a x b = ?

[RobertoB400]

"What is the value of a x b?"
(1) a = b +1
(2) a^2 = b+1

I assumed that the answer was D since we can go all the way through the calculation with each statement and define the result of a x b = 0 for all cases. Tell me where I'm wrong please as the OA is C.

Thanks

[NikhilJ635]

Yes/No or Value?

The question asks for the value of a*b

AD
BCE

We start we A--

a = b+1

Since this is a linear equation, all points on a line defined by this equation will satisfy the equation. a and b, therefore, can have an infinite number of values. Since b = a -1, For (a,b)

(3,2) a*b = 6
(4,3) a*b = 12
...

A is clearly insufficient.

Cross AD.

We start with B--

a^2 = b + 1
Again, this is a non linear equation in two variables. Specifically, representing a curve. All points on a curve will satisfy this equation. Since b = a^2 - 1, for (a,b)

(2, 3) a*b = 6
(3, 8) a*b = 24
...

B is insufficient.

Cross B.

We move onto C--

We now have two simultaneous equations--

a = b +1 and b = a^2 - 1. Since one is linear and the other not, they will intersect at a maximum of two points (for a quadratic curve). If you have also noticed the fact that the hyperbola's y intercept is (0,-1) [because the value of b can go to a minimum of -1 for a=0], you will immediately realize that (0,-1) is a solution to both of the equations.

Case 1 (you have noticed this fact and you've seen a lot of curves) -- It will be clear to you that the line b = a - 1 (rapidly rushing from -infinity will meet the hyperbola only at (0,-1) and (1,0) -- if you've studied your lines and curves.

Case 2 (you never really cared for hyperbolas) -- All you need to do is substitute the value of a in the (ii) equation or the value of b in the (i) equation.

a = b + 1 >
a = a^2 -1 + 1 >
a = a^2

It is important here to solve this as a quadratic equation instead of arriving at a hurried conclusion.

a - a^2 = 0 >
a(a-1) = 0 >
a = 0 , 1

The corresponding values of B for which will be -1, 0. You'll realize now that the values of (a,b) that satisfy the two equations are --

(0,-1) and (1,0) and in both cases a*b = 0.

Therefore both the statements taken together (C) is the correct option.

[RonPurewal]

"What is the value of a x b?"
(1) a = b +1
(2) a^2 = b+1

I assumed that the answer was D since we can go all the way through the calculation with each statement and define the result of a x b = 0 for all cases. Tell me where I'm wrong please as the OA is C.

Thanks

there seems to be a fundamental lack of understanding here-- it should be plain that the individual statements are insufficient.

e.g., in statement 1, a and b can be any two numbers that differ by 1. accordingly, there are going to be lots and lots and lots of different possible products.
likewise for statement 2, in which you can have any two numbers such that a^2 is 1 more than b.

it's only once we combine the statements that the action starts to get interesting, since in that case a^2 = a (because both are equal to b + 1).

[RonPurewal]

in any case, could you please post a brief summary of how you came to the conclusion that the individual statements are sufficient?
if you reached that conclusion, then, as i stated above, there's a fundamental problem, which needs to be rectified at once (lest it become further entrenched in your mind!).

perhaps you're just confusing choice D (= "each statement alone is sufficient") with choice C (= "you need to use both statements together to have sufficiency")?

or perhaps you're combining the statements too early?

please let us know, so that we can address the problem, whatever it might be. thanks.