A family has a child every j years. The oldest child is t years old.

Question

A family has a child every j years. The oldest child is t years old. If they have a child 2 years from now, how many children will they have in total.

A. t/j +1

B. 2/j +1

C. (t+2)/j -1

D. (t+2)/j

E. (t+2)/j +1

chetan2u · Accepted Answer

Hi  Mo2men 
The question means that a kid is born every j years and after two years another kid will be born, so TEO years from now, the age of the eldest will be a multiple of j, so let that be X...
So jX=t+2.....X=(t+2)/j..
But the first kid was right at start that is 0, which has to be added back, so the number of kids will be X+1= \frac{t+2}{j} +1

You could take a value say after every 5 years a child is born so J=5..
Let the eldest be 18 year old so t=18...
After 2 years, the eldest will be 18+2=20..
So after every 5 year means 20/5 or 4, but we have to add one more as this does not include the eldest as he is born at 0..
C--5years--C--10years--C--15years--C--20years--C.....Total 5..
Look for the choice that gives you 5 as the answer..
E.(18+2)/5+1=(20/5)+1=4+1=5

E

Archit3110 · Answer

i used plugin technique
let t=18 and j=5
oldest child after 2 years = 20 years old
so we have 20/5 = 4 children + 0 years old ; 5 total 
IMO E option e gives 5 children if 0 is also considered

Lampard42 · Answer

Assume t=14, J=8 and in next 2 years they will have three kids including the oldest+ 8 year old + just born
Sub in options A=14/8+1; B=2/8+1; C=(14+2)/8-1=1; D=(14+2)/8=2; E= (14+2)/8+1=3 So IMO E as they ask for number of kids in 2 years.

CareerGeek · Answer

The series is in AP,
With age of oldest child = last term = t 
Age of next new child = 1st term = -2
Common difference = j

Use Last term of AP,
t = -2 + (n - 1)j
--> t + 2 = (n - 1)j
--> n - 1 = (t + 2)/j
--> n = (t + 2)/j + 1

IMO Option E

Pls Hit Kudos if you like the solution

Mo2men · Answer

IanStewart   ArvindCrackVerbal   pushpitkc   chetan2u

Can you please share your thoughts in this question?

Thanks in advance

CareerGeek · Answer

Hi  chetan2u

Let’s say the eldest kid is 3 years old
And j = 5

(t + 2)/j = 5/5 = 1

As of today there is only kid right?

Isn’t the option D ?

Posted from my mobile device

chetan2u · Answer

Answer would depend on the wordings..

In the present scenario, it is..

If they have a child 2 years from now, how many children will they have in total.
The WILL tells you we are talking of future when the kid is born after two years.
So E is the answer

But say the wordings were..

If they WILL have a child 2 years from now, how many children DO they have in total.
We are talking of now and D will be the answer

rxb266 · Answer

According to the question : A family has a child every j years.  Let's assume J to be 4...

The oldest child is t years old.  Lets assume t to be 10.

Therefore the no. of the children they have :  (3 children in total)  10 yrs, 6 yrs and 2 yrs
after 2 years, no. of children they will have :  (4 children in total)  12 yrs, 8 yrs, 4 yrs and 0 yrs

In option C, when we substitute the value of  T =10 and J =4  we get 4 as the answer. Hence,  Option C is correct !!

CareerGeek · Answer

You meant to say E is the answer ?

Posted from my mobile device

Mo2men · Answer

Thanks  chetan2u  for you help but I'm not able to understand the example above on the time line.

When the oldest kid appear and where the 2 years start related to her?

You elaboration more is highly required

Thanks in asdvance

chetan2u · Answer

(oldest child born and the time is 0 years)  ---5 years pass--( second child is born and time is 5 years)  ---5 years pass--( third child is born and time is 10 years)  ---5 years pass--( fourth child is born and time is 15 years)   --3 years--(PRESENT time, Oldest is 15+3 or t)   --2 years--(Fifth child is born and time is 18+2 or 20 or t+2)

urshi · Answer

T - total years under consideration.
T+2 - multiple of j (let the number of kids the couple will have be n)

T+2 = nj
N = (T+2)/j -> The number of kids the family will have in 2 years.

Currently, it must be (T+2)/j -1 + 1 => (T+2)/j. (+1 is to add the eldest kid born)

Hence Option D.

Example :

T = 16
J = 3

Kid 1 : 16 years
Kid 2 : 13 years
Kid 3 : 10 years
Kid 4 : 7 years
Kid 5 : 4 years
Kid 6 : 1 year

Hence : (T+2)/j = 16+2/3 = 6

Kindly correct me if am wrong.

