In a monogamous culture, 100% of the adults are married. The average

Question

In a monogamous culture, 100% of the adults are married. The average number of children per family is five and over-population is a threat. Programs to encourage birth-control have been ineffective. It has been suggested that this failure is due to these programs ignoring a tradition that values male children very highly, so that every parent wants to have at least one son. It is proposed that couples be encouraged to use birth-control measures after the birth of their first son.

If this proposal is widely accepted in the culture, we may expect that:

(A) the rate of population increase will be slowed, and future generations will contain a disproportionately high number of females.

(B) the rate of population increase will be slowed, and the gender balance in future generations will remain as it is at present.

(C) the rate of population growth will remain the same, and future generations will contain a disproportionately high number of females.

(D) there will be no significant effect either on population growth or on gender balance.

(E) the population will decline precipitously, because approximately half of all families will have only a single child.

durgesh79 · Accepted Answer

lets put some quants in this ...

lets assume probability of a birth of a male or female child is same 1/2.... 
 
So if the program is effective there'll be parents who'll stop at 1st, 2nd, 3rd ..... child, so the rate of population grwith will go down ... option C and D are out

even if half of the familes will have only one child, there'll be familes with more than 2 children also ... so option E is also out.

between A and B, I'd go for B, it wont effect the balance ...... Suppose there are 16 familes, so with a probability of 1/2, the birth of M and F child will have a pettern like this

First birth : 8M 8F
Second birth : 4M, 4F (only with F in first round will go for second) 
Third birth : 2M, 2F (same logic as above) 
Forth birts : 1M, 1F

Total M = Total F = 15 ... so there will be a balance......

Answer B

sayantanc2k · Answer

Let us consider a simplified mathematical model:

The society consists of 16 families:

After 1st round of reproduction: 8 male + 8 female
The families which have a male child stops reproducing. So other 8 families reproduce in the second round - of them 4 male and 4 female are born.
After 2nd round of reproduction: 12 male + 12 female
Similarly after 3rd round: 14 male + 14 female
After, 4th round 15 male and 15 female.

Now this mental experiment can be generalized with n number of families, and it will be seen that after mth round of reproduction, the number of male and female will be same = n/2 + n/4 +... upto m terms.

Moreover as time passes (m increases), the rate at which the increase in no. of child happens goes on decreasing. ( 1st round: increased by 16(n), second round: increased by 8(n/2), 3rd round: increased by (n/4) and so on.

Therefore answer B is correct.

Nevernevergiveup · Answer

The average number of children per family is five. 
Failure is due to these programs ignoring a tradition that values male children very highly, 
so that every parent wants to have at least one son.

Proposal: couples be encouraged to use birth-control measures after the birth of their first son.

If this proposal is widely accepted in the culture, we may expect that:
(Application question......if x plan is applied then what can happen.....)

We have two scenarios 
1. first child is male child and birth control measures are taken(male:female gets higher)
2. first child is not male child and let us say 4 female and one male(female:male is higher)

this will ensure that rate of population increase will be slowed, but gender imbalance will remain.

A. the rate of population increase will be slowed, and future generations will contain a disproportionately high number of females.
 (high no of females is possible as per case 2 but not case 1)

B. the rate of population increase will be slowed, and the gender balance in future generations will remain as it is at present.
 (This is possible in all circumstances of both cases 1 & 2)

C. the rate of population growth will remain the same, and future generations will contain a disproportionately high number of females.
 (high no of females is possible as per case 2 but not case 1 and rate will not remain same)

D. there will be no significant effect either on population growth or on gender balance.
 (This cannot be true in any case)

E. the population will decline precipitously, because approximately half of all families will have only a single child.
 (there is no guarantee that approx half will have single male child)

bhatiagp · Answer

clubzzang ur on a roll... one good question after the other...

+1 for this one too

Althouh Im not too sure, I would answer B for this...

As it is every parents wants atleast one son. Currently,they dont adopt birth control measures to have a son..

If one has to adopt birth control measures after they have a son.. the gender balance essentially remains the same, but the population may dwindle, as people adopt birth control measures after their first son..

abhirules · Answer

I will go with B although i am not convinced that there  WILL  be gender balance. Simply because birth is a natural occurrence. Many factors such as birth mortality and trans gender births need to be taken into account when determining the gender balance.

My reasoning is

C and D are out because rate of increase will    NOT SLOW DOWN   
E is out because population will not decline    precipitously

between A and B. 
A is out because there absolutely no way to conclude that future generations will have   disproportionately high number of females

I would have chosen A if it mentioned "the rate of population increase will be slowed,   and the gender balance in future generations will not remain as it is at present

Only B survives the POE

mbaprep2016 · Answer

Hi  sayantanc2k  
as per my understanding ...first two premise "all adults are married" and "avg number is 5" tells nothing about male to female ration currently.
now with successful birth control ,we have two scenarios 
1. first child is male child and birth control measures are taken(male:female gets higher)
2. first child is not male child and let us say 4 female and one male(female:male is higher)

B tells the gender balance in future generations will remain as it is at present.
please explain the same.

mbaprep2016 · Answer

I apologies I am still confused , you stared with equal ratio
lets say 16 families 
After 1st round of reproduction: 10 male + 6 female
The families which have a male child stops reproducing. So other 6 families reproduce in the second round - and have 6 male.
now ratio will 16 + 6 
I am sure I am missing something very important

sayantanc2k · Answer

The assumption is that the probability of getting a male child and that of getting a female child is 1:1. So when 16 families reproduce, 8 males and 8 females are born. Now read the above post. (I did not quite understand how you got 10 males and 6 females after 1st round)

If you still have doubt, please post again.

abhimahna · Answer

Earlier Tradition : Male children very highly valued.

