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Triangle problem

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by gmat009 » Tue Oct 07, 2008 7:38 pm
In the triangle above[see attached diagram], is x > 90?
(1) a2 + b2 < 15
(2) c > 4
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |
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by mbaquest » Tue Oct 07, 2008 8:00 pm
1) a^2 + b^2 < 15,

pick two values, a & b e.g. 2,3

<c is 90, when c = 5, however, c should always be <5 , so <c is never > 90. You can try taking other possible values and shud get the same answer.

2) Not sufficient

So, I will go with A.
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by gmat009 » Tue Oct 07, 2008 8:15 pm
mbaquest wrote:1) a^2 + b^2 < 15,

pick two values, a & b e.g. 2,3

<c is 90, when c = 5, however, c should always be <5 , so <c is never > 90. You can try taking other possible values and shud get the same answer.

2) Not sufficient

So, I will go with A.
OA is C. Can someone plz. explain
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by mbaquest » Tue Oct 07, 2008 9:11 pm
I guess I was wrong the last time. However C seems to be right.

Here is my explanation,

In a triangle with sides A, B & C and corresponding angles a,b,c

C^2 = A^2 + B^2 - 2AB cos c

1) A^2 + B^2 < 15, we can have multiple values of c, depending on the value of C

Not sufficient

2) C > 4,

No information about A & B so not sufficient.

3) Taking both together,

As C > 4 the term -2AB cos c must be +ve, so cos c should be -ve.
cos c is negetive when c > 90.

Sufficient.
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by msd_2008 » Sun Oct 12, 2008 9:42 pm
Is there any other way to answer this question, without using trigonometry?
When the going gets tough, the tough gets going.
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by stubbornp » Mon Oct 13, 2008 12:54 am
acc to pythagorous theoram,

In rt angle triangle

a^2 + b^2= c^2


stmt a A^2 + B^2 < 15----

no value for c---insufficient

stmt b-c>4

no values for a & b--insufficient

combining both,a^2 + b^2<c2....So it must be greater than 90..Hope it helps..IMO C
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by bujuji » Fri Aug 05, 2011 4:08 am
hi all,

answer is C. when both conditions are conbined, we can difine x>90:

c>4, so c^2>16 and a^2+b^2<15, that is 15<16 so we get x<90

hint: if a^2+b^2<c^2, x>90, and if a^2+b^2>c^2, x>90.
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by Deepna K » Tue Jul 17, 2012 6:39 am
stubbornp wrote:acc to pythagorous theoram,

In rt angle triangle

a^2 + b^2= c^2


stmt a A^2 + B^2 < 15----

no value for c---insufficient

stmt b-c>4

no values for a & b--insufficient

combining both,a^2 + b^2<c2....So it must be greater than 90..Hope it helps..IMO C
Hello
could you explain using values please
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by tisrar02 » Tue Jul 17, 2012 7:29 pm
Note: A right triangle will ALWAYS follow= A^2 + B^2= C^2

1) NS--> We have A and B but no C... Could be greater than 90 or less. We dont know.. Move on

2) We get C as a number greater than 4.. We have no idea about A or B so we move on.. NS

1) and 2)--> A^2 +B^2<15= Assume- 2^2 + 3^2= 4+9= 13... But BECAUSE C^2 HAS TO BE GREATER THAN 16, we think Pythag's theorem and figure out that it MUST be greater than 90 degrees and thus SUFFICIENT!!!!

ANSWER: C

Let me know if this helps!
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by das.ashmita » Tue Jul 17, 2012 10:21 pm
we need to find if x>90
or in other words c^2 > a^2 + b^2

1. a^2 + b^2 <15
no info about c ... hence Insuff

2. c>4 => c^2 > 16
no info abt a&b ... hence Insuff

combining both we know
c^2 > a^2 + b^2
hence Suff

So ans is C
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by AMT » Thu Aug 09, 2012 8:08 pm
ANS : C
Please refer to the attached figure...
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Please refer to this image
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