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Bunuel
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IMO E

b+d can take all the 3 values .
Minimum val is 232
Max is 298.
All the 3 comes in range so E

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Explanation:
30<a<64
Highest value for angle a is 63
Lowest value for angle a is 31
as, a=c & a+b+c+d = 360
taking a=63
Angle b+d = 360-(2x63)= 234 (Lowest Value)
taking a=31
Angle b+d = 360-62= 298 (Highest Value)
So, Value of b+d lies in the range of from 234 to 298

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Image
If 30 < a < 64, which of the following could be the value of b + d ?

I. 232
II. 247
III. 289

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

30 < a < 64 and 30 < c < 64 since a = c
Adding,
60 < a + c < 128
60 < 360 - (b + d) < 128 [a +b + c + d = 360]
- 60 > b + d - 360 > -128
- 60 + 360 > b + d > 360 - 128
300 > b + d > 232

Only II and III satisfy.

Answer D.
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IMO D

If 30 < a < 64, which of the following could be the value of b + d ?

From Figure, b= 180- a & d=180-a
So, b+d= 360-2a = 360- [60 < 2a < 128 ]
232 < b+d < 300

option II & III satisfy
II. 247
III. 289


D. II and III only
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a, b,c,d are four angles, where a, c and b d and vertically opposite angles hence equal. Now a+B = 180 and 30<a<64 , hence the value of B will be 116<B<150, therefore B+d will be between 232-300 (B=d: vertically opposite angles)
Hence "D" should be the answer

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Quote:
If 30 < a < 64, which of the following could be the value of b + d ?

I. 232
II. 247
III. 289

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

a and c are vertical angles, so a=c. Therefore 60<a+c<128. Conversely, 300>b+d>232

II and III are both within the range but I is outside of the range and is eliminated.

ANSWER: D
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Quote:
If 30 < a < 64, which of the following could be the value of b + d ?

I. 232
II. 247
III. 289

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

a=c,b=d
30<a<64
60<a+c<128
360-128<b+d<360-60
232<b+d<300
Ans (D)
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Bunuel

Competition Mode Question




If 30 < a < 64, which of the following could be the value of b + d ?

I. 232
II. 247
III. 289

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Attachment:
1.jpg

total angle = 360
min a=c=31
max a=c=63

min a+c = 62
max a+c = 126

360-126 <= b+d <= 360-62
234 <= b+d <=298

Ans D
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a + b + c + d = 360

We know the value of b + d so,

a+c = 360 - 232 = 128
We know that a=c

2a = 128
a = 64
Cannot be possible as a is less than 64.


a+c = 360 - 247 = 113
a = 56.5
This value is possible

a+c = 360 - 289 = 71
a = 35.5
This value is also possible

Hence statment 2 and 3 are sufficient. D

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