DILR practice set 4

DILR Practice Set – 19 Quiz

DILR Practice Set – 4

Refer to the data below and answer the ques ons that follow.

Smartkids playschool is planning to distribute chocolates among the children of the school on the occasion of the Founda on day of the school. The school administra on has bought three types of chocolates: Caramel, Dark Chocolate and Crunchy Bar. The prices of these three types of chocolates are Rs. 5, Rs. 10 and Rs. 20 respec vely. Each class has at least 10 students and each student gets exactly one chocolate. The distribu on of chocolates is to be done in such a way that each class must get chocolates worth Rs. 200.)

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1. The nursery class has fewer than 15 children and the children in the class get more Crunchy Bars chocolates than any other type of chocolates. In how many different ways can the chocolates be distributed to the children in the class?

Option A: 7
Option B: 8
Option C: 9
Option D: 10

Correct Answer: C (9) - Let 'a' be the number of Crunchy Bars, 'b' be the number of Dark Chocolates and 'c' be the number of Caramel chocolates. We have, 10 ≤ a + b + c < 15 and b, c < a Also, 20a + 10b + 5c = 200 or 4a + 2b + c = 40 Consider a + b + c = 10 and 4a + 2b + c = 40 Therefore, 3a + b = 30 3a + b = 30 ⇒ (a, b) = (10, 0), (9, 3), (8, 6), … and so on. But (a + b) cannot be greater than 10. So, the only possibility in this case is (a, b, c) = (10, 0, 0) Consider a + b + c = 11 and 4a + 2b + c = 40 Therefore, 3a + b = 29 3a + b = 29 ⇒ (a, b) = (9, 2), (8, 5), … and so on. But (a + b) cannot be greater than 11. So, the only possibility in this case is (a, b, c) = (9, 2, 0) Consider a + b + c = 12 and 4a + 2b + c = 40 Therefore, 3a + b = 28 3a + b = 28 ⇒ (a, b) = (9, 1), (8, 4), (7, 7)… and so on. But (a + b) cannot be greater than 12. So, the only possibility in this case is (a, b, c) = (9, 1, 2) and (8, 4, 0) Working on similar lines we get following: table

There are nine solutions. Hence, [3].

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2. The Junior-KG class has more than 15 children and the children in the class get more Crunchy Bars chocolates than any other type of chocolates. What is the number of Crunchy Bars chocolates distributed in the class? Enter your response (as an integer) using the virtual keyboard in the box provided below.

Let 'a' be the number of Crunchy Bars, 'b' be the number of Dark Chocolates and 'c' be the number of Caramel chocolates. Here, we have two following conditions: a + b + c > 15 20a + 10b + 5c = 200 or 4a + 2b + c = 40 and (a > b , c) ∴ 3a + b ≤ 24 For 3a + b = 24 ⇒ (a, b) = (8, 0), (7, 3), (6, 6) and so on. Therefore, (a, b, c) = (8, 0, 8), (7, 3, 6), (6, 6, 4) and so on. As a > b, c; the only valid solution in this case is (a, b, c) = (7, 3, 6) We can further check that there is no valid solution for a + b + c = 17, 18, …. Thus, there is only one possible solution: a = 7, b = 3, c = 6 Therefore, the required answer is 7

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3. The Senior-KG class has 20 children and the children in the class get more chocolates of type Dark Chocolate than any other type of chocolates. In how many different ways can the chocolates be distributed to the children in the class?

Option A: 4
Option B: 5
Option C: 6
Option D: 7

Correct Answer: A (4) - Let 'a' be the number of Crunchy Bars, 'b' be the number of Dark Chocolates and 'c' be the number of Caramel chocolates. Here, we have two following conditions: a + b + c = 20 and (b > a , c) ⇒ b ≥ 7 20a + 10b + 5c = 200 or 4a + 2b + c = 40 Therefore 3a + b = 20 ∴ (20 – b) is divisible by 3. As b ≥ 7, b = 8, 11, 14, 17, 20 Thus, the chocolates can be distributed in Senior-KG class as: 1. All 20 Dark Chocolates. 2. 17 Dark Chocolates, 1 Crunchy Bar and 2 Caramel chocolates. 3. 14 Dark Chocolates, 2 Crunchy Bars and 4 Caramel chocolates. 4. 11 Dark Chocolates, 3 Crunchy Bars and 6 Caramel chocolates. 5. 8 Dark Chocolates, 4 Crunchy Bars and 8 Caramel chocolates (it violates the condition that the class gets more Dark Chocolates than any other type chocolates). So there are total 4 ways. Hence, [1].

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4. Suppose the school has ten classes. The school authorities bought total 50 chocolates of the type 'Crunchy Bar' and a sufficient number of chocolates of all other types. What is the maximum number of classes that can get more Crunchy Bars chocolates than any other type of chocolates? Enter your response (as an integer) using the virtual keyboard in the box provided below.

To get the maximum number of classes which could have got more Crunchy Bars than any other chocolates type; the maximum number of classes must get 7 Crunchy Bars and 6 Dark Chocolates or the number of Dark Chocolates and Caramel chocolates can vary as per given in the solution of the first question of the set. Since total number of Crunchy Bars is 50, the maximum number of classes which can get more Crunchy Bars than any other chocolates type = 50/7 = 7.17; thus 7 classes. Therefore, the required answer is 7.

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