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+x ^{2}) and R = (1+y+y^{2}), what is the value of PxR?**

**A. x ^{2}y^{2} + x^{2}y + xy^{2} + x^{2} + xy + y^{2} + x + xy + 1**

**B. x ^{2}y^{2} + x^{2}y + xy^{2} + x^{2} + xy + y^{2} + x + y + 1**

**C. x ^{2}y^{2} + x^{2}y + xy^{2} + x^{2} + xy + y^{2} + y^{2}x + 1**

**D. x ^{2}y^{2} + x^{2}y + xy^{2} + x^{2} + xy + y^{2} + xy + xy + x + 1**

**E. x ^{2}y^{2} + x^{2}y + xy^{2} + x^{2} + xy + y^{2} + x + xy + x + 1**

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

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â€¦.

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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+x^{2}) and R = (1+y+y^{2}) 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+x^{2})(1+y+y^{2}) 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+x^{2})(1+y+y^{2}).

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 y^{2}x terms but only 1 x^{2}y 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™‚