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Mgmat CAT PS question

by G- Unit30 » Sun Mar 03, 2013 7:14 pm
Hi,
I got this question on a MGMAT CAT exam. I don't really understand the explanation they provided to the problem...Can anyone help shed some light on this? Or perhaps an alternate method to solve?

Thanks

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




Anwser:

D

t may be easiest to represent the ages of Joan, Kylie, Lillian and Miriam (J, K, L and M) on a number line. If we do so, we will see that the ages represent consecutive integers as shown in the diagram.



Since the ages are consecutive integers, they can all be expressed in terms of L: L, L + 1,
L + 2, L + 3. The sum of the four ages then would be 4L + 6. Since L must be an integer (it's Lillian's age), the expression 4L + 6 describes a number that is two more than a multiple of 4:

4L + 6 = (4L + 4) + 2
[4L + 4 describes a multiple of 4, since it can be factored into 4(L + 1) or 4 * an integer.]

54 is the only number in the answer choices that is two more than a multiple of 4 (namely, 52).

The correct answer is D.
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by GMATGuruNY » Sun Mar 03, 2013 8:06 pm
GmatKiss 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?

· 51
· 52
· 53
· 54
· 55
The ages are all close together.
The answer choices imply that the sum of the 4 ages is between 51 and 55, inclusive.
Since 52/4 = 13, the average age must be around 13.

Let J=13.
Since Joan is 2 years younger than Kyle, K=15.
Since Kyle is 3 years older than Lillian, L=12.
Since Miriam is 1 year older than Joan, M=14.
Sum = 13+15+12+14 = 54.

The correct answer is D.
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by G- Unit30 » Sun Mar 03, 2013 8:42 pm
Thank you so much, that makes much more sense to me
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by Anurag@Gurome » Sun Mar 03, 2013 9:03 pm
G- Unit30 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?
Here is the explanation for official answer...

Let assume the ages of Joan, Kylie, Lillian, and Miriam are J, K, L, and M, respectively.
Hence, J = (K - 2), K = (L + 3), M = (J + 1)
Expressing them all with respect to L only,
  • K = (L + 3), J = (L + 1), and M = (L + 2)
Hence, combined age of all four women = (L + 3) + (L + 2) + (L + 1) + L = (4L + 6) = (4L + 4) + 2 = (Some multiple of 4) + 2

Hence, the answer must be 2 more than a multiple of 4.
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by subhakam » Wed Mar 13, 2013 6:06 pm
Anurag@Gurome wrote:
G- Unit30 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?
Here is the explanation for official answer...

Let assume the ages of Joan, Kylie, Lillian, and Miriam are J, K, L, and M, respectively.
Hence, J = (K - 2), K = (L + 3), M = (J + 1)
Expressing them all with respect to L only,
  • K = (L + 3), J = (L + 1), and M = (L + 2)
Hence, combined age of all four women = (L + 3) + (L + 2) + (L + 1) + L = (4L + 6) = (4L + 4) + 2 = (Some multiple of 4) + 2

Hence, the answer must be 2 more than a multiple of 4.
THANK YOU that helps (in other words- (4L + 6)= 2(2L+3) only time we get an integer value for L is when it is 54
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