In Part I of this Article we have discussed about GRE’s obsession with Pythagorean Triples. Let’s continue.

**Interesting Quantitative Comparison Questions Involving Right Triangles**

Here is a simple one.

**Q. No. 4: ** In the triangle ABC above, AB = 4 and AC = 3

Quantity A | Quantity B |

BC | 5 |

*Note:* This is an easy one. Where does it tell you that angle CAB is a right angle? In a quantitative comparison question, you cannot trust the figure. Angle CAB may look like 90o, but that doesn’t mean angle CAB = 90o. Hence the answer is (D).

**Here is the next version**

**Q. No. 5: ** In right triangle ABC, two sides AB and AC measure 3 and 4 respectively.

Quantity A | Quantity B |

Length of the third side BC of the triangle ABC | 5 |

*Note:* This time you know that triangle ABC is a right triangle. You may be tempted to pick (C) as the answer, but wait a moment again. Where does it tell you which angle is the right angle? The side AC may be the hypotenuse. The answer is (D) again.

**Let’s look at another version.**

**Q. No. 6: ** In right triangle ABC, two sides AB and AC measure 3 and 4 respectively.

Quantity A | Quantity B |

Length of the third side BC of the triangle ABC | 2 |

*Note:* You cannot just use the third side rule and pick (D) as the answer. Mind that the triangle ABC is a right triangle. You must examine all the possibilities. However, there are just two possibilities. Either BC is the hypotenuse, in which case BC = 5, or AC is the hypotenuse, in which case BC = √7. In either case the Quantity A is greater. Hence, the answer is (A).

**Other possible variations of the questions 4, 5, and 6:**

**Q. No. 7**: What would be the answer if the Quantity B were 3?

**Q. No. 8**: What would be the answer if the Quantity B were 4?

**Q. No. 9**: What would be the answer if the Quantity B were 6?

*Note:* The answers to Q. Nos. 7 and 8 would be (D), but the answer to the Q. No. 9 would be (B) because √7 < 3 < 5, but √7 and 5 both are less than 6.

It is interesting to note how the difficulty levels of the questions change from one question to another although GRE is testing you on the same concept. At Manya – The Princeton Review, we say that a question is hard not because it is testing you on a difficult concept; it’s hard because most of the people get it wrong! At Manya – The Princeton Review, we teach you how to avoid traps and figure out what a question is testing. The better you are at figuring that out, the better you are at taking the GRE.

**Thus GRE may be obsessed with Pythagorean Triples, but they may also try to trap you using the same Pythagorean Triples, and you may get trapped if you are obsessed with Pythagorean Triples yourself!**

**At Manya – The Princeton Review, in our Quant classes, along with learning the math concepts, you learn how to outsmart the creators of the GRE Test.**

Remember the question at the end of Part I? We are sure you were able to spot the Pythagorean Triples in the numbers below !!

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