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C Let angle RSQ = S1 = RQS Let angle RTP = T Let angle TSU = S2 = SUT

S1 + S2 + X = 180.....................1 In triangle TSU we have S2 + s2 + T = 180 2s2 + T = 180 ........................2

In triangle PRT we have P + R + T = 180 90 + T + (180 - 2S1) = 180 (angle R is calculated from triangle RQS) or 2S2 + 2S1 = 270 or S1 + S2 = 135 Put it in eq 1 135 + X = 180 X = 45.

Ive noticed that most of the times when information given is very little in gmat questions, the problem requires a conceptual approach, and its usually easier to solve with principles (rules of triangles in this case) rather than taking variables or numbers.

I will just share how i solved it mentally

Sttmt 1) only gives triangle RQS is isoceles, obviously cannot find x Sttmt 2) Again,... gives that triangle STU is isoceles, not sufficient.

Combining since the big triangle is right angled, Angles QRS and STU are complementary, ie their sum is also 90......(I) the two smaller triangles RQS and STU are isoceles, so Angle rqs = rsq and Angles tsu = tus in each of the smaller triangles, if the sum of two angles qrs + stu = 90 (from I above), then sum of the other two pairs should also be 90 ie. rqs + rsq + tsu + tus = 90

or 2rsq + 2 tsu = 90

As soon as we know this, we know we can solve for x, because we are getting rsq + tsu. so dont even need to calculate beyond this.

It may look complicated at the first glance (if you look at the wordiness of the explanation) , but really it is very easy if you try make images in your mind and solve.

[in each of the smaller triangles, if the sum of two angles qrs + stu = 90 (from I above), then sum of the other two pairs should also be 90 ie. rqs + rsq + tsu + tus = 90 .[/quote]

I didn't get this statement. how the sum of other two pairs is equal to 90, it should be 270

(the sum of all the angles of two smaller triangles is 360, if take the complementary angles out then the sum becomes 270). Kindly correct me if I am wrong.
_________________

I didn't get this statement. how the sum of other two pairs is equal to 90, it should be 270

(the sum of all the angles of two smaller triangles is 360, if take the complementary angles out then the sum becomes 270). Kindly correct me if I am wrong.

Yes, you are right, should be 270.

I didn't do the calculations, because we were not required to find the value of x, thus, the calculation error sorry for the inconvenience though.

Ive noticed that most of the times when information given is very little in gmat questions, the problem requires a conceptual approach, and its usually easier to solve with principles (rules of triangles in this case) rather than taking variables or numbers.

I will just share how i solved it mentally

Sttmt 1) only gives triangle RQS is isoceles, obviously cannot find x Sttmt 2) Again,... gives that triangle STU is isoceles, not sufficient.

Combining since the big triangle is right angled, Angles QRS and STU are complementary, ie their sum is also 90......(I) the two smaller triangles RQS and STU are isoceles, so Angle rqs = rsq and Angles tsu = tus in each of the smaller triangles, if the sum of two angles qrs + stu = 90 (from I above), then sum of the other two pairs should also be 90 ie. rqs + rsq + tsu + tus = 90

or 2rsq + 2 tsu = 90

As soon as we know this, we know we can solve for x, because we are getting rsq + tsu. so dont even need to calculate beyond this.

It may look complicated at the first glance (if you look at the wordiness of the explanation) , but really it is very easy if you try make images in your mind and solve.

I know this is a few years old but could someone help me with the problem? I am trying to wrap my head around the bolded part. What sum of two pairs are we really talking about? Because how I am understanding this shouldn't rqs+rsq+tsu+tus=180? (I know that the calculation was corrected to 270 in another post). I don't understand how that calculation above would equal to 270. I understand the explanation all up until this part where I just get confused and would like to understand this conceptually for any similiar future problems. Please help. Thanks.

Ive noticed that most of the times when information given is very little in gmat questions, the problem requires a conceptual approach, and its usually easier to solve with principles (rules of triangles in this case) rather than taking variables or numbers.

I will just share how i solved it mentally

Sttmt 1) only gives triangle RQS is isoceles, obviously cannot find x Sttmt 2) Again,... gives that triangle STU is isoceles, not sufficient.

Combining since the big triangle is right angled, Angles QRS and STU are complementary, ie their sum is also 90......(I) the two smaller triangles RQS and STU are isoceles, so Angle rqs = rsq and Angles tsu = tus in each of the smaller triangles, if the sum of two angles qrs + stu = 90 (from I above), then sum of the other two pairs should also be 90 ie. rqs + rsq + tsu + tus = 90

or 2rsq + 2 tsu = 90

As soon as we know this, we know we can solve for x, because we are getting rsq + tsu. so dont even need to calculate beyond this.

It may look complicated at the first glance (if you look at the wordiness of the explanation) , but really it is very easy if you try make images in your mind and solve.

I know this is a few years old but could someone help me with the problem? I am trying to wrap my head around the bolded part. What sum of two pairs are we really talking about? Because how I am understanding this shouldn't rqs+rsq+tsu+tus=180? (I know that the calculation was corrected to 270 in another post). I don't understand how that calculation above would equal to 270. I understand the explanation all up until this part where I just get confused and would like to understand this conceptually for any similiar future problems. Please help. Thanks.

In the figure shown, what is the value of x?

x+<QSR+<UST=180 (straight line =180) and <R+<T=90 (as PRT is right angle)

(1) The length of line segment QR is equal to the length of line segment RS --> QRS is isosceles --> <RQS=<QSR=(180-R)/2 (as <RQS+<QSR+<R=180 --> 2<QSR+<R=180 --> <QSR=(180-R)/2). Not sufficient.

(2) The legnth of line segment ST is equal to the length of line segment TU --> UST is isosceles --> <SUT=<UST=(180-T)/2. Not sufficient.

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