Percents

[BTGmoderatorRO]

In a town there are 60% married Males, 40% married Females. What is the % married?

A. 20%
B. 30%
C. 40%
D. 48%
E. 50%

OA is D.
PLs I am kind of confused can someone help me out with this tricky question.

[EconomistGMATTutor]

Hi Roland2rule,
Let's take a look at your question.

We will suppose that there are a total of 100 males in the town.
60% of them are married, which means that the total number of males married out of 100 is 60.
If 60 males are married then we can say that 60 females are married as well to those 60 males.

The question states that 40% of females is married.
We already know that 60 of the females are married, therefore, if x represents the total number of females, we can write:

$$60\ =\ \left(40\%\right)x$$
$$60\ =\ \left(\frac{40}{100}\right)x$$
$$60\ =\ \left(0.4\right)x$$
$$x=\frac{60}{0.4}$$
$$x=150$$
Therefore total population of females is 150.

We need to calculate the percentage of married people now.
Total Population of males and females = 100 + 150 = 250
Total married people = 60 (males) + 60(females) = 120

$$Percentage\ =\ \frac{120}{250}\times100%$$
$$Percentage\ =\ 48\%$$

Therefore Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

[Scott@TargetTestPrep]

In a town there are 60% married Males, 40% married Females. What is the % married?

A. 20%
B. 30%
C. 40%
D. 48%
E. 50%

We are assuming here that all the males are married to the females who are in the town and vice versa (that is, no male or female has a spouse who lives out of town). Thus, the number of married males must equal the number of married females. If we let the total number of males = m and the total number of females = f, we have:

0.6m = 0.4f

6m = 4f

f = 6m/4 = 1.5m

Thus, the percentage of individuals in the town who are married can be expressed as:

(0.6m + 0.4f)/(m + f)

Let's re-express this in terms of m only (recall that 0.4f = 0.6m and f = 1.5m):

(0.6m + 0.6m)/(m + 1.5m)

1.2m/2.5m

1.2/2.5

12/25 = 48/100 = 48%

Answer: D