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ddm: Master | Next Rank: 500 Posts; Posts: 162; Joined: Mon Jul 28, 2008 8:33 pm; Location: San Jose,CA; Thanked: 1 times

by ddm » Mon Aug 04, 2008 2:20 pm

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Source: Beat The GMAT — Problem Solving | Mon Aug 04, 2008 2:20 pm

singhr10: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Fri Mar 28, 2008 3:57 pm

by singhr10 » Mon Aug 04, 2008 6:18 pm

we have the following equations.
J = K-2
K= 3+L
M = 1+J

J+K+L+M = SUM OF AGE

K-2 +K+L+1+J
K-2 +K-2+3+L+J= SUM
K-2+K-2+K+K-2 = SUM (SUB FOR J AND K)
4K-6 =SUM

FROM THE BELOW OPTIONS
4K = 6+54 (SINCE THIS OPTION WILL ONLY BE DIVISIBLE BY 4

K= 60/4 = 15
Hence ans is 54....

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JohnRapp: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Thu Sep 15, 2011 9:41 am

by JohnRapp » Mon Nov 21, 2011 6:45 pm

ddm 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

First set up the relationships into equations:
J=K+2
K=L+3
M=J+1

Given these relationships, I ordered them from youngest to oldest with the difference in between.
L +3 K +2 J +1 M +0

The sum of the differences in relationships = 6.

The only age divisible by 6 is [spoiler]D (54)[/spoiler]

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Nov 21, 2011 9:28 pm

ddm 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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chaitanyabhansali: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sun Apr 17, 2011 7:16 amFollowed by: 1 member

by chaitanyabhansali » Tue Nov 22, 2011 10:37 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

Answer:

Let lillian's age be x today.
then, joan's age = x+1, kylie's age = x+3 and Miriam's age = x+2.

combined age = x+x+1+x+2+x+3 = 4x+6

Put the expression equal to given options one by one.

Only option 'D' i.e 54 satisfies the equation i.e when x comes out to be an integer.

4x+6 = 54
=> 4x = 48
=> x = 12

IMO: D

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Nov 22, 2011 11:50 am

ddm 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

We can guess and check VERY quickly.
Given the answer choices, the average age must be around 52/4 = 13.

Let J = 13.
Then:
K = J+2 = 15.
L = K-3 = 12.
M = J+1 = 14.
Sum = 13+15+12+14 = 54.

The correct answer is D.

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tuanquang269: Master | Next Rank: 500 Posts; Posts: 296; Joined: Sun May 29, 2011 5:10 amFollowed by: 5 members; Location: Vietnam; Thanked: 10 times

by tuanquang269 » Tue Nov 22, 2011 8:26 pm

+ 1 for D

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