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Facebook Friends Party Invites

XAT 2013 · Quantitative Ability & Data Interpretation · Hard · Set Theory

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Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that at least two of Sara's friends are connected with each other. On her birthday, Sara decides to invite her friends and the friends of her friends. How many people did she invite for her birthday party?

  1. A.

    ≥105\ge 105

  2. B.

    ≤123\le 123

  3. C.

    <125< 125

  4. D.

    ≥100 and ≤125\ge 100 \text{ and } \le 125

  5. E.

    ≥105 and ≤123\ge 105 \text{ and } \le 123

Answer

B

Explanation

Each of the 5 friends has 25 friends (including Sara, so 24 other friends). Without connections among friends, total = 5+5×24=1255 + 5 \times 24 = 125. Since at least two friends A and B are connected to each other, A is counted as B's friend and B as A's friend, reducing the maximum possible count by at least 2. Thus, the total invites ≤123\le 123.

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