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# Joy has 30 thin rods, one each of every integer length from 1 cm throu

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Senior Manager
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Joined: 02 Nov 2018
Posts: 280
Joy has 30 thin rods, one each of every integer length from 1 cm throu  [#permalink]

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13 Mar 2019, 11:11
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Difficulty:

65% (hard)

Question Stats:

48% (02:41) correct 52% (02:12) wrong based on 25 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
Senior Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 280
Re: Joy has 30 thin rods, one each of every integer length from 1 cm throu  [#permalink]

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13 Mar 2019, 22:48
1
The quadrilateral cannot be a straight line. Thus, the fourth side must be longer than 15 - (3 + 7) = 5 and shorter than 15 + 3 + 7 = 25. This means Joy can use the 19 possible integer rod lengths that fall into [6, 24]. However, she has already used the rods of length 7 cm and 15 cm
so the answer is 19 - 2 = 17
Option B
Manager
Joined: 23 Aug 2017
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Schools: ISB '21 (A)
Re: Joy has 30 thin rods, one each of every integer length from 1 cm throu  [#permalink]

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14 Mar 2019, 00:12
Whats the property to be used here?
Intern
Joined: 12 Feb 2018
Posts: 12
Re: Joy has 30 thin rods, one each of every integer length from 1 cm throu  [#permalink]

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24 Mar 2019, 07:11
1
Sum of three sides > 4th side. Therefore, 7+3+x>15 --> x>5 .........also........... 7+3+15>x --> x<25
5 < x < 25 so x -> [6,24]. As 7 and 15 are already used ---> 19 - 2 =17
Re: Joy has 30 thin rods, one each of every integer length from 1 cm throu   [#permalink] 24 Mar 2019, 07:11
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# Joy has 30 thin rods, one each of every integer length from 1 cm throu

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