Integers and Mental Math

What better way to spend the weekend than with your favorite friends: integers? Okay, maybe integers aren’t your best friends. But trust me, they are much better company than irrational numbers.

Below are five problems dealing with integers and integer properties. They are definitely not too challenging. In fact, many can be solved using mental math. That’s right: see if you can do any (or all) of the following problems in your head. Doing so will be a great way to see if your mental math skills are up to snuff. And, even if you miss a few, don’t worry—there will be scratch paper on the exam.

1. How many odd integers less than 100 are a multiple of 3 and a multiple of 5?

(A)  3

(B)  4

(C)  7

(D) 10

(E)  15

2. 5 times n is three less than twice n. What number is three less than twice n?

(A)  -5

(B)  -2

(C)  -1

(D) 3

(E)  5

3. When p is divided by 7, the remainder is 4. When p is divided by 4, the remainder is 1. How many different values of p are less than 120?

(A)  2

(B)  4

(C)  5

(D) 11

(E)  18

4. How many factors of 6! are greater than 100?

(A)  4

(B)  5

(C)  7

(D) 10

(E)  12

5. The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the series?

(A)  7

(B)  4

(C)  2

(D) 1

(E)  -2

1. A
2. A
3. B
4. B
5. D

Special Note:

To find out where integers sit in the “big picture” of GRE Quant, and what other Quant concepts you should study, check out our post entitled:

What Kind of Math is on the GRE? Breakdown of Quant Concepts by Frequency

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  • Chris Lele

    Chris Lele is the Principal Curriculum Manager (and vocabulary wizard) at Magoosh. Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He's been quoted as a subject expert in many publications, including US News, GMAC, and Business Because. In his time at Magoosh, Chris has taught countless students how to tackle the GRE, GMAT, SAT, ACT, MCAT (CARS), and LSAT exams with confidence. Some of his students have even gone on to get near-perfect scores. You can find Chris on YouTube, LinkedIn, Twitter and Facebook!