Hello!
Here is another tricky question trying to lure you in to do tons of math. But we are not going to let them. We are going to be sneaky and find the trick.
The first clue should be the number 54, which is repeated twice in the denominator. Pull it out to simplify the expression
\(\frac{
1527^{2} - 1473^{2}}{54(67+58)}\)
That's nice, but the numerator still gives me nightmares. Is it likely that the number 54 figures there as well?
Good thinking, but before you start dividing large numbers by 54, what else do you notice about the numerator?
It is a quadratic expression of the form \( x^{2} - y^{2} = (x+ y)(x - y)\)
You have to learn these standard quadratic expressions, the Special Products, as they are lifesavers on questions like these
\(1527^{2} - 1473^{2}\) is therefore equal to (1527 + 1473)(1527 - 1473)
Here unfortunately (or fortunately if you love math like I do) you have to do some math
1527 + 1473 = 3000
1527 - 1473 = 54
The numerator is therefore equal to 54(3000)
What do you know, 54 again
The whole fraction now looks like this:
\(\frac{54(3000)}{54(67+58)}\)
Cancel out the 54 from the numerator and the denominator
67 + 58 = 125
\(
\frac{3000}{125 }\) = 24
The answer is (B)
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