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

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
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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

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.

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

IanStewart ArvindCrackVerbal pushpitkc chetan2u

Can you please share your thoughts in this question?

Thanks in advance

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

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
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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 !!

You meant to say E is the answer ?

Posted from my mobile device

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

(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)
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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

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.

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.
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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!
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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

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!
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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.
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