Posted from my mobile device

RupamPaul13 · Answer

If we start the frequency of j right from when the first child is born then the answer is E but if the frequency,j, is taken from their marriage then the first child is born on the first interval of j and the answer will be D. Eagerly waiting for the OA. Although Option E makes more sense as the same frequency started right from when their first child is born.

IanStewart · Answer

In some situations, a similar question might be ambiguous - for example, if you were told "a family has been together for 24 years. If they had a child every 8 years, how many children do they have?" the answer wouldn't be clear to me: it could be 3 or 4, depending on whether you think you should count "year zero".

But that ambiguity doesn't exist in this question. Here we know the age of the oldest child is t years. So in two years, that child will be t+2 years old, and there will be a new child that is 0 years old. Since the ages of the children are j years apart, we have this equally spaced list of the ages of all of the children:

0, j, 2j, 3j... t + 2

and we know how to count the number of things n in an equally spaced list, using n = range/space + 1. So the number of children is just (t + 2 - 0)/j + 1 = (t+2)/j + 1.

CrackverbalGMAT · Answer

The best approach in this case, Mo2men, would be to plug in values and eliminate options. This also makes it the quickest, IMO.

I’d take t=10 and j=2. This means, the family had a child once every 2 years. Therefore, there are a total of 6 children till now (including the eldest). 
The questions says that the family will have another child, 2 years from now, which ties in with the 2 year gap that we have taken. 
With this child, the family will have 7 children.

Plugging in the values of t = 10 and j = 2 in the options, let’s see what we get:

Option A =  \frac{t}{j}  + 1 =  \frac{10}{2}  + 1 = 6. Incorrect, so this can be eliminated.

Option B =  \frac{2}{j}  + 1 =  \frac{2}{2}  + 1 = 2. This option doesn’t make any sense at all. Eliminated

Option C =  \frac{(t+2)}{j}  – 1 =  \frac{12}{2}  – 1 = 6 – 1 = 5. Incorrect, so this can be eliminated.

Option D =  \frac{(t+2)}{j}  =  \frac{12}{2}  = 6. Incorrect, so can be eliminated.

Option E =  \frac{(t+2)}{j}  + 1 =  \frac{12}{2}  + 1 = 6 + 1 = 7. This has to be the answer.

Just to be sure, we can take t = 10 and j = 1 and check with option E again to verify the answer.

IMHO, in such questions involving two or more variables, plugging in simple values is the best and quickest approach. You also saw that I used the number 2 given in the question statement to my advantage by taking j=2. Make full use of the data given, especially when very less numerical data is given.

It took me about 2 minutes to solve. Note that when I first looked at this question and tried to solve it mentally, I made a careless error where I had left out the eldest person and felt the answer was D, but then corrected the mistake when I actually put pen to paper.

Hope this helped!

urshi · Answer

ArvindCrackVerbal ,  Bunuel

But, this question is very ambiguous. 
How many Children will the couple have? It just meant they will have one more child in 2 years, no mention if it is their last kid. We can't predict since the final value of the number of kids the couple has planned to have in future. It could be 10, 20 or 17. I thought the question meant how many children the couple will have at the moment, since that is only logically predictable.

Hope I made sense. Can you pls correct me if am wrong.

Posted from my mobile device

CrackverbalGMAT · Answer

Hello Urshi,

Thanks for bringing this up!

IMHO, if anything, this question cannot be clearer; especially when you have this statement in the question - "The oldest child is t years old".

This means, the question is talking about the oldest child being 't' years old currently. All the answer options also use 't' in the same context. So, quite obviously, the question wants us to find out the expression which gives us the number of children, 2 years from now.

If we had to calculate the total number of children the couple COULD have (including the ones they plan to have in the future), then the data that the oldest child is t years old would become redundant. This is because we would then need to know how old the oldest child would be at THAT point in time and not NOW. The 5 options given, would not mean anything then (because they are framed based on t). Does this sound logical?

Also, note that the question does not mention anywhere that the family will have ONE child in the next 2 years. It only says that they will have a child 2 years from now. If their interval of having a child is 1 year, then, they will have 2 children in the next 2 years.

Hope this helps!

IanStewart · Answer

You make a very good point - the wording is ambiguous. "How many children will the couple have in total?" could mean "how many will they have in their lives" or "how many will they have in two years". The first interpretation didn't even occur to me, because it's an unanswerable question without more information. But as the question is written, it's perfectly logical to read it that way. If instead the question said:

"If they have a child 2 years from now, how many children will they  then  have in total"

it would become clear that the question was asking for the number of children precisely two years from now, rather than the total number of children the couple might have in their lifetimes.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A family has a child every j years. The oldest child is t 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

GMAT Problem Solving (PS) Questions

A family has a child every j years. The oldest child is t 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