Discussion

Question:

These statements provide data that may help answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions. Accordingly, choose the appropriate option given below the questions.

Harry and Sunny have randomly picked 5 cards each from a pack of 10 cards, numbered from 1 to 10. Who has randomly picked the card with number 2 written on it?

Statement I: Sum of the numbers on the cards picked by Harry is 5 more than that of Sunny.
Statement II: One has exactly four even numbered cards while the other has exactly four odd numbered cards.

Explanation:

From statement I:
The sum of all the 10 cards = 55.
The sum of the numbers picked by Harry is 30 and that picked by Sunny is 25.
A sum of 30 can be obtained if the cards picked are 2, 4, 6, 8 and 10.
A sum of 25 can be obtained if the cards picked are 2, 3, 4, 7 and 9.
∴ We cannot determine who picked card number 2.

From statement II:
We cannot ascertain who picked card number 2.

From statements I and II together:
Sum of 4 odd cards and 1 even card will always be even

∴ Harry should get 4 odd cards and 1 even card such that his sum is 30.

Case 1:
Harry picks – 1, 3, 10, 7, 9 (Sum is 30)
Sunny picks – 2, 4, 6, 8, 5 (Sum is 25)
In this case Sunny picks card 2.

Case 2:
Harry picks – 1, 8, 5, 7, 9 (Sum is 30)
Sunny picks – 2, 4, 6, 3, 10 (Sum is 25)
In this case also Sunny picks card 2.

Case 3:
Harry picks – 6, 3, 5, 7, 9 (Sum is 30)
Sunny picks – 2, 4, 1, 8, 10 (Sum is 25)
In this case also Sunny picks card 2.

There will be no other possibility.

∴ Both statements together are required to answer the question.

Hence, option (d).

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