Data Sufficiency

Night reader wrote:the answer should be E here's why
st(1) says two angle are 90` but the remaining two angles could by anything to make 180` like x+y=180`Not Sufficient
st(2) says one angle is twice the other, also Not Sufficient because we know only relationship of these angles but not have information about the other two angles;
Combined: two angles are 90 and yet the other two angles are in relationship 2:1. This can be anything to make 180 --> x+2y=180 depending on x (10,20,30...) we may have y (85, 80, 75...) hence Not Sufficient

btgyes wrote:

Night reader wrote:the answer should be E here's why
st(1) says two angle are 90` but the remaining two angles could by anything to make 180` like x+y=180`Not Sufficient
st(2) says one angle is twice the other, also Not Sufficient because we know only relationship of these angles but not have information about the other two angles;
Combined: two angles are 90 and yet the other two angles are in relationship 2:1. This can be anything to make 180 --> x+2y=180 depending on x (10,20,30...) we may have y (85, 80, 75...) hence Not Sufficient

Acc to you,
angle are
10 : 85
20:80 and
30 : 75

BUT

this doesn't satisfy 2nd statement which says that
B = 2C

only one thing satisfy this scenario and that is

120: 60

this is why i put C ans.

clock60 wrote:also think that the answer is E
possible angles of rectangle are
90,90,120,60 the answer is yes
45,90,90 135, the answer is no

ankurmit wrote:I think answer should be C only

As in 2nd stem we are given that angle ABC is twice the measure of angle BCD.

Hence possible values are only 90,90,120,60.

Anurag@Gurome wrote:(1) Angles of the quadrilateral are 90º, 90º, x, and y, where x + y = 180º.
Clearly, x and y can take any values so that they add to 180. So, we don't get a unique answer.
Hence, (1) is NOT SUFFICIENT.

(2)

x + 2x + a + d = 360º
Again, we don't get a unique answer.
Hence, (2) is NOT SUFFICIENT.

Combining (1) and (2), we don't know which two angles of ABCD are 90º.
It may be possible that 2x = 90 or x = 45, which implies angles of the quadrilateral are 90, 90, 45, and 135 (notice here that 90 = 2(45), which satisfies the 2nd condition.)
If a = d = 90, x = 60, and 2x = 120, then one of the interior angles is 60º.
From the above examples, it is clear, that one of the interior angles may or may not be 60º.
So, combining the two statements is also NOT SUFFICIENT.

The correct answer is E.

Night reader wrote:good spot - let me correct an example for statement (2). I should have taken 2:1 precisely and not 2x+y
OK, look here --> if you pair one 90` and the other 90` you have also 45` and 45`, Agree?
it's good that you made up x+y=180 and x=2y from which x=60` only, BUT as you see it can be 45` too - hence Not Sufficient
one angle is 50` and the other is 130`, OR another set one is 40` and the other is

btgyes wrote:

Night reader wrote:the answer should be E here's why
st(1) says two angle are 90` but the remaining two angles could by anything to make 180` like x+y=180`Not Sufficient
st(2) says one angle is twice the other, also Not Sufficient because we know only relationship of these angles but not have information about the other two angles;
Combined: two angles are 90 and yet the other two angles are in relationship 2:1. This can be anything to make 180 --> x+2y=180 depending on x (10,20,30...) we may have y (85, 80, 75...) hence Not Sufficient

Acc to you,
angle are
10 : 85
20:80 and
30 : 75

BUT

this doesn't satisfy 2nd statement which says that
B = 2C

only one thing satisfy this scenario and that is

120: 60

this is why i put C ans.

Night reader wrote:it just takes reading the post carefully, before asking to explain

Night reader wrote:good spot - let me correct an example for statement (2). I should have taken 2:1 precisely and not 2x+y
OK, look here --> if you pair one 90` and the other 90` you have also 45` and 45`, Agree?
it's good that you made up x+y=180 and x=2y from which x=60` only, BUT as you see it can be 45` too - hence Not Sufficient
one angle is 50` and the other is 130`, OR another set one is 40` and the other is

btgyes wrote:

Night reader wrote:the answer should be E here's why
st(1) says two angle are 90` but the remaining two angles could by anything to make 180` like x+y=180`Not Sufficient
st(2) says one angle is twice the other, also Not Sufficient because we know only relationship of these angles but not have information about the other two angles;
Combined: two angles are 90 and yet the other two angles are in relationship 2:1. This can be anything to make 180 --> x+2y=180 depending on x (10,20,30...) we may have y (85, 80, 75...) hence Not Sufficient

Acc to you,
angle are
10 : 85
20:80 and
30 : 75

BUT

this doesn't satisfy 2nd statement which says that
B = 2C

only one thing satisfy this scenario and that is

120: 60

this is why i put C ans.