Class 8 Playing with Numbers

Transcription

1 ID : in-8-playing-with-numbers [1] Class 8 Playing with Numbers For more such worksheets visit Answer the questions (1) If a number is divided by 5, remainder is 4. What should be the last digit of the number? (2) Find the value of Q following multiplication. 1 Q Q 7 Q (3) The cost of a ball is a two digit number (for example Rs. xy). Its selling prices has same digits as cost with digits interchanged (Rs. yx). If its profit margin is divided by 9, find the remainder of division. (4) Find the value of A and B, from following summation. A B 6 A (5) Ram's roll number is a two digit number. His friend Saina's roll number has the same digits as Ram's roll number, but with digits interchanged. If they add their roll number, and divide the sum by 11. Find the remainder of this division. (6) Find the value of A and B, from following summation. A B A (7) Find the one's digit of the cube of (8) {a m } is a sequence of integers such that a 1 = 1, and and a m+n = a m + a n + mn, for all positive integers m and n. What is the value of a 15? (9) If a number is divided by 5, remainder is 1. If same number is divided by 2, remainder is 0. What should be the last digit of the number? (10) Lovleen picks a three digit number and subtract it from the same number after reversing order of its digits. If this difference is divided by 11, find the remainder. (11) If 86y9892 is a seven digit number which is divisible by 9, find the smallest value of y.

2 (12) Find the value of A and B, from following summation. ID : in-8-playing-with-numbers [2] 8 B + A A Choose correct answer(s) from the given choices (13) Sulekha picks a three digit number and subtract it from the same number after reversing order of its digits. This difference will always be fully divisible by which of following number? a. 18 b. 11 c. 24 d Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : in-8-playing-with-numbers [3] (1) 4 or 9 This solution can be explained by an example. If 14 is divided by 5, the remainder is 4. If 19 is divided by 5 then the remainder is also 4. So the last digit could be 4 or 9 A simple way of remembering it is that the last digit when a number is divided by 5 could be the remainder itself (4) or the 5 + remainder(9). (2) Q = 5 Since we see that one's digit of the product of Q * Q, is Q, so the possible options of Q is 1, 5, 6. We can see that it is not a case of 1, as the same number is not being replicated as the product. So the possible options are 5 or 6. If it is 5, we know the carryover will be 2 as 5*5 = 25. So we check if 5 *1 + 2 = 7. Here it is equal so, Q = 5. (3) 0 Let the cost of ball is Rs. xy. Another way of depicting the cost is 10x + y. So the selling price of the ball will be Rs. yx. Another way of depicting the selling price is 10y + x. So the profit is Selling Price - Cost price. The difference between the two prices would be 9x-9y or 9y-9x. So the price would be 9(x-y) or 9(y-x), which would be a multiple of 9. Step 4 Therefore the remainder when divided by 9 will always be 0. For example - if cost is Rs. 46, then selling price will be Rs. 64. So profit will be = 18. Since 18 is a multiple of 9, so the remainder when divided by 9 will be 0.

4 (4) A = 2, B = 4 ID : in-8-playing-with-numbers [4] We will first evaluate A. We know A + 3 = 6. So A can be 3 or 2 (if the case of carryover). Since 3 and 2 is less than that of 8, we know it is a case of carryover. So A = 2. So B +8 = Therefore B = 4 (5) 0 Let Ram's roll number be xy. Another way of depicting this is 10x + y. So the roll number of Saina will be yx. Another way of depicting it is 10y + x. So the sum of their roll numbers would be 11x + 11y or 11(x+y),which is a multiple of 11. Step 4 So the remainder will always be 0 when divided by 11. (6) A = 4, B = 2 We will first evaluate A. We know A + 9 = 13. So A can be 4 or 3 (if the case of carryover). Since 4 and 3 is greater than or equal to that of 2, there is no carryover. So A= 4. So B + 2 = 4. Therefore B = 2. (7) 4 Since we have to find the one's digits of 's cube, so all we have to do is find the one's digit of the cube of the number in the one's place. In this case, the one's place is 4. So it's cube is 64. So the one's place is 4, and therefore the one's place for is also 4

5 (8) 120 ID : in-8-playing-with-numbers [5] We see that a 1 = 1 a 2 = a 1 + a = 3 a 3 = a 2 + a = 6 a 4 = a 3 + a = 10 and so on... Seeing the sequence we can find out the pattern, which is (num)*(num+1)/2. So the value of a 15 is 15*(15+1)/2 = 120. (9) 6 We know that when a number is divided by 5 the last digit could be the remainder itself(1) or 5 + remainder (6). We know that if remainder when number is divided by 2 is 0, then the number is even. Therefore the last digit of the number should be even and therefore the answer is 6. (10) 0 Let the number be xyz. Another way of depicting it 100x+10y+z. So when we reverse it, the number would be zyx. Another way of depicting it is 100z+10y+x. When we subtract these two numbers, we get 99x-99z or 99z-99x, which is 99(x-z) or 99(z-x) Step 4 This is a multiple of 9,11,99. So the remainder when divided by 11 is always 0.

6 (11) 3 ID : in-8-playing-with-numbers [6] The divisibility rule of 9 states that a number is divisible by 9, if the sum of digits of the number is a multiple of 9. So the sum of the digits should be divisible by 9. The sum of the digits turns out to be 42. So the smallest number needed to make it a multiple by 9 is 3. (12) A = 2, B = 3 We will first evaluate A. We know A + 8 = 11. So A can be 3 or 2 (if the case of carryover). Since 3 and 2 is less than that of 9, we know it is a case of carryover. So A = 2. So B +9 = Therefore B = 3 (13) b. 11