Townville has X residents, and Y of them are females. If half of Townv

Number of people = x
Females = y
men = x-y
Half of the men are smoker(x-y)/2, that means the remaining men (x-y)/2 are non smokers.
1/z females are smoker, so (y-1)/z are non smokers

So, total number of non smokers in the town are (x-y)/2+(y-1)/z = x/2+y/2-1/z, which is close to answer 'D'.

Either something wrong with the answer option 'D' (typo error) or i am doing it wrong. Comments people !!!

The easiest way is to assume numbers for the variables.

x=100, y=50, z=10 (Not going against any information by assuming these values!)

Thus per the information, female smokers = 50/10 = 5 , female non smokers = 50-5=45

Male smokers = (100-50 )/2 = 25

Thus total non smokers = 45+25=70

Check the options now:


A) X – 2Y – Z = 0 Eliminate
B) X - Y/Z - Y = 45 Eliminate
C) 2X – Y - ZX = 1150 Eliminate
D) X/2 + Y/2 – Y/Z = 70 keep
E) X + 2Y – 4Z = 160 Eliminate

Thus only option D gives the correct value and is thus the correct answer.

As for your solution, refer to the text above in red. You are making a mistake in your calculation for female non smokers. Refer above (text in blue) for the corrections.

Hope this helps.
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I used these assumptions, X=100,Y=40 and Z=5. The targeted answer was 62 (working through double square matrix method ) and only option D gives the same answer.
My choice is D

Number of people = x
Females = y
men = x-y
Half of the men are smoker(x-y)/2. Remaining men (x-y)/2 are non smokers.
1/z females are smoker, so (1-1/z)y are non smokers

Total number of non smokers are (x-y)/2+(y)(1-1/z) = x/2+y/2-y/z,

Answer is 'D'.

No of non smokers (female) = y(1-1/z)
not (y-1)/z.

Hope this helps!

GMAT Prep Now OFFICIAL SOLUTION:

Algebraic Approach

Since the question tells us about the residents who are smokers, let’s determine the total number of smokers and then subtract that amount from the total number of residents in Townville.

Male smokers: There are X residents, and Y are females. So, the number of males = X – Y. If half of the males smoke, then the number of male smokers = (1/2)(X – Y) = X/2 – Y/2

Female smokers: There are Y females, and 1/Z of them smoke. So, the number of female smokers = (1/Z)(Y) = Y/Z

So, the total number of smokers = X/2 – Y/2 + Y/Z

The total number of NON-smokers = (total number of residents) – (total number of smokers)
= X – (X/2 – Y/2 + Y/Z)
= 2X/2 – X/2 + Y/2 - Y/Z
= X/2 + Y/2 – Y/Z

So, the correct answer is D


Input-Output Approach

For the Input-Output approach, we’ll arbitrarily select values for the variables and then use those chosen values to answer the question. We’ll then plug those same values into the answer choices and see which one yields the same answer to the question.

So, let’s say there are 10 residents in Townville (X = 10). Let’s also say that there are 6 females (Y = 6), and that 1/3 of them smoke (Z = 3).

We’ll now use these selected values to answer the question.

First, if 6 of the 10 residents are females, then the other 4 residents are males. Since half of the males smoke, there must be 2 male smokers.

Next, since 1/3 of the 6 females are smokers, we can conclude that there must be 2 female smokers.

So, in total, there are 4 smokers in Townville, which means there are 6 residents who do not smoke.

In other words, when we INPUT X = 10, Y = 6 andZ = 3, the OUTPUT is 6 non-smokers.

At this point, we’ll plug the three chosen values into the five answer choices to see which one yields and output of 6.

A) X – 2Y – Z: 10 – 2(6) – 3 =-5
B) X - Y/Z - Y: 10 – 6/3 – 6 = 2
C) 2X – Y – ZX: 2(10) – 6 – (3)(10) = -16
D) X/2 + Y/2 – Y/Z: 10/2 + 6/2 – 6/3 = 6
E) X + 2Y – 4Z: 10 + 2(6) – 4(3) = 10

Since D is the only answer choice that correctly yields the output 6, it must be the correct answer.

Conclusion

In this article, we examined two ways to approach VIACs. Most students prefer the Input-Output approach, because it involves little or no algebra, and because it often reveals the correct answer quickly. That said, this approach is not without issues.
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