IMO C
Option 1 makes triangle RQS eqilateral and hence Angle RSQ as 60 degree but doesnt say anything about angle UST
Option 2 makes triangle UST eqilateral and hence Angle UST as 60 degree but doesnt say anything about angle RSQ
Merging both the angle together makes equestion as angle RSQ + x + angle UST = 180 and hence x = 60degree
OA please
gmatprep - tough triangle problem
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tendays2go
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IMO C
Let angles PTR & PRT be y and 90-y respectively.
first stmt => QR=RS
i.e. angles RQS and RSQ are equal, say z
therefore, 2z + (90-y) = 180 or z = 45 + 0.5*y
or angle RSQ = 45 + 0.5*y
this info alone is unsufficient to answer the question.
second stmt => ST = TU
i.e. angles SUT and UST are equal say w
therefore, 2w+ y = 180
or angle UST = w = 90 - 0.5*y
clearly, this info alone is unsufficient to answer the question too.
combining both of them and since:
angle RSQ + x + angle UST = 180
i.e. [45 + 0.5*y] + x + [90 - 0.5*y] = 180
or x + 135 = 180 i.e. x = 45
Thus, (C) is the answer by using both the stmts
Let angles PTR & PRT be y and 90-y respectively.
first stmt => QR=RS
i.e. angles RQS and RSQ are equal, say z
therefore, 2z + (90-y) = 180 or z = 45 + 0.5*y
or angle RSQ = 45 + 0.5*y
this info alone is unsufficient to answer the question.
second stmt => ST = TU
i.e. angles SUT and UST are equal say w
therefore, 2w+ y = 180
or angle UST = w = 90 - 0.5*y
clearly, this info alone is unsufficient to answer the question too.
combining both of them and since:
angle RSQ + x + angle UST = 180
i.e. [45 + 0.5*y] + x + [90 - 0.5*y] = 180
or x + 135 = 180 i.e. x = 45
Thus, (C) is the answer by using both the stmts
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lunarpower
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first off, note that the conditions given in statements (1) and (2), individually, are identical. (i.e., if you flip the triangle around, statement 1 becomes statement 2, and vice versa.) that's a humble observation, but it serves to eliminate choices a and b in a hurry: if statement (1) is sufficient then statement (2) must be as well, and vice versa.
that leaves us with the last 3 choices.
you can visualize the fact that one of the two statements alone won't do the job:
imagine that statement (1) alone is true, making triangle QRS isosceles. that means segment QS is fixed in place.
however, there are no restrictions on triangle STU. that means, in effect, that we can move point U wherever we feel like moving it.
as we 'slide' point U along the bottom of the triangle, the value of x changes; therefore, statement (1) alone (and hence statement (2) alone) is insufficient.
if you don't buy the above argument, or if it's just something you'd never possibly think of within the time limit, then you could always try plugging in numbers and seeing that x can have different values.
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statements (1) and (2) together:
since the triangle is a right triangle, we know that angles R and T must add to 90 degrees. let angle R be y degrees, and let angle T be (90 - y) degrees.
then
each of angles RQS and RSQ is (180 - y)/2 = 90 - y/2 degrees; and
each of angles TSU and TUS is (180 - (90 - y))/2 = 45 + y/2 degrees.
therefore, since angle RSQ, x, and angle TSU make a straight line together,
x = 180 - RSQ - TSU
= 180 - (90 - y/2) - (45 + y/2)
= 45 degrees.
sufficient
answer = c
note that you should not use more than one variable when you have the two statements together. it's tempting to use "y" and "z", but you should just lower your head and charge through all those fractions like a raging bull.
that leaves us with the last 3 choices.
you can visualize the fact that one of the two statements alone won't do the job:
imagine that statement (1) alone is true, making triangle QRS isosceles. that means segment QS is fixed in place.
however, there are no restrictions on triangle STU. that means, in effect, that we can move point U wherever we feel like moving it.
as we 'slide' point U along the bottom of the triangle, the value of x changes; therefore, statement (1) alone (and hence statement (2) alone) is insufficient.
if you don't buy the above argument, or if it's just something you'd never possibly think of within the time limit, then you could always try plugging in numbers and seeing that x can have different values.
--
statements (1) and (2) together:
since the triangle is a right triangle, we know that angles R and T must add to 90 degrees. let angle R be y degrees, and let angle T be (90 - y) degrees.
then
each of angles RQS and RSQ is (180 - y)/2 = 90 - y/2 degrees; and
each of angles TSU and TUS is (180 - (90 - y))/2 = 45 + y/2 degrees.
therefore, since angle RSQ, x, and angle TSU make a straight line together,
x = 180 - RSQ - TSU
= 180 - (90 - y/2) - (45 + y/2)
= 45 degrees.
sufficient
answer = c
note that you should not use more than one variable when you have the two statements together. it's tempting to use "y" and "z", but you should just lower your head and charge through all those fractions like a raging bull.
Ron has been teaching various standardized tests for 20 years.
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Voit esittää kysymyksiä Ron:lle myös suomeksi
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jackcrystal
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Please read Ron's explanation and then my simple solution.
x = 180 - RSQ - TSU
= 180 -1/2(180-R) - 1/2(180-T)
= 1/2 R + 1/2 T
= 1/2(90)
= 45
(C)
x = 180 - RSQ - TSU
= 180 -1/2(180-R) - 1/2(180-T)
= 1/2 R + 1/2 T
= 1/2(90)
= 45
(C)
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lunarpower
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this is good.jackcrystal wrote:Please read Ron's explanation and then my simple solution.
x = 180 - RSQ - TSU
= 180 -1/2(180-R) - 1/2(180-T)
= 1/2 R + 1/2 T
= 1/2(90)
= 45
(C)
it's not that different from the algebraic solution in my post, except in that it uses 2 variables instead of 1 variable.
this works out well here, although it's still a good idea to try to stick to 1 variable whenever possible; in many problems, adding a second variable is a time-wasting detour.
still, remember the most important axiom of all, which is that you should always go with the first viable solution method that comes to mind.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Learn more about ron
