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

A number was divided successively in order by $4,5$ and $6$. The remainders were respectively $2,3$ and $4$. The number is:
  1. $214$
  2. $476$
  3. $954$
  4. $1908$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Successive division means N = 4 * q1 + 2, q1 = 5 * q2 + 3, and q2 = 6 * q3 + 4. Substituting the equations backward with the smallest non-negative quotient q3 = 0 gives q2 = 4, q1 = 23, and N = 94. The general solution is N = 94 + 120k for any non-negative integer k. For k = 1, we get N = 214, which is one of the options.

Multiple choice

In dividing a number by $585$, a student employed the method of short division. He divided the number successively by $5,9$ and $13$ (factors $585$) and got the remainders $4,8,12$ respectively. If he had divided the number by $585$, the remainder would have been.
  1. $24$
  2. $144$
  3. $292$
  4. $584$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the Chinese Remainder Theorem or successive division logic, the number N = 585k + R. The remainders 4, 8, 12 from 5, 9, 13 imply N = 584.

Multiple choice

Match the columns. Column-I Column-II (i) When an odd Integer 'a' is divided by $2$, then remainder r can be (p) $5$ (ii) When an integer 'a' whose unit digit is $4$ is divided by $5$, then remainder r can be (q) $1$ (iii) A whole number lying between $\sqrt{2}$ and $2\sqrt{2}$ is (r) $2$ (iv) If the digit at the units place of a number is $5$, then it is surely divisible by (s) $4$
  1. (i) $\rightarrow$ (p), (ii) $\rightarrow$ (r), (iii) $\rightarrow$ (s), (iv) $\rightarrow$ (q)
  2. (i) $\rightarrow$ (q), (ii) $\rightarrow$ (s), (iii) $\rightarrow$ (p), (iv) $\rightarrow$ (r)
  3. (i) $\rightarrow$ (p), (ii) $\rightarrow$ (r), (iii) $\rightarrow$ (q), (iv) $\rightarrow$ (s)
  4. (i) $\rightarrow$ (q), (ii) $\rightarrow$ (s), (iii) $\rightarrow$ (r), (iv) $\rightarrow$ (p)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(i) Odd integer divided by 2 leaves remainder 1. (ii) Unit digit 4 divided by 5 leaves remainder 4. (iii) Whole number between sqrt(2) (1.414) and 2*sqrt(2) (2.828) is 2. (iv) Unit digit 5 is divisible by 5.