Tyler York

June 3, 2023

In this video, Achievable GRE course author Matt Roy explains how to use number properties to automatically eliminate answer choices in multiple choice questions. He will show you how to determine if a sum or product must be odd or even and how to handle prime numbers.

Try this odds, evens, and prime numbers problem yourself in our GRE prep course.

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00:00:03 This next problem is a number properties problem in disguise. So the problem asks which of the following could be the sum of two different prime numbers that are both greater than two. Well let's first ask ourself what are those numbers? Well the first one is 3, then 57111317 and so on so. 00:00:27 We don't actually have to check though the sum of all of these different prime numbers together to check which ones add up to these possible answers. So what could we do? Well, first we need to understand that all prime numbers greater than two are odd. So really what we're asking here is what is the sum of 2 odd numbers? 00:00:58 The reason why that is important is because if you look at the list, you can see that many of them most of them are odd and only two of them are even. And we know for sure from number understanding number properties that an odd number plus an odd number is guaranteed to be even if you wanted to check that. 00:01:27 You can just ask yourself, is 1 + 1 odd or even? Well, it's obviously two. That works with multiplication as well and subtraction. If you ever wanted to know if the sum or the the product of two different numbers was odd or even, just ask yourself, is one or two replacing the odd number or the even number? 00:01:55 Does that give you a solution that's odd or even? It is going to be consistent across all numbers, no matter how big it is. Any odd number plus any other odd number is guaranteed to be even. That's the point, because 1 + 1 is 2. While looking at the answer choices, we can see that there are only two of them that are actually even, the number four and the number 14. Well, four is the sum of. 00:02:24 Two and two, which is a prime number, but it asks for two different prime numbers. Another point though is it doesn't just ask for two different prime numbers, it also asks for prime numbers that are greater than two. Well, that that leaves out four. That really just leaves us with 14 and. 00:02:51 The final point I want to make is in the GRE, oftentimes you can you can logically determine what the answer must be without even knowing exactly why it's that answer. You know, we didn't even check which are the two prime numbers that add up to 14. But we can know for sure through process of elimination that 14 must be the answer because we've eliminated all odd answers and we've eliminated 4 but. 00:03:21 Just so you know, the two prime numbers are three and 11.

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