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Mr. Jones has eight children of different ages. On a family trip his

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New post 26 Mar 2019, 05:52
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

41% (02:21) correct 59% (02:51) wrong based on 32 sessions

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Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Which of the following is not the age of one of Mr. Jones's children?


(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

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Mr. Jones has eight children of different ages. On a family trip his  [#permalink]

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New post 09 Apr 2019, 14:15
Bunuel wrote:
Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Which of the following is not the age of one of Mr. Jones's children?


(A) 4
(B) 5
(C) 6
(D) 7
(E) 8


We can immediately eliminate A and C.
A: In this case we'd have the age 8 which is a multiple of 4.
C: In this case we'd have the ages 2 and 3 so the 4-digit number must be divisible by 6.

B, D and E are left. The 4-digit number must be a multiple of one of the below LCMs:
\(LCM : 1,2,3,4,5,6,7,9 = 1260\)
\(LCM : 1,2,3,4,5,6,8,9 = 360\)
\(LCM : 1,2,3,4,6,7,8,9 = 504\) --> \(504 * 11 = 5544\)

We only get a multiple satisfying the conditions without the 5 so Answer: B.
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Re: Mr. Jones has eight children of different ages. On a family trip his  [#permalink]

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New post 10 Apr 2019, 08:11
Last two digits happen to be my age,says the oldest child whose age is 9. Last two digits are 9. Divisibility rule of 5. Units digit should be 5 or 0. Hence number not divisible by 5. Ans B

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Re: Mr. Jones has eight children of different ages. On a family trip his   [#permalink] 10 Apr 2019, 08:11
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