Special A and B - Question 14 CAT test 1

[MaraR978]

Hi Everyone,

Does anyone understand the special A and B problem (question 14 of the first CAT)? It is a data sufficiency question that tests quadratic equations and fractions.

Question:
If a > 0, is 2/(a-b) + 2/(a+b) = 1?

(1) b = 0

Response: If you plug 0 in, you can the question, does 2/a +2/a = 1? INSUFFICIENT Because we don't know what a is, we can't determine the answer to the question.

(2) a^2 − b^2 = 4a

Response: You can factor the equation above to get (a+b)(a-b), both of which are in the equation the problem talks about, but I don't understand how the factored version of the equation could be used to answer the question if a > 0, is 2/(a-b) + 2/(a+b) = 1? Could anyone help me?

The answer is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. See below for the full explanation.

___________

The question stem contains an equation with fractions. We can simplify this equation by multiplying both sides by the common denominator, (a + b)(a – b), and then simplify:
2(a – b) + 2(a + b) = (a + b)(a – b)
2a − 2b + 2a + 2b = (a + b)(a – b)
4a = (a + b)(a – b)

Notice that the right-hand side of the equation is one of our three special products. There are two ways to write any special product; when we see one form, we should always write both ways. The other form of this special product is:
4a = a2 − b2

[RonPurewal]

that's a pretty awful-looking question, right?

the point is that algebraic manipulation is algebraic manipulation, and you can do it wherever it's legitimate.
mostly, you're thinking in terms of doing algebra on the statements... but, if the question itself is weirdly un-simplified, you should work on the question, too.

just don't forget that the question is still the question.

the original question is:

is 2/(a-b) + 2/(a+b) = 1 ?

multiply by (a + b)(a – b):
is 2(a – b) + 2(a + b) = (a + b)(a – b) ?

then more simplification:
is 2a − 2b + 2a + 2b = (a + b)(a – b) ?

is 4a = (a + b)(a – b) ?

at this point it should be pretty clear how statement 2 plays into this.

[RonPurewal]

the point is that you should do work wherever it makes the most sense to do the work.

it seems you were looking for a way to work FROM statement 2 INTO the original form of the question. that'd be much harder and less intuitive, because you would essentially have to "un-simplify" to do that.

so, instead, you can get rid of the fractions in the question. just don't forget to keep the "is" and the "?" when you simplify questions (otherwise it's too easy to mistakenly think you're looking at a known fact).