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Word Problem - Ages question

Expert replies
by aaggar7 » Fri Mar 08, 2013 3:26 am
Hi,I have tried two approach for the below question and I am getting different answers.
Please suggest which one is correct and where I am going wrong on the other approach

Jane started baby-sitting when she was 18 years old. Whenever she baby-sat
for a child, that child was no more than half her age at the time. Jane is currently
32 years old, and she stopped baby-sitting 10 years ago. What is the
current age of the oldest person for whom Jane could have baby-sat?


Jane's age = J
Child age = C

Approach 1
-----------
Let J=18 at start of babysitting
C's maximum age at that time=9

Jane's has stopped babysitting at 22,so the max age of C at that time will be 11.
J's current age = 32
After 10 yrs the C's age will be 11+10=22

Answer = 22

Approach 2
-----------
J started baby sitting started at 18 and current age is 32.Diff is (32-18)= 14
Age of C at start = 9,current age = 9 + 14 = 23

Answer = 23
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Source: — Problem Solving |

by Anurag@Gurome » Fri Mar 08, 2013 3:48 am
aaggar7 wrote:Approach 1
-----------
Let J=18 at start of babysitting
C's maximum age at that time=9

Jane's has stopped babysitting at 22,so the max age of C at that time will be 11.
J's current age = 32
After 10 yrs the C's age will be 11+10=22

Answer = 22

Approach 2
-----------
J started baby sitting started at 18 and current age is 32.Diff is (32-18)= 14
Age of C at start = 9,current age = 9 + 14 = 23

Answer = 23
These are not two approaches, these are calculating the maximum age of the child Jane could have baby-sit at two different points in the time, i.e. when she started baby-sitting and stopped it.

Obviously the greater of the two will be the potential correct answer.

A proper mathematical approach to solve this problem will be as follows...
For example, let us assume at some point of time in the past Jane's age was J and the age of the child she was baby-sitting at that time was C.

According to the question, maximum value of C is J/2.

Now, Jane's current age is 32.
Hence, Jane was J years old (32 - J) years ago.
Hence, the child's current age is C + (32 - J) years.

We need to find the maximum possible value of C + (32 - J)
Hence, we need to maximize C and minimize J.
As maximum value of C depends on J, we'll minimize J first.
Minimum possible value of J is 18 --> Maximum possible value of C is 18/2 = 9

Hence, maximum possible value of C + (32 - J) = 9 + (32 - 18) = 9 + 14 = 23
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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by apoorva.rattan » Fri Mar 08, 2013 4:16 pm
I am a little confused. Is this the greatest age of a person she baby-say OR current age of the oldest person she baby-sat ?

Jane stopped baby-sitting at age 22 (Current age 32 - 10 years) . So, the oldest person Jane could have baby-sat would have been 11.
At age 18, she could have baby-sat a person with age 9 years.

Therefore, shouldn't the current age of the oldest person she could have baby-sat be 11 + 10 = 21 years.

@Anurag: Thoughts ?
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