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by \'manpreet singh » Thu Aug 22, 2013 11:38 pm
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

I want to know a faster approach to solve such a problem.?
Whats the steps that i need to start with such a age problem involving 4 variables.
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by [email protected] » Thu Aug 22, 2013 11:48 pm
Hi manpreet singh,

The first part of this question requires translating sentences into formulas:

J + 2 = K
L + 3 = K
J + 1 = M

Even if you translated these formulas differently, you still have a relationship among the 4 variables that needs to be discovered. TEST the variables to figure out the relationship:

If K = 10, then
J = 8
L = 7
M = 9

Now we know that the 4 values are consecutive.

To solve, you can either use "brute-force" (since the answers are small) or algebra:

Brute-Force:
11 + 12 + 13 + 14 = 50 NOT ENOUGH BASED ON THE ANSWERS
12 + 13 + 14 + 15 = 54 WINNER

Algebra:
Call the youngest person X
X + (X+1) + (X+2) + (X+3) = 4X + 6
If X = 11, total = 50 NOT ENOUGH BASED ON THE ANSWERS
If X = 12, total = 54 WINNER

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by GMATGuruNY » Fri Aug 23, 2013 2:24 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?

· 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 Kylie, K=15.
Since Kylie 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 faraz_jeddah » Fri Aug 23, 2013 4:59 am
If you are not sure what values to Test, Heres my approach. Let me know what you think of it.

What we need to find is
Total (T) = J+K+L+M

Given:
J = K - 2 _____________ (1)
K = L + 3 _____________ (2)
M = J + 1 _____________ (3)

Adding (1) (2) (3)

J + K + M = J + L + K +2

==> M-L = 2
OR M = L+2 ____________ (4)

Also,
From (1) and (2)
J = L + 1 _______________ (5)

Now back to the question

T = J + K + L + M

Substitute (4)

T = J + K + L + L + 2
= J + K + 2L + 2

Substitute (2) and (5)

= L + 1 + L + 3 + 2L + 2
T = 4L + 6

This shows you that that total age should be a multiple of 4 plus 6

Of the answer choices only 54 fits i,e 4(12) + 6

Answer is D
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by ganeshrkamath » Fri Aug 23, 2013 5:32 am
'manpreet singh 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

I want to know a faster approach to solve such a problem.?
Whats the steps that i need to start with such a age problem involving 4 variables.
Let J,K,L,M represent the ages of Joan, Kylie, Lillian, Miriam respectively.
J = K-2
K = L+3
M = J+1
L seems to be the youngest.
So write everyone's age in terms of L.
K = L+3
J = L+1
M = L+2
So sum of ages = L + L+3 + L+1 + L+2
= 4L + 6
So sum is an even number.
Eliminate A,C,E.
Option B = 52 = 4L + 6
L = 46/4 which is not an integer (all celebrate their birthday today. So every age should be an integer)
Eliminate B.

Choose D

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by Brent@GMATPrepNow » Fri Aug 23, 2013 5:33 am
manpreet singh 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 solve the question using 1 variable.

Let's let Joan's age = J (aside: we could assign the initial variable to someone else's age, but at first glance Joan appears to be one of the younger people, and it's often easier to assign the first variable to the smallest/smaller value)

Joan is 2 years younger than Kylie: So, Kylie's age = J+2
Kylie is 3 years older than Lillian: In other words, Lillian's age is 3 years less than Kylie's age. So, Lillian's age = (J+2)-3 = J-1
Miriam is one year older than Joan: So, Miriam's age = J+1

The sum of all 4 ages = J + (J+2) + (J-1) + (J+1) = 4J+2

IMPORTANT: The sum of the ages is 2 more than some multiple of 4.
Scan the answer choices.
52 is a multiple of 4.
So, 54 is 2 more than some multiple of 4
Answer = D

Cheers,
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by ani781 » Sat Aug 24, 2013 6:49 am
I approached this problem in the following way :
Let L = x ;
=> K = x+3 ; J = (x+3)-2 ; M = x+2.

So, adding them, 4x + 6 = 2(2x+3) is the sum.

So we can eliminate 51, 53 & 55.

52/2 = 26 , not possible ( as 2x+3 is Odd). So correct answer is 54.
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