A Town T has 20,000 residents, 60 percent of whom are female. What per

SOLUTION

A Town T has 20,000 residents, 60 percent of whom are female. What percent of the residents were born in Town T?

(1) The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.

Not sufficient.

(2) The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T.

Not sufficient.

(1)+(2)

Sufficient.

Answer: C.


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From ques stimulus:no. of females=60% of 20000=12,000
no. of males=8000
From S1:Let no. of females born in town be 2x
Therefore no. of females not born=12000-2x
And no. of males not born=x
Also.no. of males born=8000-x
But this doesn't give us value of x.Insufficient.

From S2:No. of females not born=2x
Therefore,no. of females born=x
And 2x+x=12000
x=4000
But we still don't know the no. of males born and not born in town.Insufficient.

Combining the two statments we can find the no. of residents born in town T.
Ans.C

We are given no. of Female is 60% of Total Population so 12000 and no. of Male =8000

No From St 1 we get Only No Information (Refer Table 1)
From St 2, we can find no. of Female born and not born in the city so not enough cause we don't know about men.

Combined we No. of Male born in the city is half of female born in the city so a=x/2=2000
So Total Refer table 3, We can find the no. of people born in the city.

Ans C
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The no. of residents in town T is 20,000. We, need to find the % of residents born in town T.

As 60% of them are female, the no. of female residents = 60% or (3/5) * 20,000 = 12,000;
So, the no. of male residents = 20,000 - 12,000 = 8,000;

We can assign the no. of Male and Female born in town T as MB and FB respecitively.
Similary, we can assign the no. of Male and Female not born in town T as MNB and FNB respectively.

Statement (1):
FB = 2 * MNB; Insufficient as we do not know the ratio of Born and Not Born.

Statement (2):
FNB = 2 * FB;
Since, we know the total no. of female residents in town T as 12,000, they can be classified as either Born or Not Born in town T.
Therefore, FB + FNB = 12,000;
FB + 2FB = 12,000;
3FB = 12,000;
FB = 4,000 and therefore FNB = 8,000;
Since we do not know the male strength born in town T, this statement is Insufficient too.

Combining, MNB = FB/2 = 4,000/2 = 2,000;
Therefore, MB = 8,000 - 2,000 = 6,000;

% of residents born in town T = (FB + MB)/Total = 4,000 + 6,000 = 10,000/20,000 = 50%;

Ans is (C).

Note: Most of the calculation done here is not required as it is a DS question. Press kudos if you think my explanation makes sense.

On this question, although the actual number of residents is provided, there is no need to use actual numbers to determine sufficiency.

If you glance at Statement 1 and 2, you can see that no absolute numbers are provided. So for simplicity, just use the number of residents as 100. The calculations are useful though, to understand the problem (this very well could be a problem solving question).

For students who are curious about whether the Matrix/Table method is the only method to solve such questions, here's how you could also solve this question using the Venn Diagrams.



Here,

y: females born in T
z: females not born in T
x: non-females (that is, males) born in T
w: males not born in T

As per given information:

x + y + z + w = 20,000
y + z = 60% of 20,000 = 12,000 . . . (1)

=> x + w = 20,000 - 12,000 = 8000 . . . (2)

Required to find:\(\frac{(x+y)}{20,000}*100\)

So, we need to know the value of x + y.

Statement 1: y = 2w . . . (3)

By substituting (3) in (2), we'll know the value of x + \(\frac{y}{2}\), not of x + y.

Therefore, Not Sufficient.

Statement 2: z = 2y . . . (4)

By substituting (4) in (1), we can get the value of y. But no idea about the value of x. So, Not Sufficient.

Statements 1 + 2:

We have 4 equations and 4 variables. So, sufficient to determine the unique values of x and y, and hence of x + y.

Most of the Matrix/Table questions can be solved using the Venn Diagrams and vice-versa.

Hope this helped!

Japinder
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Why is statement 2 alone not sufficient??
As per stem there are 12000 females which were only 2 types either born in town or born outside town.
now as The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T.
we can divide 12000 into 3 equal parts in which one part is born in town ie 4000 and anotther 8000 not born in town

Pleaz clear...

thanks

The question is what percent of the residents were born in Town T? Not, what percent of the female residents were born in Town T?
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We are given that of the 20,000 residents in Town T, 20,000 x 0.6 = 12,000 are female, and thus 8,000 are male. We need to determine the percentage of residents who were born in Town T.

Statement One Alone:

The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.

We can let the number of male residents born in Town T = m, and the number of female residents born in Town T = f. Thus, (8,000 - m) males and (12,000 - f) females were not born in Town T.

From the statement, we see that f = 2(8,000 - m). However, we still cannot determine the percentage of residents who were born in Town T. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T.

We can let the number of female residents born in town T = f. Thus, (12,000 - f) females were not born in Town T.

From the statement, we see that (12,000 - f) = 2f. Solving for f, we have:

3f = 12,000

f = 4,000

However, we still cannot determine the percentage of residents who were born in Town T, since we don’t know the number of males who were born in Town T. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements, we see that f = 2(8,000 - m) and f = 4,000. Thus:

4,000 = 2(8,000 - m)

4,000 = 16,000 - 2m

2m = 12,000

m = 6,000

So, 4,000 females and 6,000 males were born in Town T, which is 10,000 people.

Thus, 10,000/20,000 = 50% of the residents were born in Town T.

Answer: C
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