Mental Maths<\/strong> Question 2. Multiple Choice Questions<\/strong> Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Value Based Question<\/strong> It is a sort of gambling which is against Higher Order Thinking Skills (Hots)<\/strong>
\nQuestion 1.
\nFill in the blanks:
\n(i) The sum of a 2-digit number and number obtained by reversing the digits is always divisible by 11 and ……….
\n(ii) The difference of a 2-digit number and number obtained by reversing the digits is always divisible by ………. and ……….
\n(iii) The difference of a 3=digit number a b c (a > c) and the number obtained by reversing the digits is always divisible by ………. and ……….
\n(iv) The next number of the series 0, 1, 1, 2, 3, 5, 8, 13, ………. is ……….
\n(v) The general form of a 2 digit number 57 is ……….
\n(vi) Usual form of number 100 \u00d7 7 + 10 \u00d7 4 + 1 is ……….
\n(vii) If the division N \u00f7 5 leaves remainder 4 and the division N \u00f7 2 leaves remainder 1, then unit’s digit of N must be ……….
\n(viii)If 213×52 is divisible by 9, then digit x is ……….
\nSolution:
\n(i) The sum of a 2-digit number and number obtained by
\nreversing the digits is always divisible by 11 and sum of digits.
\n(ii) The difference of a 2-digit number and number obtained by
\nreversing the digits is always divisible by 9 and difference of the digits.
\n(iii) The difference of a 3=digit number a b c (a > c)
\nand number obtained by reversing the digits is always divisible by 99 and (a – c).
\n(iv) The next number of the series 0, 1, 1, 2, 3, 5, 8, 13, is 21 and 34.
\n{\u2235 8 + 13 = 21
\n21 + 13 = 34}
\n(v) General form of a 2 digit number 57 is 10 \u00d7 5 + 7 \u00d7 1.
\n(vi) Usual form of number 100 \u00d7 7 + 10 \u00d7 4 + 1 is 100 \u00d7 7 + 10 \u00d7 4 + 1 is 741.
\n(vii) If the division N \u00f7 5 leaves remainder 4 and the division
\nN \u00f7 2 leaves remainder 1, then unit’s digit of N must be 9.
\n(viii) If 213×52 is divisible by 9, then digit x is 5.
\nSum of digits = 2 + 1 + 3 + 5 + 2 + x is divisibility 9
\n= 13 + x is divisible by 9
\n\u2234 x = 5 or 13 + 5 = 18 – 9 = 2<\/p>\n
\nState whether the following statements are true (T) or false (F):
\n(i) If the division N \u00f7 5 leaves a remainder 4, then unit’s digit of N maybe 1 or 6.
\n(ii) If the division N \u00f7 2 leaves a remainder 1, then unit’s digit of N maybe 1, 3, 5, 7 or 9.
\n(iii) If a number is divisible by any number m, then it will also be divisible by each of the factors of m.
\n(iv) If a number is divisible by sum of two numbers then it will also be divisible by each of the two numbers separately.
\n(v) If 3651x is divisble by 9, then value of digit x is 3.
\n(vi) If 42×7 is divisible by 3, then value of digit x is 4.
\n(vii) The number 152875 is divisible by 9.
\n(viii)The number 389072 is divisible by 8.
\n(ix) The number 27402 is divisible by 6.
\n(x) The number 359249 is not divisible by 11.
\nSolution:
\n(i) If the division N = 5 leaves a remainder 4,
\nthen unit’s digit of N may be 1 or 6. False
\nCorrect:
\nThe unit digit will be 4 or 9.
\n(ii) If the division N \u00f7 2 leaves a remainder 1,
\nthen unit’s digit of N may be 1, 3, 5, 7 or 9. True
\n(iii) If a number is divisible by any number m,
\nthen it will also be divisible by each of the factors of m. True
\n(iv) If a number is divisible by sum of two numbers then
\nit will also be divisible by each of the two numbers separately. False
\nCorrect:
\nAs if 33 is divisible by 7 + 4 = 11, then it will not divisibly by 7 or 4 seperately.
\n(v) If 3651x is divisble by 9, then value of digit x is 3. True
\n(vi) If 42×7 is divisible by 3, then value of digit x is 4. False
\nCorrect:
\nAs in 4247, sum of digits 4 + 2 + 4 + 7 = 17 is not divisible by 3.
\n(vii) The number 152875 is divisible by 9. False
\nCorrect:
\nAs digits of 152875 = 1 + 5 + 2 + 8 + 7 + 5 = 28
\nwhich is not divisible by 9.
\n(viii)The number 389072 is divisible by 8. True
\n(ix) The number 27402 is divisible by 6. True
\n(x) The number 359249 is not divisible by 11.
\nFalse
\nCorrect:
\nAs it is divisible by 11<\/p>\n
\nChoose the correct answer from the given four options (3 to 13):<\/strong>
\nQuestion 3.
