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30 Dec 2021, 02:30
Kudos
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B
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Difficulty:
55%
(hard)
Question Stats:
38% (02:16) correct
63%
(02:22)
wrong
based on 8
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
30 Dec 2021, 04:10
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Bunuel
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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