Page 313 - Start Up Mathematics_8 (Non CCE)

Problems Related to Thinking Skills

1. The given figure shows a 3 × 3 grid. Place the digits 0–9 in squares such that the
sum of each row and each column is different.

2 3 ?
1
2. 4 3 2 4 2
3 5 6

The given set of figures shows the same die from different angles. Which number should come in
place of the question mark?
3. Which is the least three-digit number that is divisible by 13 but is not divisible by 2, 3, 5, 7 or 11?

AT a Glance

1. A 2-digit number ab can be expressed in generalized form as 10a + b.
2. The sum of a 2-digit number ab and the number obtained by reversing the digits, when divided by
(a) a + b gives quotient as 11. (b) 11 gives quotient as a + b.
3. If ab is a 2-digit number, then ab – ba, when divided by
(a) a – b gives remainder as 9. (b) 9 gives remainder as a – b.
4. A 3-digit number abc can be expressed in generalized form as 100a + 10b + c.
5. For a 3-digit number abc, abc + bca + cab equals 111 (a + b + c) or 3 × 37 × (a + b + c).
6. For a 3-digit number abc, abc – cba = 99 × (a – c) or 9 × 11 × (a – c).
7. A number is divisible by 2 if its ones digit has 0, 2, 4, 6 or 8.
8. A number is divisible by 3 if the sum of its digits is divisible by 3.
9. A number is divisible by 4 if the number formed by the tens and ones digits is divisible by 4 or the digits
at tens and ones place are both 0.
10. A number is divisible by 5 if the ones digit of the number is either 0 or 5.
11. A number is divisible by 6 if it is divisible by both 2 and 3.
12. A number is divisible by 9 if the sum of its digits is divisible by 9.
13. A number is divisible by 10 if the digits at its ones place is 0.
14. A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of
its digits at even places is either 0 or a multiple of 11.

Review Exercises

Multiple ChoiCe Questions
1. If A × C × AC = CCC, where A and C are different digits, then the values of A and C are:
(a) A = 3, C = 7 (b) A = 7, C = 3 (c) A = 4, C = 7 (d) A = 7, C = 4
2. If * and o are two operations such that a * b = a × b + 2 and a o b = a + b – 1, then the value of
{(3 * 3)*3} o 3 is:
(a) 35 (b) 37 (c) 38 (d) 39
3. If abc is a 3-digit number, then abc – cba when divided by 99 will give quotient as:
(a) a – c (b) a + b (c) b + c (d) b – c
4. If abc is a 3-digit number, then abc + bca + cab when divided by 37 will give quotient as:
(a) a + b + c (b) 111 (c) 3(a + b + c) (d) a – b – c
5. For a 2-digit number ab, ab – ba when divided by a – b, gives quotient as:
(a) 111 (b) 99 (c) 11 (d) 9

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