GMAT Math : Symmetry

Many GMAT Math questions can be easily solved by using the principle of symmetry

Let’s illustrate this with an example:

If P = (1+x+x2) and R = (1+y+y2), what is the value of PxR?

A. x2y2 + x2y + xy2 + x2 + xy + y2 + x + xy + 1

B. x2y2 + x2y + xy2 + x2 + xy + y2 + x + y + 1

C. x2y2 + x2y + xy2 + x2 + xy + y2 + y2x + 1

D. x2y2 + x2y + xy2 + x2 + xy + y2 + xy + xy + x + 1

E. x2y2 + x2y + xy2 + x2 + xy + y2 + x + xy + x + 1

Wow, lots of xs and ys! Readers are encouraged to take a crack ðŸ™‚

â€¦.

â€¦.

â€¦.

â€¦.

Yes, we know this is a straightforward GMAT question. But why spend the 20-30 seconds multiplying P with R and then double checking your solution for another 20-30 secondsâ€“ when there is a way to solve this is less than 10 seconds ðŸ™‚

Trick: Look for symmetry. What this means is if two or more terms are symmetrical in the question, the correct answer may often need to preserve the symmetry

P = (1+x+x2) and R = (1+y+y2) are super symmetrical. If you replace x with y in P you will get R and if you replace y with x in R you will get P.

So, PxR i.e (1+x+x2)(1+y+y2) should also preserve symmetry and this is true â€“ just replace x with y and y with x and you are still left with (1+x+x2)(1+y+y2).

This means the answer equation should have similar terms for x as it does for y â€“ there should not be an â€˜imbalanceâ€™.

Option (A) has an â€˜xâ€™ term but no â€˜yâ€™ term

Option (C) has 2 of y2x terms but only 1 x2y term.

Option (D) has an â€˜xâ€™ term but no â€˜yâ€™ term

Option (E) has two â€˜xâ€™ terms but no â€˜yâ€™ term.

â€¦so we go with Option (B) which is perfectly balanced. No pen was needed to solve this question, just a sharp eye for symmetry ðŸ™‚