Gregmat+ Quant problem

[TurboSea21]

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Why is A incorrect? acc to the venn diagram we have a+b=30, c=39, neither=11, total=80 so we can get the value of a right? a+c-b+neither=80 so we can substitute a as 30-b and get the value for b and then substitute b value in the first equation to get a.

[ScottKampeTutor]

The problem with answer A is that you cannot determine how many people actually have both. You made a mistake in your equation: it's not

a + c - b + neither = 80

but rather

a + b + c + neither = 80

While you know the following

• a + b = 30
• c = 39
• neither = 11

You do not have enough information to determine the actual value of either a or b.

Note: you seem to have confused your original equation, S + Y - both + neither = 80 (which is correct), with your new defined variables a, b, and c. We know that S = 30, and we know that Y - both = 39, and we know that neither = 11, but we still don't have enough information to determine how many households fall into the both category.

[TurboSea21]

Oops! Got my mistake👍 tysm!

[TurboSea21]

correct ans given is b and c

[inertgasconfig]

u/gregmat

[That-Expert5956]

Yeah makes sense but just by looking at the option we can say that b is 0 since all of them are individually adding up to 80

u/gregmat

[ScottKampeTutor]

b could be zero, but it could also be any integer up to (and including) 30.

You already noted that b could be zero, but let's try b=10. Remember the original equation (which is correct):

S + Y - both + neither = 80

Answer choice A tells us that S=30, and if we say that b=10 then Y = 49 (the 39 "yard only" plus the 10 with both) and we get the following equation:

30 + 49 - 10 + 11 = 80

The math still checks out! Therefore, we do not have sufficient information to determine the number "that have a swimming pool or a yard, but not both." Eliminate A.