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Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink]
09 Feb 2012, 02:57

3

This post received KUDOS

Expert's post

I attached the diagram, which was missing in initial post.

Attachment:

Trianlge.PNG [ 1.74 KiB | Viewed 4271 times ]

In the triangle above, is x > 90?

(1) a^2 + b^2 <15 (2) c > 4

Each statement alone is clearly insufficient. When taken together: If angle x were 90 degrees than we would have a^2+b^2=4^2, since a^2+b^2<15<16 then angle x must be greater than 90 degrees (c^2 is greater than a^2+b^2 then the angel opposite c must be greater than 90).

ABC with a trainagle with three sides abc and one of the angle is x

In the triangle above, 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.

E for me.
(1) don't know c
INSUFFICIENT

(2) Only know c
INSUFFICIENT

Together, if a^2 + b^2 < 15
We know that at least one angle in the triangle is greater than 90 if a=2.99, b=3.99, c=5. But other angles are less than 90. We don't know where x is; thus, insufficient.

ABC with a trainagle with three sides abc and one of the angle is x

In the triangle above, is x > 90? (1) a2 + b2 <15> 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.

Note that for a right triangle, c^2 = a^2+b^2, where c is the length of the side opposite the right angle C.

We don't have to know which angle is x. Question is asking, whether any of the angle in the triangle is greater than 90.

since c^2 > a^2 + b^2 , we know tht angle opposite to side c will be greater than 90.

So, both the statements are required to answer the question. My choice is C.

Together, we are told that the triangle is obtuse- one interior angle is greater than 90º. However, we don't know which which angle is being asked about

We don't have to know which angle is x. Question is asking, whether any of the angle in the triangle is greater than 90.

since c^2 > a^2 + b^2 , we know tht angle opposite to side c will be greater than 90.

So, both the statements are required to answer the question. My choice is C.

Its not asking whether any of the angle in the triangle is greater than 90.
It is asking that one of the angle is x, Is x > 90? Means one perticular angle.N we dont know which is the one ?

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink]
17 Feb 2012, 01:27

Whenever Asqr + Bsqr Is equal to Csqr than angle X is 90 degrees Look at both options carefully ,

Asqr + Bsqr Is less than 15 and C greater than 4 means any value more than 4 for c and will automatically increase angle X bcoz as C increases angle 8 increases

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink]
17 Feb 2012, 01:42

Expert's post

SergeNew wrote:

Quote:

c^2 is greater than a^2+b^2 then the angel opposite c must be greater than 90

Hi Guys,

Would anyone be able to explain why the angle is greater than 90 if c^2 is greater than a^2+b^2?

Serge.

If c^2 were equal to a^2+b^2 then we would have a^2+b^2=c^2, which would mean that angle x is 90 degrees. Now, since c^2 is more than a^2+b^2, then angle x, which is opposite c, must be more than 90 degrees: try to increase side c and you'll notice that angle x will increase too.

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink]
26 Jan 2013, 20:15

Bunuel wrote:

I attached the diagram, which was missing in initial post.

Attachment:

Trianlge.PNG

In the triangle above, is x > 90?

(1) a^2 + b^2 <15 (2) c > 4

Each statement alone is clearly insufficient. When taken together: If angle x were 90 degrees than we would have a^2+b^2=4^2, since a^2+b^2<15<16 then angle x must be greater than 90 degrees (c^2 is greater than a^2+b^2 then the angel opposite c must be greater than 90).

Answer: C.

Hope it helps.

What would happen is the statement was c>3? how would this question be framed such that the angle could be always below 90 degrees. Since in this particular question the solution will always be greater, what would be the opposite case? _________________

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink]
26 Jan 2013, 20:50

fozzzy wrote:

Bunuel wrote:

I attached the diagram, which was missing in initial post.

Attachment:

Trianlge.PNG

In the triangle above, is x > 90?

(1) a^2 + b^2 <15 (2) c > 4

Each statement alone is clearly insufficient. When taken together: If angle x were 90 degrees than we would have a^2+b^2=4^2, since a^2+b^2<15<16 then angle x must be greater than 90 degrees (c^2 is greater than a^2+b^2 then the angel opposite c must be greater than 90).

Answer: C.

Hope it helps.

What would happen is the statement was c>3? how would this question be framed such that the angle could be always below 90 degrees. Since in this particular question the solution will always be greater, what would be the opposite case?

If you reverse the values, such as: (1) a^2 + b^2 >16 (2) c < 4 You would get a case where angle x would be less than 90, provided a triangle is still formed. (Note that a+b will tend to be bigger and C tends to be smaller in this option) _________________

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink]
24 Feb 2013, 20:46

smily_buddy wrote:

Attachment:

Trianlge.PNG

In the triangle above, is x > 90?

(1) a^2 + b^2 <15 (2) c > 4

If a^2 + b^2 = c^2 then x= 90. But , as given in st2, minimum value of C = 5, then C^2 = 25. It means a^2 + b^2 < c^2.Thus, x <90. Therefore, C. _________________

Re: ABC with a trainagle with three sides abc and one of the [#permalink]
24 Feb 2013, 22:14

abhi47 wrote:

E is the correct answer. Both statements are insufficient.

from one, possible values of (a,b) = (1,2) or (1,3) or (2,3) or (2,2) from 2nd, given that c>4 Property of triangle is = sum of two sides > third side therefor only possible values are a= 2, b=3 and c = 5 or a = 3 and b = 2 and c =5 since a^2 + b ^2 = c^2 hence it is a right angle triangle hence both conditions required to answer so option(c)

gmatclubot

Re: ABC with a trainagle with three sides abc and one of the
[#permalink]
24 Feb 2013, 22:14