What is the value of

Question

What is the value of.PNG

Regor60 · Answer

We are free to plug in whatever values we want that don't put 0 in a denominator,so

Set a^(1/2) = 2
 b^(1/2) = 1

Plugging in:

((2+1)/1)-(4/3))/(3+(1/3)) =

((9/3)-(4/3))/(3+(1/3)) =

(5/3)/(10/3) =

1/2

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IanStewart · Answer

It's naturally possible to solve algebraically, but I'd use the approach Regor60 used above, since the algebra looks annoying. Faster still is to plug in a = 1 and b = 0, because then we just get (1 - 0)/(1 + 1) = 1/2.

jsam98 · Answer

Why does this work??

Regor60 · Answer

The short answer is to recognize that you're being told there's only one solution.

Well, normally you couldn't arrive at the answer without knowing A and B.

Since you don't know A and B but are being told there's only one answer, logically A and B can't matter.

It works because if you were to go through the algebraic approach the A's and B's would be seen to cancel, leaving only 1/2 as a result, so that it wouldn't matter what you assumed for those variables.

How do we know they'd cancel ?

Well, there is no restriction in the problem statement as to what values A and B can take other than the standard restrictions on not dividing by 0 or finding square root of negative numbers, so it must be that these values don't matter.

So, rather than going through the algebra, we pick two numbers to plug into the equation that can be calculated easily, as above.

Isha2701 · Answer

I didn't quite understand the solution, why did you take a=1 an b=0? how can we do that?  karishma  can u pls help here?

Bunuel · Answer

In a GMAT problem-solving question, only one option can be correct. Here we are asked for the value of an ugly algebraic expression, so that value must be the same no matter what valid values of a and b we use.

Therefore, we can substitute any valid values for a and b and still get that same answer.

Therefore, we can substitute any valid values for a and b and still get that same answer.

Isha2701 · Answer

How do we know what are the valid values of a and b? how do we select the values?

Bunuel · Answer

The valid values are those for which the expression is defined for real numbers. So those would be the numbers for which the values under the square root are nonnegative and those for which the denominator is not zero, because even roots of negative numbers are not defined on the GMAT, and we also cannot divide by zero.

As for how to select the numbers, you would usually choose the easiest numbers to work with. So a = 1 and b = 0 seem to be the easiest values to plug in and operate with.

What is the value of

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What is the value of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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