New Proposal: Couples be encouraged to use birth-control measures after the birth of their first son.

If this proposal is widely accepted in the culture, we may expect that:

A. the rate of population increase will be slowed, and future generations will contain a disproportionately high number of females.  How do we know females would be high? It could men who are very high in number. So, Incorrect.

B. the rate of population increase will be slowed, and the gender balance in future generations will remain as it is at present.  : Correct.

C. the rate of population growth will remain the same, and future generations will contain a disproportionately high number of females.  : No, population growth will obviously change.

D. there will be no significant effect either on population growth or on gender balance.  : Really? I don't think so.

E. the population will decline precipitously, because approximately half of all families will have only a single child.  :How can we say Half will have only a single child? Too extreme to consider.

Bambi2021 · Answer

In every birth, there is always a 50-50 (not exactly but we assume this) ratio of getting either a boy or girl. It doesnt matter when couples stop producing, the next birth going on somewhere else will still have a 50-50 ratio of boys-girls. At least thats how I make the conclusion this wont affect the gender balance.

I mean, just as many times as we get

GIRL-GIRL-GIRL-BOY - Stop
GIRL-GIRL-BOY - Stop
GIRL-GIRL-GIRL-GIRL-GIRL-BOY - Stop

we will get

BOY Stop
BOY Stop
BOY Stop
BOY Stop
BOY Stop

Biology ensures that gender balance will remain.

Aliprep · Answer

To be honest, not convinced with the answer. 
Chose D as an answer. 
Because if we consider that there is already tradition that families value high male child, it is possible that families already choosing to stop after birth of a boy. 
So it is possible that it won't change, I think.

NicoBJ · Answer

sayantanc2k   VeritasKarishma   GMATNinja   nightblade354   mikemcgarry

Hello experts!

I have some doubts regarding this question. If you may, would you help me clarify them?

Assuming a 50% probability of having a male son, I understand it becomes a mathematical problem (n/(2.ki)), and then it is true that the population growth will be lowered, and that the female to male ratio will balance.

That is certainly a logical assumption, but it's not in the argument itself. When I did the problem I assumed that the previous birth control programs (BCP1) did not work (and people were having on average 5 kids) because those people wanted  at least  one male son. Therefore, I thought: maybe the probability of having a male son was less than 50% probability.

Then (assuming people would stop reproducing after the first male son):

If the population rate keeps increasing => there will be more female kids, and f:m should increase.
If the population rate was reduced => there will be fewer female kids, and f:m should decrease.
If the population rate was kept constant => the proportion f:m should stay somewhere similar.

1. If the probability of having a male son is 50%, and people want at least one male son, then why did the BCP1 fail? There has to be another reason.

2. Is this so because the argument says "It has been  suggested  that...."? If that is the case, it is very tricky...

Thank you for your help.

Kind regards,

Nicolas

KarishmaB · Answer

I don't know what the source of this question is. It doesn't make much sense.

In case, the average number of children is 5 and if the reason for that is that all families want at least one male child (if that is the reason the birth control programs are failing), it means the probability of getting a male child is not 1/2. It needs to be substantially lower than 1/2. Or for many families, a male child would happen after many girls. That is why the average would bump up to 5. These families will still continue to have the same number of children. So why would we expect the population to get controlled?

Ignore this question.

thecardinal · Answer

If " In a monogamous society 100% of adults are married" is true doesn't that mean that in this society whatever happens male and female population is 1:1 and cant we presume that this will remain the case in this hypothetical scenario as it is a condition?

Is this reasoning wrong?

if it it is valid it is pretty obvious why B is the answer

Is this reasoning wrong?

if it it is valid it is pretty obvious why B is the answer

EthanTheTutor · Answer

If we assume only that:

Before the plan: 
- Families may stop after any child, but not before the first boy 
- Expected value of children: 5

After the plan: 
- Families will stop after the first boy, regardless of the total number of children

Definitions: 
B = number of boys 
G = number of girls 
p = probability of having a boy 
1-p = probability of having a girl

Before the plan (by Wald's equation): 
- Expected ratio  \frac{B}{G} = \frac{5p}{5(1-p)} = \frac{p}{1-p}  
- Expected total children:  5

After the plan (geometric distribution over number of children before/including a boy): 
- Expected ratio  \frac{B}{G} = \frac{1}{\frac{1-p}{p}} = \frac{p}{1-p}  
- Expected total children:  \frac{1}{p}

Notice that the B/G ratio is equal in both cases.

Example calculations: 
- If  p = 0.2 , population growth remains the same before and after the plan
- If  p > 0.2 , population growth slows. 
 -  p = 0.4  →  2.5  children on average 
 -  p = 0.5  →  2  children on average

Moral of the story: the answer is B, unless the probability of having a boy is less than  1/5 . We don't need to make extra assumptions about boys and girls being equally likely, or why the average is 5 kids before the plan.

In a monogamous culture, 100% of the adults are married. The average

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 Critical Reasoning (CR) Questions

In a monogamous culture, 100% of the adults are married. The average

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