Several people are sitting around a round table playing...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Several people are sitting around a round table playing...

by BTGmoderatorLU » Wed Mar 21, 2018 3:13 pm

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Several people are sitting around a round table playing a card game with a deck of 50 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?

A. 4
B. 5
C. 7
D. 11
E. 13

The OA is C.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Wed Mar 21, 2018 3:13 pm

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by [email protected] » Wed Mar 21, 2018 5:18 pm

Hi LUANDATO,

We're told that several people are sitting around a round table playing a card game with a deck of 50 cards, each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the FIRST card of the deck AND the LAST card of the deck, which of the following COULD be the total number of people sitting at the table. This question can be solved by TESTing THE ANSWERS.

This question is a 'remainder' question, although you might not realize it at first. If you've ever played a card game in which each player is dealt the SAME number of cards, you know that whoever is dealt the first card will not be the same person who is dealt the last card. With each rotation around the table, each player will receive 1 card. The ONLY way that the first person would receive the last card is if there was one 'extra' card that ended up being dealt to that person as the cards were dealt clockwise. Thus, we're looking for a number that will divide into 50 and leave a remainder of 1.

Answer A: 4 players.... 50/4 = 12 r2. The first person would NOT receive the last card (the 2nd player would)
Answer B: 5 players.... 50/5 = 10 r0. The first person would NOT receive the last card (the 5th player would)
Answer C: 7 players.... 50/7 = 7 r1. The first person WOULD receive the last card.

Final Answer: C

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by GMATGuruNY » Thu Mar 22, 2018 2:31 am

LUANDATO wrote:Several people are sitting around a round table playing a card game with a deck of 50 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?

A. 4
B. 5
C. 7
D. 11
E. 13

Algebraic approach:

Let p = the number of people at the table.
After the p people at the table each receive c cards -- for a total of pc cards -- the 1 remaining card is given to Martin, with the result that he receives the last card.
Since the deck is composed of 50 cards, we get:
pc + 1 = 50
pc = 49.
The resulting equation indicates that p must be a FACTOR OF 49.

The correct answer is C.

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by Scott@TargetTestPrep » Fri May 24, 2019 3:09 pm

BTGmoderatorLU wrote:Several people are sitting around a round table playing a card game with a deck of 50 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?

A. 4
B. 5
C. 7
D. 11
E. 13

The OA is C.

n = the number of people at the table, so we have 50/n = q R 1 for some integer q. With this in mind, let's analyze each answer choice.

A) 50/4 = 12 R 2 (This is not the correct choice.)

B) 50/5 = 10 R 0 (This is not the correct choice.)

C) 50/7 = 7 R 1 (This is the correct choice.)

Alternate Solution:

If there are n people at the table, then Martin is dealt the 1st, n + 1st, 2n + 1st etc. cards. Thus, 50 = kn + 1 for some k; or, equivalently, 49 = kn for some k. In other words, the number of people on the table is a factor of 49. Examining the answer choices, we see that only 7 is a factor of 49; therefore, that's the only possible value for n.

Answer: C

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