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taken from the gmat math bible: In triangle MNP, if MN = x, [#permalink]
 06 Aug 2009, 01:55
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taken from the gmat math bible:
In triangle MNP, if MN = x, NP = 2x, and MP = y, which of the three angles has the greatest degree measure?
(1) MNP is a right triangle.
(2) y < 2x
I dont' agree with the answer provided. i can post later how i disproved it. What do you think should be the answer?
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[quote="tomirisk"]taken from the gmat math bible:
In triangle MNP, if MN = x, NP = 2x, and MP = y, which of the three angles has the greatest degree measure?
(1) MNP is a right triangle.
(2) y < 2x
from 1
no relation between the sides lenghts .....insuff
from 2
y<2x, 2x>x thus surely the angel corresponding to the 2x is the largest.
I d say B
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yezz wrote: tomirisk wrote: taken from the gmat math bible:
In triangle MNP, if MN = x, NP = 2x, and MP = y, which of the three angles has the greatest degree measure?
(1) MNP is a right triangle.
(2) y < 2x
from 1
no relation between the sides lenghts .....insuff
from 2
y<2x, 2x>x thus surely the angel corresponding to the 2x is the largest.
I d say B what about the pythagorian triplet: x:x(sqrt3):2x? is this not sufficient for comleting relation in the statement 1?
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i think ans is BStatement (1) MNP is a right triangle .... in any right angle triangle 90 deg is the greatest angle...since it is not given which angle is 90 ...there are two possibilities...( as 2x > x this means x cannot be hypoteneous as 2x will always be there as a higher side qualifying to be a hypoteneous... and hence P cannot be 90.... thus MN cannot be hypoteneous) angle N = 90 or [M = 90 deg (pythagorian triplet)]..... insufficient Statement (2) y < 2x also we know that x < 2x (similar explination as in statement 1....possibility of N = 90 is negated by this statement) only possibility is M = 90 ....sufficient if u lik my post.....consider it for Kudos 
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bhushan252 wrote: i think ans is BStatement (1) MNP is a right triangle .... in any right angle triangle 90 deg is the greatest angle...since it is not given which angle is 90 ...there are two possibilities...( as 2x > x this means x cannot be hypoteneous as 2x will always be there as a higher side qualifying to be a hypoteneous... and hence P cannot be 90.... thus MN cannot be hypoteneous) angle N = 90 or [M = 90 deg (pythagorian triplet)]..... insufficient Statement (2) y < 2x also we know that x < 2x (similar explination as in statement 1....possibility of N = 90 is negated by this statement) only possibility is M = 90 ....sufficient if u lik my post.....consider it for Kudos bhushan252, thank you for your post, but as a little challenge can you provide any example of a right triangle in a situation when angle N= 90, thus x and 2x are legs and y hypothenuse? try to pick real numbers.
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IMO B....
1) Insuff....sa right angle can be at M,N or p...
2) Suff as y < 2x ...so angle opposite to 2x will be greatest...
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thank you guys for explanations..i was just overthinking the question. Tried different numbers and yes, it is possible for N or M to be=90, which makes the 1 stm insufficient, and thus B is the answer.
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tomirisk wrote: bhushan252 wrote: i think ans is BStatement (1) MNP is a right triangle .... in any right angle triangle 90 deg is the greatest angle...since it is not given which angle is 90 ...there are two possibilities...( as 2x > x this means x cannot be hypoteneous as 2x will always be there as a higher side qualifying to be a hypoteneous... and hence P cannot be 90.... thus MN cannot be hypoteneous) angle N = 90 or [M = 90 deg (pythagorian triplet)]..... insufficient Statement (2) y < 2x also we know that x < 2x (similar explination as in statement 1....possibility of N = 90 is negated by this statement) only possibility is M = 90 ....sufficient if u lik my post.....consider it for Kudos bhushan252, thank you for your post, but as a little challenge can you provide any example of a right triangle in a situation when angle N= 90, thus x and 2x are legs and y hypothenuse? try to pick real numbers. ok..dont go for substitution try this out...if N = 90....then (2x)^2 + x^2 = y^2 that gives y= sqrt5 * x which is 2.23x...highest now plug any values for x
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