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Is K not prime?

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by KylieAquino87 » Wed Apr 09, 2014 9:28 pm
Hello all,

I just finished watching the Magoosh prep video on DS rephrasing, and their last example was the following problem:

"If k is an integer greater than 1, and S is the sum of all positive divisors of k, is S>k+1?"

The rephrase as displayed on the video was "Is k not prime?"

The logic behind this rephrase was not expounded upon and I'm stumped trying to figure it out...

Any tips or other insight would be greatly appreciated!

Milles mercis !
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Source: — Data Sufficiency |

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by [email protected] » Wed Apr 09, 2014 10:21 pm
Hi KylieAquino87,

This DS question (like many DS questions) is based on a Number Property.

The term "prime number" refers to a positive integer that is divisible by just 2 things: itself and the number 1.

Here are some primes: 2, 3, 5, 7, 11....

Since most numbers are NOT prime, they have additional factors.

For example, the factors of 8 are 1, 2, 4 and 8

This means that when you sum up all the factors (divisors) of a number, you'd get a total that is GREATER than that number + 1. With prime numbers however, you would get a sum that was EQUAL to that number + 1.

In this question, if K = 8, then S = 1+2+4+8 = 15 and the answer to the question would be YES
In this question, if K = 2, then S = 1+2 = 3 and the answer to the question would be NO.

In effect, it's asking whether K is a prime number or not.

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Rich
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