GMAT Math Sample Questions  Number Theory
You may get three to five questions from Number systems, number properties and number theory in the GMAT quant section  in both variants viz., problem solving and data sufficiency. The concepts tested include LCM, HCF, perfect squares, prime factorization, number of factors, remainders, factorials, odd and even numbers. A collection of GMAT practice questions in number system and number properties is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.
If both 11^{2} and 3^{3} are factors of the number a * 4^{3} * 6^{2} * 13^{11}, then what is the smallest possible value of a?
 121
 3267
 363
 33
 None of the above
 Correct AnswerChoice (C).
The smallest value possible for 'a' is 363. Correct answer  Explanatory Answer
 Factors & Divisibility
 Medium
How many different positive integers exist between 10^{6} and 10^{7}, the sum of whose digits is equal to 2?
 6
 7
 5
 8
 18
 Correct AnswerChoice (B).
7 such positive integers exist. Correct answer  Explanatory Answer
 Number Properties
 Easy
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
 13
 59
 35
 37
 12
 Correct AnswerChoice (D).
The value of the divisor is 37. Correct answer  Explanatory Answer
 Divisors & Remainders
 Medium
How many keystrokes are needed to type numbers from 1 to 1000?
 3001
 2893
 2704
 2890
 None of these
 Correct AnswerChoice (B).
2893 keystrokes are required. Correct answer  Explanatory Answer
 Counting Methods
 Easy
When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. When the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
 11
 17
 13
 23
 None of these
 Correct AnswerChoice (C).
The value of the divisor is 13. Correct answer  Explanatory Answer
 Remainders & Divisors
 Medium
How many integral divisors does the number 120 have?
 14
 16
 12
 20
 None of these
 Correct AnswerChoice (B).
120 has 16 integral divisors. Correct answer  Explanatory Answer
 Number of Divisors
 Medium
How many trailing zeros will be there after the rightmost nonzero digit in the value of 25! (factorial 25)?
 25
 8
 6
 5
 2
 Correct AnswerChoice (C).
There are 6 trailing zeroes in 25!. Correct answer  Explanatory Answer
 Factorials
 Medium
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
 3
 27
 30
 21
 18
 Correct AnswerChoice (C).
The remainder is 30. Correct answer  Explanatory Answer
 Remainders
 Medium
Data Sufficiency : Is x^{3} > x^{2} ?
 x > 0
 x < 1
 Correct AnswerChoice (B).
Statement 2 alone is sufficient; statement 1 is not. Correct answer  Explanatory Answer
 Indices
 Medium
Data Sufficiency : Is a terminating decimal?
 x is a multiple of 2
 y is a multiple of 3
 Correct AnswerChoice (E).
The two statements together are NOT sufficient. Correct answer  Explanatory Answer
 Terminating Decimals
 Medium
Data Sufficiency : Is the positive integer X divisible by 21?
 When X is divided by 14, the remainder is 4
 When X is divided by 15, the remainder is 5
 Correct AnswerChoice (D).
EACH statement ALONE is sufficient. Correct answer  Explanatory Answer
 Test of Divisibility
 Easy
Data Sufficiency : If x and y are positive integers, is y odd?
 x is odd.
 xy is odd.
 Correct AnswerChoice (B).
Statement 2 alone is sufficient; statement 1 is not. Correct answer  Explanatory Answer
 Odd and even integers
 Easy
Data Sufficiency : Is xy < 0?
 5x + y = 0
 x + 5y = 0
 Correct AnswerChoice (D).
EACH statement ALONE is sufficient. Correct answer  Explanatory Answer
 Absolute values
 Medium
Data Sufficiency : When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?
 When 2x is divided by d, the remainder is 23.
 When 3x is divided by d, the remainder is 22.
 Correct AnswerChoice (A).
Statement 1 alone is sufficient; statement 2 is not. Correct answer  Explanatory Answer
 Divisors & Remainders
 Hard
Data Sufficiency : How many of the numbers x, y, and z are positive if each of these numbers is less than 10?
 x + y + z = 20
 x + y = 14
 Correct AnswerChoice (A).
Statement 1 alone is sufficient; statement 2 is not. Correct answer  Explanatory Answer
 Number Properties
 Medium
Free GMAT Prep Questions
 Algebra
 Sequences & Series
 Statistics
 Inequalities
 Geometry
 Mensuration
 Coordinate Geometry
 Number Properties & Theory
 Percents
 Permutation & Probability
 Profits
 Quadratic Equations
 Ratio Proportion
 Sets
 Simple & Compound Interest
 Rates : Speed distance time
 Rates : Work time
 Data sufficiency
 Sentence Correction
 Free Quiz
Next GMAT Batches @ Chennai

July 16, 2016
 Weekend Morning Batch
 Class Timings
 Sat: 10:30 AM to 1:30 PM
 Sun: 10:30 AM to 1:30 PM
 Fees : Rs.17,500
Aug 13, 2016
 Weekend Morning Batch
 Class Timings
 Sat: 10:30 AM to 1:30 PM
 Sun: 10:30 AM to 1:30 PM
 Fees : Rs.17,500
Contact Us
4GMAT  GMAT Classes
II floor, Kanya West Wing
48/1 Velachery Taramani Road
Velachery. Chennai 600042.
Contact : Mr. Baskar
Call 95000 48484
Center Open: Sat and Sun: 10 AM to 7:30 PM. 
June 25, 2016
 'SundayOnly' Batch
 Class Timings
 Session 1: 6:30 AM to 9:30 AM
 Session 2: 10:30 AM to 1:30 PM
 Fees : Rs.17,500
June 30, 2016
 Weekday  Morning Batch
 Class Timings
 Monday to Friday: 6:30 AM to 9:30 AM
 Duration: 5 weeks
 Fees : Rs.17,500
Contact Us
4GMAT  GMAT Classes
14B/1 Dr Thirumurthy Nagar I Street
Nungambakkam
Chennai 600034.
Contact : Mr.Baskar
Call 044 4500 8484  95000 48484
Useful Links
Prep Freebies
Contact Us
4GMAT  GMAT Classes
14B/1 Dr Thirumurthy Nagar I St.
Nungambakkam, Chennai 600 034
E mail : info@4gmat.com
Phone : +91 44 4500 8484
Mobile : +91 95000 48484
@ Bangalore : +91 74060 48484
GMAT™ and GMAC™ are registered trademarks of the Graduate Management Admission Council™. The Graduate Management Admission Council™ does not endorse, nor is it affiliated in any way with the owner or any content of this web site.
Copyright 2004  16 4GMAT.COM, A division of Test Catalyst (India) Private Limited. All rights reserved.
Terms and Conditions  Privacy policy  Disclaimer