# CAT LRDI Questions [Difficult] SET

Ms. Radiance went to a supermarket with her two bright kids Chotu and Motu. Chotu and Motu were always proud of identifying fruits of special kind. If a fruit was either an apple or an orange, Chotu would always identify it correctly and if a fruit was a mango or a guava or a watermelon, then Motu would always identify it correctly. in that supermarket, five baskets of fruits were there.

In each basket, there were twenty fruits, which included at least one fruit each of the above mentioned five types. Chotu identified the fruits in each of the five baskets and came up with the following details.

 Fruit Basket I Basket II Basket III Basket IV Basket V Apple 5 2 1 2 7 Orange 3 3 3 2 7 Mango 7 5 8 2 4 Guava 4 4 2 3 2 Watermelon 1 6 6 11 0 Total 20 20 20 20 20

Motu, then identified the fruits in every basket and came up with following details.

 Fruit Basket I Basket II Basket III Basket IV Basket V Apple 5 1 2 2 9 Orange 1 1 2 1 2 Mango 1 2 2 4 3 Guava 2 5 6 7 4 Watermelon 11 11 8 6 2 Total 20 20 20 20 20

Q1. Find the least possible number of watermelons in all the baskets put together.

1. 38
2. 28
3. 35
4. 31
5. 25

Q2. Which of the following statements is definitely false?

1. The number of mangoes in basket IV is 1.
2. The number of mangoes in basket IV is 3.
3. The number of apples in basket I is 3.
4. The number of watermelons in basket II is 9.
5. None of the above

Q3. If the number of guavas in basket IV is 6, then find the number of oranges in basket IV.

1. 2
2. 1
3. 3
4. Cannot be determined
5. Data inconsistent

Q4. With the given information, in how many of the five baskets can the number of mangoes be determined correctly?

1. 2
2. 1
3. 0
4. 3
5. More than3

A = {Apple, Orange}

B = {Mango, Guava, Watermelon}

Chotu identifies fruits of set A correctly and Motu identifies fruits of set B correctly.

Now, if we look at the given information.

Chotu: Identifies apples and oranges correctly i.e., if he looks at an apple, he identifies it as an apple and if he looks at an orange he will identify that as an orange and he cannot identify the other types of fruits properly i.e., if he looks at a guava, he may name it as an apple / orange / mango / guava / watermelon.

If Chotu says there are five apples in basket I, there are not more than five apples in basket I and similarly in basket I, there are not more than 3 oranges. But from table I, we cannot say anything definite about the other three varieties of fruits.

Similarly, from the second table, in basket I, Motu is saying there are 14 fruits of set B, the number of this set B fruits is at most 14 and thus that of set A fruits is at least 6.  Now by combining the information from Chotu and Motu.  In basket I, there are at least six and at most eight fruits of set A and at least twelve and at most fourteen fruits of set B.

Range of number of fruits

 Basket I II III IV V Fruits Min / Max Min / Max Min / Max Min / Max Min / Max A 6/8 2/5 4/4 3/4 11/14 B 12/14 15/18 '6/16 16/17 6/9

Q1. We have to make the number of watermelons as least as possible. For that, the number of total fruits of set 8 must be as least as possible and the other varieties of fruits of set B must be as maximum as possible. In basket I, there must be only 12 fruits of set B, there can be at most 2 guavas and 1 mango.

Therefore, there must be at least 9 watermelons. Similarly, in baskets II, III, IV and V there must be at least 8, 8, 5 and 1 watermelons respectively. Therefore, there are at least 31 watermelons on the whole. Choice (4)

Q2. In basket IV, the least possible number of mangoes = least possible number of fruits of set B — (maximum possible number of (guavas + watermelons))

= 16 — (6 + 7): 3. Hence, (1) is false.

Whereas the other three statements can be true. Choice (1)

Q3. Number of Guavas in Basket IV = 6.

Therefore, one extra fruit which is identified as Guava by Motu must be from set A.

Therefore,  total number of fruits of set A must be at least 1 + 2 + 1 i.e., 4.

From the above table, the number of fruits is set A must be exactly 4. Since Chotu identified only 4 fruits [2 apples and 2 oranges] of set A, there are only 2 oranges and 2 apples in basket IV. Choice (1)

Q4. As Motu [who identifies mangoes as mangoes] identified only 1 mango in basket I, and there is at least one fruit of each type in each box, there is only one mango In basket I.

From the above table, we can say that in basket III the total number of fruits in set A is 4 and that of in set B is 16.

As Motu identified 2 mangoes, 6 guavas and 8 watermelons, in basket III, which add upto 16, there will

be exactly 2 mangoes in basket Ill.

The number of mangoes in the other baskets cannot be found uniquely.