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\ 06-Jan-2025 Surendra Prajapati Proof-6 Reader’s Sign _______________________ Date __________

Chapter assessment
A. Choose the correct option.

1. The difference of a three-digit number abc and the number obtained by interchanging its ones and
hundreds digits such that a and c are non-zero and c  b  a is not divisible by
(a) 3 (b) 9 (c) 11 (d) 37
2. If x + y + z = 6 and z is an odd digit, then the 3-digit number xyz is

(a) an odd multiple of 3 (b) an odd multiple of 6
(c) an even multiple of 3 (d) an even multiple of 9
3. For what value of x, a number of the form (x × 100 + 6 × 10 + 8) is divisible by 3?

(a) 5 (b) 8 (c) 7 (d) 9
4. Which of the following numbers is divisible by 21?
(a) 2359 (b) 2595 (c) 2706 (d) 672

5. In a certain code language KING is written as 41. In the same code language, QUEEN will be written
as

(a) 62 (b) 57 (c) 67 (d) 66
B. Assertion and Reason Type Questions.
In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a 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.

1. Assertion (A): If the number 1x5 is divisible by 3, then x is equal to 0 or 3 or 6 or 9.
Reason (R): As per the divisibility rule of 3, any big number is exactly divisible by 3 if the sum
of the digits is a multiple of 3.
2. Assertion (A): If the number 7y9 is a multiple of 9, then y = 2.
Reason (R): As per the divisibility rule of 9, any number greater than 10 is exactly divisible by 9
if the sum of the digits is a multiple of 9.
3. Assertion (A): If the three-digit number 6y8 is divisible by 3, then the value of y is 1 or 4 or 7.

Reason (R): A number is divisible by 3, if the sum of the digits is a multiple of 3 or if the sum of
its digits is divisible by 3.
4. Assertion (A): The number 57204 is divisible by 9.
Reason (R): A number is divisible by 9, if the sum of the digits is a multiple of 9 or if the sum of
its digits is divisible by 9.
C. Fill in the blanks.

1. Generalised form of a 3-digit number ‘abc’ is ............... .
2. Without performing actual division and addition, the quotient when the sum of 81 and 18 is divided
by 11 is ............... .

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