Playing with Numbers MCQ

Ans. a) 10 × 5 + 2

Explanation. Any two-digit number ab having digits a and b can be written in the form:

ab= 10 × a + b = 10a + b

Therefore, the number 73 made of digits 7 and 3 can be written as:

73= 10 × 7 + 3

Ans. c) 100b + 10c + d

Explanation: Generally, any 3-digit number bcd containing digits can be written as

bcd= 100 × b + 10 × c + d = 100b + 10c + d 

Ans. b) 100 + 20 + 8

Explanation: Since, 128 is a 3-digit number and any 3-digit number abc can be written in general form as:

abc= 100a + 10b + c

Therefore, 128 can be written as: 128= 100 × 1 + 10 × 2 + 8= 100 + 20 + 8

Ans. c) 56

Explanation: Here, the number 10 × 5 + 6 is in the general form of 10 × a + b. After comparing, we get a = 5 and b = 6. So, it can be concluded that 56 is the usual form of 10 × 5 + 6.

Ans. b) 234

Explanation: Comparing the number 2 × 100 +3 × 10 + 4 to the general form 100 × a + 10 × b + c, we get: a = 2, b = 3, c = 4. From these values, we can form the number 234 which is the usual form of 2 × 100 +3 × 10 + 4

Ans. b) 718

Explanation: The number 100 × 7 + 10 × 1 + 8 is in general form and from this generalized form we get a = 7, b = 1 and c = 8 which forms a 3-digit number 718. So, we can say that 718 is the usual form of 100 × 7 + 10 × 1 + 8.

Ans. c) 96

Explanation: Any number, whose sum of the digits is divisible by 3 is also divisible by 3. Here, the sum of the digits of the number 96 is 9 + 6= 15 which is completely divisible by 3. So, 96 is also divisible by 3.

Ans. d) 235

Explanation: if any number contains the digits 0 or 5 at its ones place, it is divisible by 5. Here, the number 235 is divisible by 5 as it has the digit 5 at ones place.

Ans. b) 658

Explanation: Any three-digit number can be reversed by interchanging the place of its digits at ones place and hundreds place. So, 856 can be reversed by interchanging the place of digits 8 at hundreds place and 6 at ones place forming the reversed number 658.

Ans. a) 8

Explanation: The sum of digits at ones place R + 3 will give the digit 1 at ones place only if R = 8. So, the value of R is 8.

Ans. a) A=7, B=8

Explanation: The sum A + 6 at ones place will give 3 at ones place only if A = 7. Moreover, the sum at tens place gives 1 + 4 + 3 = 8 which forms the value of B.

So, A = 7 and B = 8

Ans. d) 5

Explanation: Here, the product B x B will give B at ones place if and only if B = 5. Therefore, taking B = 5 we get

15 × 5 = 75

Ans. d) B=5, C=0, D=1

Explanation: The product C × 3 will give the same digit C at its ones place if C = 5 or C = 0. Same is true for the product B × 3 = DB. To get the result BC × 3 = DBC, we must take B = 5 and C = 0 which gives:

50 × 3 = 150.

From the above equation, we get B = 5, C = 0 and D = 1

Ans. c) 927

Explanation: Any number whose sum of the digits is divisible by both 9 and 3 is also divisible by 9 and 3. Here the number 927 is divisible by both 3 and 9 as the sum of its digits, 9 + 2 + 7 = 18, is also divisible by both 3 and 9.

Ans. c) 2

Explanation: To be completely divisible by 9, the sum of the digits of the number must be divisible by 9. Here, the sum of the digits of the number 88A is divisible by 9 if A = 2. So, the sum of the digits of the number 882 is 8 + 8 + 2 = 18, which is divisible by 9.

Ans. b) 98345

Explanation: If the sum of the digits of a number is divisible by 9 then the number is also completely divisible by 9. Otherwise, the number will not be divisible by 9. Here the sum of the digits of the number 98345 is 9 + 8 + 3 + 4 + 5 = 29. But the resultant number 29 is not divisible by 9 which implies that the number 98345 is also not divisible by 9.

Ans. d) 85

Explanation: Here the number 85 is divisible by 5 as it contains the digit 5 at its ones place.

Hence, 85 ÷ 5 = 17

Ans. d) 1235

Explanation: Any number is divisible by 10 if and only if it has the digit 0 at its ones place. Here, the number 1235 is not having the digit 0 at its ones place so, it is not divisible by 10.

Ans. c) 78

Explanation: Any number is divisible by 2 if the digit at ones place of the number is 0, 2, 4, 6, or 8. Here, the number 78 has the digit 8 at its ones place which shows that the number 78 is completely divisible by 2

Hence, 78 ÷ 2 = 39

Ans. b) 8

Explanation: If the ones digit of a number is among the numbers 0, 2, 4, 6, or 8 the number is divisible by 2. Here, the number 73X is completely divisible by 2 if and only if X = 8.

Hence, 738 ÷ 2 = 369