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655-705 (Hard)|   Geometry|      
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Bunuel
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Joy has 30 thin rods, one each of every integer length from 1 cm throu 30 Dec 2021, 02:30
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Difficulty:

55% (hard)

Question Stats:

38% (02:16) correct 63% (02:22) wrong based on 8 sessions

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Joy has 30 thin rods, one each of every integer length from 1 cm through 30cm. She places the rods with lengths 3 cm, 7 cm, and 15 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?

(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
 
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B
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Joy has 30 thin rods, one each of every integer length from 1 cm throu 30 Dec 2021, 04:10
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Bunuel
Joy has 30 thin rods, one each of every integer length from 1 cm through 30cm. She places the rods with lengths 3 cm, 7 cm, and 15 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?

(A) 16

(B) 17

(C) 18

(D) 19

(E) 20

 
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In a triangle sum of two sides is always greater than the third side.
So, value of BD has to be less than 10 |7+3
Let's take the max value possible 9.
Now in triangle BDC max length of CD possible is <15+9
i.e 23
So there are 23 values that can be the fourth side but 3 numbers are already taken : 3 , 7 and 15 so we are left with 20 numbers.
E is the answer.­
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Bunuel
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