Many hard GMAT quantitative questions present problems because of the exceedingly time-consuming calculations needed to solve, or because the way to solve the problem isn’t easily apparent. One solution to these kinds of problems can often be found by identifying and using patterns. Here’s some helpful information to help you utilize the presence of patterns to improve your accuracy and efficiency (which is what you should seek rather than speed) on GMAT Quant:

Identifying patterns is an effective way to determine the solution to a problem while cutting down on the calculations involved (and thereby saving time).

To Spot a “Pattern” problem watch out for questions that involve **a seemingly insurmountable number of calculations **or amount of work.

To Solve a “Pattern” problem:

- Begin working through the calculations (this is where most test-takers fail; they seek to find answers without “looking”).
- After your first few steps investigate the result, keeping an eye out for types of numbers (i.e. even/odd/multiples) or relationships (i.e. each subsequent result is two more than the previous one). When you’ve seen the pattern occur at least three times, you can consider it verified.
- Apply the pattern to the entire problem.

Let’s take a look at how this works by applying it to a GMAT question:

What is the remainder when 3

^{43}is divided by 5?(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

**Spot the Pattern Problem: **

Here we should realize right off the bat that we’re certainly ** not** going to find out what the value of 3

^{43}, much less divide it by 5 to find the remainder. Because there’d so much work involved in figuring out the answer with straight-forward math calculations and concepts, we should recognize the potential of patterns to help us reach an answer.

**Solve the Pattern Problem:**

We know that the remainder is the part left over after division, while exponents tell us how many times we multiply the base by itself. This information should lead to the conclusion that perhaps there is a pattern in the exponent itself that will limit the possible remainders for different kinds of exponents. Let’s start with the smaller powers of 3 to see what kinds of remainders we get:

Power of 3 | Value | Remainder |

3^{1} |
3 | 3 |

3^{2} |
9 | 4 |

3^{3} |
27 | 2 |

3^{4} |
81 | 1 |

3^{5} |
243 | 3 |

By now, with the repetition of the 1 as a remainder, we should begin to think we might have found the pattern. It seems that the only possible remainders when a power of 3 is divided by 5 are: 3, 4, 2, 1.

Let’s take a look at a couple more just to confirm:

Power of 3 | Value | Remainder |

3^{6} |
729 | 4 |

3^{7} |
2187 | 2 |

This repetition is enough to allow us to consider the pattern set. Thus, our pattern is 3, 4, 2, 1, which comprise our pattern unit.

The next step is to apply what we know about the pattern to 3^{43}. Since our pattern unit has 4 elements, we should find the closest multiple of 4 we can to the number 3^{43}; that number is 3^{40}, which we would now know has a remainder of 1.

Thus, we can use our pattern for the last three powers:

Power of 3 | Remainder |

3^{41} |
3 |

3^{42} |
4 |

3^{43} |
2 |

From this we see that our remainder when 3^{43} is divided by 5 is 2.

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