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all celebrate their birthdays today

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by sanju09 » Fri Mar 04, 2011 1:24 am
Joan, Kylie, Lillian, and Miriam all celebrate their birthdays today. Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women today?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 55
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by Anurag@Gurome » Fri Mar 04, 2011 1:42 am
sanju09 wrote:Joan, Kylie, Lillian, and Miriam all celebrate their birthdays today. Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women today?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 55
Say, age of Kylie is n years.
=> Age of Joan is (n - 2) years
=> Age of Lilian is (n - 3) years
=> Age of Miriam is (n - 1) years

Hence, total age = (4n - 6) years

Hence, the total age must be 6 less than an integer multiple of 4, i.e. 2 less than an integer multiple of 4. Only such option is 54.

Hence, the correct answer is D.
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