CrackMath Question...please help!
Started by YourDentition
'A' is wrong because the absolute value of y is always positive (y can't be 0) and x is always positive (x also can't be 0). And positive * positive is NOT less than 0.Hi, This is a question that I couldn't figure out. Would appreciate your help. Thanks
'B' is wrong because the highest value of x^2 happens when x = 2 and the highest value of y^2 happens when y = -2. This gives a value of 10. While it's true that 10 = 10, the statement fails with any other combination of x and y. For instance if x = 1 and y = -1, you would get x^2 + y^2 + 2 = 1 + 1 + 2 = 5. This is clearly not greater than or equal to 10.
'D' is wrong with a little thought... sin(x) will always be less than or equal to 1 so you need to find a value of x such that x*sin(x) is greater than 1. I think it's easiest to work with values of pi that you know between 0 and 2. A good choice is pi/2 (about 1.57). You know that sin(pi/2) is 1, so pi/2 * sin(pi/2) is pi/2. This is clearly greater than 1. So 'D' is wrong.
Let me point out that we got lucky on this one. Had we chosen something else, such as pi/4, we'd have pi/4 * sin(pi/4) = pi/4 * sqrt(2)/2 = pi*sqrt(2) / 8 = 3.14*1.4 / 8. The numerator isn't more than 5 so that would be less than 5/8 which is less than 1. In this case we'd have to just try again.
'E' is wrong and we do it the same way. This time we have a lot more freedom. Since we need to find one value of x and y where x*cos👍 is less than or equal to 2, we just choose x and y intelligently. We can choose x to be VERY small, such as 0.0001. Now remember that cos👍 is never greater than 1. So with x = 0.0001, we have x*cos👍 equal to AT MOST 0.0001! In fact, this statement can NEVER be true. The largest value of x is 2 and the largest value of cos👍 is 1. So multiplied together, they can never be greater than 2.
**AT THIS POINT MARK C AS THE ANSWER**
Now why is C true (for your information)?
We want y*cos👍 to be greater than -2. How low can this value actually be? Well, cos👍 ranges from -1 to 1 for all values of y. And for this case we're limited with -2 <= y < 0. Considering the most extreme case, we could have 1 * -2 = -2. This would be the only case to make it false. Can it happen? When y is -2, cos👍 is NOT 1. So no, this case never happens. All other cases are above -2. So the statement is true.
