Jane started baby-sitting when she was 18 years old.

Question

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?

(a) 20
(b) 21
(c) 22
(d) 23
(e) 24

A. 20
B. 21
C. 22
D. 23
E. 24

Bunuel · Accepted Answer

D (23) is not a trap answer, it's a correct answer.

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? 
A. 20
B. 21
C. 22
D. 23
E. 24

Check two extreme cases:
Jane = 18, child = 9, years ago = 32-18 = 14 --> child's age now = 9+14 = 23;
Jane = 22, child = 11, years ago = 32-22 = 10 --> child's age now = 11+10 = 21.

Answer: D.

fluke · Answer

Jane's Age Then    Oldest Child's Age Then    Years Elapsed so far    The same Child's Age now   
  18  9  14  9+14=23  
  19  9.5  13  9.5+13=22.5  
  20  10  12  10+12=22  
  21  10.5  11  10.5+11=21.5  
  22  11  10  11+10=21

Now,

The current age of the oldest person among the people she ever baby-sat=23
The current age of the oldest person she ever baby-sat=21

Ans: "B"

subhashghosh · Answer

When she sat initially Jane's age = 18, and the child's max age = 9

10 yrs back, she was 22 yrs old, so the child's age max age possible = 22/2 = 11

So the child would be now 22 + 10 = 21 yrs old

Answer - B

kamalkicks · Answer

first: read question carefully 
 the trap is between answer 23 and 21 , and trap is 
 
so simply she could have baby sat oldest person at 22 years of age  (32-10)

=> 22/2 = 11

10 years hence  11 +10 = 21 (current age of person)
hence answer is B

sudhir18n · Answer

As far as I remember think the OA has to be D.
when Jane was 18 = the child was 9 yrs old
after 14 years 9+14 = 23 ..
the question is asking oldest person (now) , for whom jane have baby sat.
The question isn't asking the oldest person ( at the point of baby -sitting), for whom Jane baby sat. In this case it would have been 21(11+10)

PS: Attached the MGMAT answer

MHIKER · Answer

But the Question is asking for  whom Jane could have baby-sat?

IEsailor · Answer

I got D too.
When Jane was 18 yrs old, the child would have been no more than 9 yrs old.
Now after 14 yrs
Jane is 18+14 = 32
Child is 9 + 14 = 23

Spidy001 · Answer

I agree with @sudhir18n 's reply.

when jane is 18, the oldest she could have baby sat = 9 yr old

as jane is 32 . i.e after 14 years that oldest baby would be 9+14 = 23

Answer is 23 D.

there is another post out there where they are asking for youngest .

if the question is asking for youngest then answer is 21 . if its asking for oldest then it got to be 23.

Old post:
Jane started baby-sitting when she was 18 years old, however, she only baby-sat children that were, at most, half her age. Jane is currently 32 years old, and she stopped baby-sitting ten years ago. What is the current age of the youngest child that Jane could have baby-sat?

amit2k9 · Answer

at 18, max age of child = 9.
at 22,max age of child = 11.

thus adding 10 years to this = 21 yrs.

GMATD11 · Answer

I got the answer right but
Jane started baby sitting at 18
max age of child at that time will be 9
Jane left baby sitting at the age of 22
At that time age of child will be 11
As current age of jane is 32
Current age of child will be 11+10=21

I want to discuss the trap answer 23

Jane started baby sitting at 18
max age of child at that time will be 9
As current age of jane is 32
Current age of child will be 9+14=23

Take away we need to imply the statement as mentioned in the Word Problem.

M i correct...
Basically i also want to discuss the strategy for solving Word Problems
Generally I write as i read any implied statement and following this strategy since childhood & comfortable with it.But my friend told that your strategy is wrong.

Pls comment

GMATD11 · Answer

Thanks Bunuel

Whats the best strategy for solving Word Problems.

Bunuel · Answer

It really depends on the question itself, there is no general "best strategy". Check this: word-problems-made-easy-87346.html, it might helps in word translation.

LalaB · Answer

if when she was 18, a kid was 9 (half of her age), then at the age 22 (32-10) that kid will be 11 years old (22*9)/18

11+10=21

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

DS questions on Arithmetic: search.php?search_id=tag&tag_id=30
PS questions on Arithmetic: search.php?search_id=tag&tag_id=51

EMPOWERgmatRichC · Answer

Hi melissamartin,

This question comes with a minor "twist" - you have to account for the number of years SINCE Jane baby-sat any of those children.

We're told that that the children were no more than HALF of Jane's age at the time AND we have to account for the change in time since Jane baby-sat each child.

When Jane was....
18....the oldest a child could have been was 9. Since that was 14 years ago, the child would now be 9+14 = 23

20....the oldest a child could have been was 10, but that was 12 years ago, so the child would now be 10+12 = 22

22....the oldest a child could have been was 11, but that was 10 years ago, so the child would now be 11+10 = 21

This oldest that any of those children could be NOW is 23.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

muthappashivani · Answer

The question clearly says that the age of the child is no more than half of Janes age at the time of baby sitting. So  The  age of 18 years the oldest child whom she baby sat was < 9 years so the maximum age is 8 and the maximum age of the oldest child when she baby sat  The  age of 22 is < 11 years. Where am I going wrong in my understanding of the problem??

Bunuel · Answer

No no more than half her age does not mean less than half her age.

The correct relationship is  \{baby's \ age\} \leq \frac{\{Jane's \ age\}}{2} .

hellosanthosh2k2 · Answer

i think wording of the question matters very much.

Had the question been, what is current age of oldest child, she could have baby-sat, then answer is 21. (Even i fell for this)
but actual question is , what is current age of oldest person, she could have baby-sat, then answer is 23 (as shown above)

Need to have my eyes wide open

Jane121393 · Answer

Hi,  Bunuel , please help me review my solution. 
I set the equation between the age of the child (C) and the age of Jane (J) at the time she began baby - sat the child is that:
C ≤ 1/2 J => C max = 1/2 J
C (current) = 1/2 J + 32 - J = 32 - 1/2 J
C (current) max if (32 - 1/2 J) max => J min.
We know 18 ≤ J ≤ 22 then J min = 18 => C (current) max = 32-9=23

Jane started baby-sitting when she was 18 years old.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Jane's Age Then	Oldest Child's Age Then	Years Elapsed so far	The same Child's Age now
18	9	14	9+14=23
19	9.5	13	9.5+13=22.5
20	10	12	10+12=22
21	10.5	11	10.5+11=21.5
22	11	10	11+10=21

GMAT Problem Solving (PS) Questions

Jane started baby-sitting when she was 18 years old.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards