Quantitative Aptitude

Number System

616 Questions
All HCF and LCM Word Problems 416 Remainder Theorems 122 Number Properties and Series 21 Successive Division 20 Divisibility Rules 19 Digit Word Problems 9 Decimal and Fraction Operations 6 Unit Digit and Last Digits 2 BODMAS Simplification 1

Number System Questions

Multiple choice

Directions: Read the given statements and select the most appropriate option. Statement-I: If the sum of remainders obtained when 38,64,335 divisible by 382 and 300 is twice the remainder when a least four-digit number is divisible by 32, then that number is 1,021 Statement-II: 45! - 1 is a prime number.

  1. Statement-I is false, but statement-II is true.

  2. Both statement-I and statement-II are true.

  3. Statement-I is true, but statement-II is false.

  4. Both statement-I and statement-II are false.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement-I is true: the remainder calculation for 1021 satisfies the condition. Statement-II is false because 45! - 1 is not necessarily prime; for example, 45! is divisible by many primes less than 45, and 45! - 1 is not guaranteed to be prime.

Multiple choice

The sum of all two digit numbers that that give a remainder 2 when divided by 7 is

  1. 652

  2. 654

  3. 658

  4. 690

  5. 696
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The two-digit numbers giving a remainder of 2 when divided by 7 are of the form 7n + 2. The sequence is 16, 23, ..., 93. This is an arithmetic progression with first term 16, last term 93, and common difference 7. The number of terms is (93-16)/7 + 1 = 12. The sum is (12/2) * (16 + 93) = 6 * 109 = 654.

Multiple choice

Directions : The question below is followed by two statements numbered I and II. Study the data provided in the two statements I and II along with the information given in the question and determine which statement/s is/are sufficient to answer the question by selecting the most appropriate option. What is the remainder when a six - digit number A1BC25 is divided by 625? I. A three - digit number ABC is divisible by 125. II. The remainder when a three - digit number ABC is divided by 100 is 45.

  1. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

  2. The question can be answered by using either of the statements alone.

  3. The question can be answered by using both statements together, but cannot be answered using either of the statements alone.

  4. The question cannot be answered even by using both statements together.

  5. 5
Reveal answer Fill a bubble to check yourself
B Correct answer