Lines & Angles Q 1
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- aditiniyer
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x-q = s-y
x+y = q+s.
Angles inside a triangle must sum to 180.
Since x, y and z must sum to 180, x+y = 180-z.
Since r, q and s must sum to 180, q+s = 180-r.
Substituting x+y = 180-z and q+s = 180-r into x+y = q+s, we get:
180-z = 180-r
r = z.
Statement 1: xq + sy + sx + yq = zr
xq + sy + sx + yq = zr
x(q+s) + y(q+s) = zr
(q+s)(x+y) = zr.
Substituting q+s = x+y on the left side and r=z on the right side, we get:
(x+y)(x+y) = zz
(x+y)² = z²
x+y = z.
Since (x+y) and z must sum to 180 -- and (x+y) and z are EQUAL -- we get:
x+y=90 and z=90.
SUFFICIENT.
Statement 2: zq - ry = rx - zs
zq + zs = rx + ry
z(q+s) = r(x+y)
z/(x+y) = r/(q+s).
It's possible that z=r=10 and x+y = q+s = 170, with the result that the angles inside each triangle sum to 180.
It's possible that z=r=20 and x+y = q+s = 160, with the result that the angles inside each triangle sum to 180.
Since z can be different values, INSUFFICIENT.
The correct answer is A.
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Dear GAMT GuruGMATGuruNY wrote:
Statement 2: zq - ry = rx - zs
zq + zs = rx + ry
z(q+s) = r(x+y)
z/(x+y) = r/(q+s).
It's possible that z=r=10 and x+y = q+s = 170, with the result that the angles inside each triangle sum to 180.
It's possible that z=r=20 and x+y = q+s = 160, with the result that the angles inside each triangle sum to 180.
Since z can be different values, INSUFFICIENT.
The correct answer is A.
In S2, As (q+s)= (x+y) so we can rule them out and we get z=r which is NOT new info...Hence it is insufficient.
Is my line of reasoning acceptable?
Thanks
- GMATGuruNY
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Perfect!Mo2men wrote:Dear GAMT GuruGMATGuruNY wrote:
Statement 2: zq - ry = rx - zs
zq + zs = rx + ry
z(q+s) = r(x+y)
z/(x+y) = r/(q+s).
It's possible that z=r=10 and x+y = q+s = 170, with the result that the angles inside each triangle sum to 180.
It's possible that z=r=20 and x+y = q+s = 160, with the result that the angles inside each triangle sum to 180.
Since z can be different values, INSUFFICIENT.
The correct answer is A.
In S2, As (q+s)= (x+y) so we can rule them out and we get z=r which is NOT new info...Hence it is insufficient.
Is my line of reasoning acceptable?
Thanks
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3