Of the 60 families in a certain neighborhood, 38 have a cat. How many of the families in this neighborhood have a dog?
(1) 28 of the families in this neighborhood have a cat but not a dog
(2) The number of families in the neighborhood who have a dog and a cat is the same as the number of families who have neither a cat nor a dog.
OA B
I have found that statement 1 alone is insufficient.
I am facing problem regarding calculation in statement B even though I know that statement 2 alone is sufficient.
Kindly see my calculation thoroughly and let me know where I am doing mistake.
I have solved this in matrix form.
Please find the attachment
I found the number of the families in this neighborhood have a dog which is 22(highlighted in yellow)through this way. So I found statement 2 is sufficient.
When I am calculating this below way I also able to find the answer:
D = no of the families have a dog.
60 = 38+D-X+X
or, D = 22.
But my problem is when I am solving this below way I am not able to solve X.
60 = 38-X+X+X+22-X (refer my above matrix in order to find how I got this expression)
Then I do not know how to solve.
I know I am doing here some mistake. Please point out my mistake in this calculation.
Of the 60 families in a certain neighborhood
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Your use of the matrix was perfect here, and it allowed you to get to the right answer. Why are you also trying to solve algebraically? There's no need to solve twice!
If I understand what you're saying, you're able to solve for D (number of dogs) algebraically, but that you're not able to solve for X. But why are you trying to solve for X? The question is asking about the number of dogs, so finding D is sufficient. It doesn't matter what X is at all. In fact, consider these scenarios:
Here's one possible solution for X:
But here's another scenario that also works:
Statement 2 is not sufficient to solve for X, but who cares?! It's sufficient to solve for D, and that's all we need.
If I understand what you're saying, you're able to solve for D (number of dogs) algebraically, but that you're not able to solve for X. But why are you trying to solve for X? The question is asking about the number of dogs, so finding D is sufficient. It doesn't matter what X is at all. In fact, consider these scenarios:
Here's one possible solution for X:
But here's another scenario that also works:
Statement 2 is not sufficient to solve for X, but who cares?! It's sufficient to solve for D, and that's all we need.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education