Sample QuestionsPlaying with Numbers questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Mark $(\checkmark)$ against the correct answer: If $6\times5$ is exactly divisible by $9,$ then the least value of $x$ is
Answer: C.
View full solution →Tick $(\checkmark)$ the correct answer of following. If the $4-$digit number $x27y$ is exactly divisible by $9,$ then the least value of $(x + y)$ is:
Answer: D.
View full solution →Mark $(\checkmark)$ against the correct answer: If $x48y$ is exactly divisible by $9$ then the least value of $(x + y)$is:
Answer: C.
View full solution →Tick $(\checkmark)$ the correct answer of following. If $1A2B5$ is exactly divisible by $9,$ then the least value of $(A + B)$ is:
Answer: B.
View full solution →Tick $(\checkmark)$ the correct answer of following. If $4xy7$ is exactly divisible by $3,$ then the least value of $(x + y)$ is:
Answer: A.
View full solution →Assertion (A): If a number is divisible by 18 it is divisible by each one of 2, 3, 6 and 9. Reason (R): A number divisible by $n$ is divisible by each of the factors of $n$.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Assertion (A): If $31 a 2$ is divisible by 6 then $a$ has 3 possible values.
Reason (R): For a number to be divisible by 6 it must be divisible by both 2 and 3 .
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): If $N \div 5$ leaves remainder 3 and $N \div 2$ leaves remainder 0 then $N \div 10$ leaves remainder 4.
Reason (R): $N$ is a multiple of 2 and leaves remainder 3 when divided by 5.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): The sum of a two-digit number and the number obtained by reversing the digits is always divisible by 11.
Reason (R): The difference of a two-digit number and the number obtained by reversing the digits is always divisible by 9.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: B.
View full solution →Assertion (A): Every three-digit number consisting of three identical digits is divisible by each one of 3, 37 and 111 .
Reason (R): $100 a+10 a+a=111 a$, which is clearly divisible by each one of 3, 37 and 111.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Find two numbers whose product is a $1-$digit number and the sum is a $2-$digit number.
View full solution →Replace $A, B, C$ by suitable numerals:
View full solution →Test the divisibility of the following numbers by $11: 7531622$
View full solution →Replace $A, B, C$ by suitable numerals. $\underline{ \ \ \ \ 4 \ \text{C B } \ 6\\+3 \ \ 6\ \ 9\text{ A}}\\ \ \ \ \ 8\ \ 1\ \ 7\ \ 3$
View full solution →Replace $A, B, C$ by suitable numerals. $\underline{ \ \ \text{ A}\\\text{+A}\\\text{+A }}\\\underline{ \text{ BA } }$
View full solution →Find all possible values of $x$ for which the $4-$digit number $320x$ is divisible by $3.$ Also, find the numbers.
View full solution →Find the values of $A, B, C$ when
View full solution →In a two-digit number, the digit at the units place is double the digit in the tens place. The number exceeds the sum of its digits by $18.$ Find the number.
View full solution →Replace $A, B, C$ by suitable numerals. $ \ \ \ \ \ \ \text{AB}\\\underline{ \ \ \ \times \ 3}\\\underline{ \ \ \text{CAB}}$
View full solution →Give five examples of numbers, each one of which is divisible by $3$ but not divisible by $9.$
View full solution →Replace $A, B, C$ by suitable numerals.
$ \ \ \ \ \ \ \ \ \ \ \ \text{A B}\\\underline{ \ \ \ \ \ \ \times\text{B A}}\\\underline{\text{(B+1)}\text{C B}}$
View full solution →The sum of the digits of a two-digit number is $15$. The number obtained by interchanging its digits exceeds the given number by $9$. Find the original number.
View full solution →a, b, c are three different nonzero digits. Using these digits, different numbers are formed.
(1) If $a>b>c$ then the difference of three-digit number $a b c$ and the number obtained by reversing the digits is always divisible by
(a) 9 only$\quad$(b) 11 only$\quad$(c) both 9 and 11$\quad$(d) none of 9 and 11
(2) How many different three-digit numbers can be formed using the given digits it being given that repetition of digits is not allowed?
(a) 3$\quad$(b) 4$\quad$(c) 6$\quad$(d) 9
(3) The sum of all possible three-digit numbers formed above, is always divisible by
(a) 2 only$\quad$(b) 37 only$\quad$(c) 111 only$\quad$(d) each one of 2, 37 and 111
(4) Which of the following is not true?
(a) The number $a a b b$ is divisible by 11$\quad$
(b) The number $a b a b$ is divisible by 101$\quad$
(c) The number $a a b b c c$ is divisible by 11$\quad$
(d) The number $a b c a b c$ is divisible by 101
View full solution →Test the divisibility of the following numers by $3:$
$591282$
View full solution →Test the divisibility of the following numbers by $10: 90$
View full solution →Test the divisibility of the following numbers by $11:22222$
View full solution →Test the divisibility of the following numbers by $10: 205$
View full solution →Test the divisibility of the following numbers by $8:66664$
View full solution →