Data Sufficiency - Card picked with number 2

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.

Accepted Answer

D. Total sum of cards 1 to 10 = 55. From Statement I, $H + S = 55$ and $H - S = 5 \implies H = 30, S = 25$. There are multiple combinations to sum to 25 or 30, so Statement I alone is insufficient. From Statement II, one has 4 evens and 1 odd, and the other has 4 odds and 1 even. Insufficient alone. Combining both: sum of 5 evens is $2+4+6+8+10 = 30$, sum of 5 odds is $1+3+5+7+9 = 25$. To get sums 30 and 25 with 4 evens/1 odd and 4 odds/1 even, we swap one even and one odd between the sets such that their sum difference is maintained. Since card 2 must be in the set with 4 evens, card 2 stays with the person who has 4 even cards (Harry). Thus, both statements together are required. Hence, option D is correct.

Answer

Statement I alone is sufficient to answer.

Answer

Statement II alone is sufficient to answer.

Answer

Either of the statement is sufficient to answer.

Answer

Both statements are required to answer.

Data Sufficiency - Card picked with number 2

Explanation

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