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Number Properties is a key topic on the GMAT and it's important to have a solid understanding of it. You'll encounter questions that test your ability to work with integers, multiples and factors, primes, odds and evens, and more. In this set of GMAT questions from GMAT Club Tests, you'll face 11 challenging problems that will put your number properties knowledge to the test. Good luck!
1. If x is an integer, what is the value of x?
(1) |23x| is a prime number
(2) \(2\sqrt{x^2}\) is a prime number.
2. If a positive integer n has exactly two positive factors what is the value of n?
(1) n/2 is one of the factors of n
(2) The lowest common multiple of n and n + 10 is an even number.
3. If 0 < x < y and x and y are consecutive perfect squares, what is the remainder when y is divided by x?
(1) Both x and y is have 3 positive factors.
(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers
4. If each digit of the positive three-digit integer \(k\) is a positive multiple of 4, what is the value of \(k\)?
(1) The units digit of \(k\) is the least common multiple of the tens and hundreds digits of \(k\).
(2) \(k\) is NOT a multiple of 3.
5. If a, b, and c are integers and a < b < c, are a, b, and c consecutive integers?
(1) The median of {a!, b!, c!} is an odd number.
(2) c! is a prime number
6. Set S consists of more than two integers. Are all the numbers in set S negative?
(1) The product of any three integers in the list is negative
(2) The product of the smallest and largest integers in the list is a prime number.
7. Is x the square of an integer?
(1) When x is divided by 12 the remainder is 6
(2) When x is divided by 14 the remainder is 2
8. List A consist of 10 terms, each of which is a reciprocal of a prime number, is the median of the list less than 1/5?
(1) Reciprocal of the median is a prime number
(2) The product of any two terms of the list is a terminating decimal
9. If [x] denotes the greatest integer less than or equal to x for any number x, is [a] + = 1 ?
(1) ab = 2
(2) 0 < a < b < 2
10. If N = 3^x*5^y, where x and y are positive integers, and N has 12 positive factors, what is the value of N?
(1) 9 is NOT a factor of N
(2) 125 is a factor of N
BONUS QUESTION:
11. If x and y are positive integers, is x a prime number?
(1) |x - 2| < 2 - y
(2) x + y - 3 = |1-y|
The solutions can be found below on this page.
Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.
DS questions in GMAT Focus encompass various types of word problems, such as:
[/b]
While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."
Check GMAT Syllabus for Focus Edition
You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.
So, you can ignore these questions. The topic is locked.
Hope it helps.
1. If x is an integer, what is the value of x?
(1) |23x| is a prime number
(2) \(2\sqrt{x^2}\) is a prime number.
2. If a positive integer n has exactly two positive factors what is the value of n?
(1) n/2 is one of the factors of n
(2) The lowest common multiple of n and n + 10 is an even number.
3. If 0 < x < y and x and y are consecutive perfect squares, what is the remainder when y is divided by x?
(1) Both x and y is have 3 positive factors.
(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers
4. If each digit of the positive three-digit integer \(k\) is a positive multiple of 4, what is the value of \(k\)?
(1) The units digit of \(k\) is the least common multiple of the tens and hundreds digits of \(k\).
(2) \(k\) is NOT a multiple of 3.
5. If a, b, and c are integers and a < b < c, are a, b, and c consecutive integers?
(1) The median of {a!, b!, c!} is an odd number.
(2) c! is a prime number
6. Set S consists of more than two integers. Are all the numbers in set S negative?
(1) The product of any three integers in the list is negative
(2) The product of the smallest and largest integers in the list is a prime number.
7. Is x the square of an integer?
(1) When x is divided by 12 the remainder is 6
(2) When x is divided by 14 the remainder is 2
8. List A consist of 10 terms, each of which is a reciprocal of a prime number, is the median of the list less than 1/5?
(1) Reciprocal of the median is a prime number
(2) The product of any two terms of the list is a terminating decimal
9. If [x] denotes the greatest integer less than or equal to x for any number x, is [a] + = 1 ?
(1) ab = 2
(2) 0 < a < b < 2
10. If N = 3^x*5^y, where x and y are positive integers, and N has 12 positive factors, what is the value of N?
(1) 9 is NOT a factor of N
(2) 125 is a factor of N
BONUS QUESTION:
11. If x and y are positive integers, is x a prime number?
(1) |x - 2| < 2 - y
(2) x + y - 3 = |1-y|
The solutions can be found below on this page.
Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.
DS questions in GMAT Focus encompass various types of word problems, such as:
[/b]
- Word Problems
- Work Problems
- Distance Problems
- Mixture Problems
- Percent and Interest Problems
- Overlapping Sets Problems
- Statistics Problems
- Combination and Probability Problems
While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."
Check GMAT Syllabus for Focus Edition
You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.
So, you can ignore these questions. The topic is locked.
Hope it helps.
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
25 Mar 2013, 07:03
Kudos
Bookmarks
If x is an integer, what is the value of x?
(1) |23x| is a prime number
Since 23 si prime,\(x\)can be \(+1\) or \(-1\)
not sufficient
(2) 2\sqrt{x^2} is a prime number.
once again \(x\) can be \(+1\) or \(-1\)
not sufficient
And since 1)+2) provides no new info IMO E
(1) |23x| is a prime number
Since 23 si prime,\(x\)can be \(+1\) or \(-1\)
not sufficient
(2) 2\sqrt{x^2} is a prime number.
once again \(x\) can be \(+1\) or \(-1\)
not sufficient
And since 1)+2) provides no new info IMO E
25 Mar 2013, 07:24
Kudos
Bookmarks
6. Set S consists of more than two integers. Are all the numbers in set S negative?
(1) The product of any three integers in the list is negative
Not sufficient
Example: \(S = {-1,3,5}\)
the product is always <0 but 2 numbers are positive
Example: \(S = {-1,-3,-5}\)
the product is always <0 and all numbers are negative
(2) The product of the smallest and largest integers in the list is a prime number.
Not sufficient
Example: \(S = {1,3,5}\)
\(1*5=5\) prime but all positive
Example: S = \({-1,-3,-5}\)
\(-1*-5=5\) prime but all negative
(1)+(2) Sufficient IMO C
Using statement 2 we know that all are positive or all are negative, using statement 1 we know that "at least" 1 is negative=> so all are negative
(1) The product of any three integers in the list is negative
Not sufficient
Example: \(S = {-1,3,5}\)
the product is always <0 but 2 numbers are positive
Example: \(S = {-1,-3,-5}\)
the product is always <0 and all numbers are negative
(2) The product of the smallest and largest integers in the list is a prime number.
Not sufficient
Example: \(S = {1,3,5}\)
\(1*5=5\) prime but all positive
Example: S = \({-1,-3,-5}\)
\(-1*-5=5\) prime but all negative
(1)+(2) Sufficient IMO C
Using statement 2 we know that all are positive or all are negative, using statement 1 we know that "at least" 1 is negative=> so all are negative
