**Additional Practice**

NOTE: In each of the above video lessons, you’ll find a **Reinforcement Activities** box containing several practice questions that are specifically related to the concepts covered in that lesson (e.g., the lesson on remainders). Conversely, the practice questions below cover a variety of topics under the umbrella of GMAT Integer Properties, and are intended for general reinforcement.

Given this, you may find it beneficial to work on the questions below __after__ you’ve mastered the module content by watching the video lessons and answering concept-specific practice questions from the Related Resources boxes. For more on this learning strategy, visit our course overview page.

__Problem Solving__** (level of difficulty: 350 to 500) **

Rhyming primes (prime numbers)

Prime factors (prime factorization)

Product wxyz (prime factorization)

Even and odd m-values (integer properties, strange operators)

__Problem Solving__** (level of difficulty: 500 to 650)**

NOT a divisor of x (divisibility, algebra)

Must be divisor of n (divisibility, remainders)

Multiple of 990 (divisibility)

GCD of 35x and 20y (divisibility)

Prime factors (divisibility)

Number of zeros (prime factorization)

Bag of chips (prime factorization)

__Problem Solving__** (level of difficulty: 650 to 800)**

Possible values of 2x + y (remainders)

Smallest value of x+y+z (remainders)

x is a factor of 2y (divisibility)

From 10! to 10! + 20 (divisibility)

__Data Sufficiency__** (level of difficulty: 350 to 500)**

Looking for an even product (integer properties)

Checking whether b is negative (divisibility, powers)

Is 4 + n/6 an integer? (divisibility)

Find the value of r (remainders)

__Data Sufficiency__** (level of difficulty: 500 to 650)**

Is x a multiple of y? (divisibility)

Looking for an integer (divisibility)

Is z even? (divisibility)

When k is divided by 10 (divisibility)

Find value of K (divisibility)

Value of xy (divisibility)

Is N odd? (integer properties, divisibility)

Is n divisible by 6? (divisibility)

Looking for a prime (divisibility)

__Data Sufficiency__** (level of difficulty: 650 to 800)**

Product divisible by 8 (divisibility, probability)

Integer root (integer properties, roots)

Value of positive integer m (divisibility, remainders)

GCD of m and n (divisibility)

Multiple of 18 (divisibility)

Is y prime? (divisibility)

**Practice from the Official Guides**

**Official Guide for GMAT Review (2018 edition)**

Problem Solving: 44, 46, 54, 62, 73, 81, 98, 121, 126, 136, 141, 154, 165, 175, 176, 178, 181, 195, 205

Data Sufficiency: 271, 277, 278, 285, 293, 317, 328, 329, 354, 356, 357, 390

**Official Guide for GMAT Review (2017 edition)**

Problem Solving: 40, 42, 48, 54, 62, 105, 108, 119, 122, 134, 149, 158, 159, 161, 168, 190, 200, 225

Data Sufficiency: 266, 270, 275, 300, 304, 314, 315, 343, 346, 347, 365, 369, 389

**Official Guide for GMAT Review (2016 edition)**

Problem Solving: 35, 38, 43, 48, 93, 96, 106, 108, 118, 132, 140, 141, 143, 151, 177, 190, 209, 222, 223

Data Sufficiency: 3, 9, 31, 36, 60, 72, 99, 102, 121, 125, 149, 174

**Official Guide for GMAT Review (2015/13th edition)**

Problem Solving: 5, 26, 40, 44, 74, 77, 87, 95, 110, 116, 117, 118, 127, 155, 174, 204, 218, 219, 221, 225

Data Sufficiency: 7, 14, 27, 32, 58, 72, 80, 83, 111, 135, 173

While answering practice questions from the *Official Guide for GMAT Review *(2018, 2017, 2016 or 2015), you can enter your responses directly into our downloadable **Improvement Chart**. This will help track your progress and identify areas of weakness.