\nWhen the sum of a 2-digit number ab and number obtained by reversing the digits is divided by (a + b), then quotient is
\n(a) a – b
\n(b) 9
\n(c) 11
\n(d) None of these
\nSolution:
\nA 2-digit number ab and number obtained by
\nreversing the digit is divided by (a + b), then the quotient is 11. (c)<\/p>\n
\nWhen the sum of a 3-digit number abc and numbers obtained by changing the order of the digits cyclically is divided by 111, then quotient is
\n(a) 37
\n(b) a – b + c
\n(c) a + b + c
\n(d) 3
\nSolution:
\nSum of 3-digit number abc and number obtained by
\nchanging the order of the digits cyclically is divided by 111,
\nthen quotient is a + b + c. (c)<\/p>\n
\nIf A + A + A = BI, where A and B are different digits, then
\n(a) A = 1, B = 5
\n(b) A = 5, B = 2
\n(c) A = 5, B = 1
\n(d) A = 7, B = 2
\nSolution:
\nA + A + A = BI, where A and B are different digits then A = 7, B = 2.
\nAs unit digit of sum = 1
\n\u2234 A will be \\(\\frac{21}{3}\\) = 7
\n{\u2235 \\(\\frac{11}{3}, \\frac{31}{3}\\) are not naturals}
\n\u2234 A = 7, B = 2 (c)<\/p>\n
\nWhich of the following numbers is not divisible by 2?
\n(a) 437218
\n(b) 437821
\n(c) 437812
\n(d) 437182
\nSolution:
\nWhich of the following is not divisible by 2
\n437821 as it’s unit digit is 1. (b)<\/p>\n
\nWhich of the following numbers is not divisible by 10?
\n(a) 32570
\n(b) 32750
\n(c) 32500
\n(d) 32075
\nSolution:
\nWhich of the given number is not divisible by 10
\n32075, (as it’s unit digit is not zero) (d)<\/p>\n
\nWhich of the following numbers is divisible by 4?
\n(a) 98764
\n(b) 98746
\n(c) 98674
\n(d) 98647
\nSolution:
\nWhich of given number is divisible by 4.
\n98764 as number forming last two digits is 64
\nwhich is divisible by 4. (a)<\/p>\n
\nWhich of the following numbers is divisible by 8?
\n(a) 32466
\n(b) 32476
\n(c) 32486
\n(d) 32456
\nSolution:
\nWhich of the following is divisible by 8.
\n32456 as number formed by last three digits 456 is divisible by 8. (d)<\/p>\n
\nWhich of the following numbers is divisible by 11?
\n(a) 725824
\n(b) 752824
\n(c) 725842
\n(d) 725482
\nSolution:
\nWhich of the following is divisible by 11.
\n725824 as the difference of the sum of digits at odd places
\nand sum of digit an even place is divisible by 11. (a)<\/p>\n
\nWhich of the following numbers is not divisible by 9?
\n(a) 24354
\n(b) 24453
\n(c) 24534
\n(d) 24564
\nSolution:
\nWhich of the following is not divisible by 9.
\n24564 as the sum of its digits is not divisible by 9. (d)<\/p>\n
\nIf 467×8 is divisible by 3, then value of x
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4
\nSolution:
\n\u2235 467×8 is divisible by 3
\n\u2234 4 + 6 + 7 + 8 + x = 25 + x is divisible by 3
\n\u2234 25 + x = 27, 30, 33
\n\u2234 x = 2, 5, 8
\nx = 2 (b)<\/p>\n
\nIf 36x52y8 is divisible by 9, then x + y is
\n(a) 2
\n(b) 3
\n(c) 4
\n(d) 5
\nSolution:
\n\u2235 36x52y8 is divisible by 9
\n\u2234 3 + 6 + 5 + 2 + 8 + x + y
\n\u21d2 24 + x + y is divisible by 9
\n24 + (x + y) = 27
\nx + y = 27 – 24 = 3 (b)<\/p>\n
\nQuestion 1.
\nRishabh plays a game with two dice in a fete. He draw three columns on a chart paper.In the left most column he write the digits less than 7 and in the right most column he write the numbers greater than 7. In the middle column he write digit 7 only. He offter people to keep money on any one of the column. He throws two dice together, if the sum of the digits on the two dice is less than 7, he doubles the money kept on the left most column and collect the money kept on remaining two columns. Similarly, he doubles the money on right most column if the sum of digits is greater than 7 and triples on the middle column if sum of the digits is 7. What digits should he write on left most and right most columns?
\nIs this game a sort of gambling? Is gambling a good way of earning money?
\nSolution:
\nTwo dice are thrown:<\/p>\n\n\n
\n Less than 7<\/strong><\/td>\n More than 7<\/strong><\/td>\n<\/tr>\n \n 1<\/td>\n 7<\/td>\n<\/tr>\n \n 2<\/td>\n 8<\/td>\n<\/tr>\n \n 3<\/td>\n 9<\/td>\n<\/tr>\n \n 4<\/td>\n 10<\/td>\n<\/tr>\n \n 5<\/td>\n 11<\/td>\n<\/tr>\n \n 6<\/td>\n 12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\nthe law of government as well as society.
\nIt should be stopped.<\/p>\n
\nQuestion 1.
\nIf the difference of two digit number and number obtained by reversing the digits is 45, then write all possible 2-digit numbers.
\nSolution:
\nThe difference of 2-digit number and
\nthe number obtained by reversing the digits is 45,
\nthen the two numbers will be
\n16, 61 (\u2235 61 – 16 = 45)
\n27, 72 (\u2235 72 – 27 = 45)
\n38, 83 (\u2235 83 – 38 = 45)
\n49, 94 (\u2235 94 – 49 = 45)<\/p>\nML Aggarwal Class 8 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"