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Hulk and Thanos each received Easter baskets containing different type

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Hulk and Thanos each received Easter baskets containing different type  [#permalink]

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New post 08 Jan 2019, 22:30
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

52% (02:47) correct 48% (03:12) wrong based on 27 sessions

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Hulk and Thanos each received Easter baskets containing different types of candy. Hulk's basket contained sour candy and chocolate candy in a ratio of 4 to 3 and sour candy to sweet candy in a ratio of 5 to 2. Thanos's basket contained sour candy to chocolate candy in a ratio of 6 to 1. If the total number of sour candies in both baskets was between 40 and 50 pieces, which of the following are possible numbers of chocolate candies in Hulk's basket?


I. 15
II. 25
III. 30


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

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Re: Hulk and Thanos each received Easter baskets containing different type  [#permalink]

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New post 09 Jan 2019, 07:05
1
Abhi077 wrote:
Hulk and Thanos each received Easter baskets containing different types of candy. Hulk's basket contained sour candy and chocolate candy in a ratio of 4 to 3 and sour candy to sweet candy in a ratio of 5 to 2. Thanos's basket contained sour candy to chocolate candy in a ratio of 6 to 1. If the total number of sour candies in both baskets was between 40 and 50 pieces, which of the following are possible numbers of chocolate candies in Hulk's basket?


I. 15
II. 25
III. 30


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


Hulk's candies
sour candy : chocolate candy = 4 : 3 and sour candy : sweet candy = 5 : 2...
As we have sour candy in terms of 4 and 5 too, the least number of sour candies will be LCM of 4 and 5, thus 20..
so sour candy : chocolate candy = 5*4 : 5*3 = 20 : 15, and sour candy : sweet candy = 4*5 : 4*2 = 20 : 8...
Therefore, sour candy : chocolate candy : sweet candy = 20 : 15 : 8 ..
Let the common term in ratio be a, so number of sour candy, chocolate candy and sweet candy are 20a, 15a and 8a ..

Thanos' candies
sour candy : chocolate candy = 6 : 1
Let the common term in ratio be b, so number of sour candy and chocolate candy are 6b and b ..

Numbers of combined sour candies is between 40 and 50..
so \(40<20a+6b<50\), so possible values of a are 1 and 2
Now, the numbers of chocolate candies of Hulk is 15a, so either 15*1 or 15*2, that is 15 or 30

Thus, C is the answer.
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Re: Hulk and Thanos each received Easter baskets containing different type   [#permalink] 09 Jan 2019, 07:05
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Hulk and Thanos each received Easter baskets containing different type

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