, -5)

Please note (diagram follows) that there are ONLY TWO points (real numbers) satisfying this statement, one of them certainly answering the question in the affirmative, the other one in the negative.

From sttm (2) we must "take out" one of the (only two) possibilities allowed by sttm (1), therefore we are done.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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arjunshn: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Wed Apr 06, 2011 11:50 pm

by arjunshn » Sat Apr 16, 2011 7:27 am

Its a great way to solve it faster..basically a shortcut or basic logic.
thanx alot for sharing it..
thank you

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Apr 18, 2011 4:41 am

arjunshn wrote:Its a great way to solve it faster..basically a shortcut or basic logic.
thanx alot for sharing it..
thank you

IÂ´m glad you like it, arjunshn!
Cheers, Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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