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1. The product of two numbers is 630. If one of the number is 18, then what is the another number?
- A. 34
- B. 36
- C. 35
- D. 38
Answer: 35
Explanation: Let second number be x Product of two numbers is 630 First number is 18 First number × Second number = 630 x 18 630× = 630x 18= x 35= Hence the second number is 35
2. The sum of 8 consecutive integers is 4. What i s the lowest integer ?
- A. -3
- B. 0
- C. -2
- D. -1
Answer: -3
Explanation: (a) Lat 8 consecutive integers = x, x+1, x+2, x+3, x+4, x + 5, x + 6, x + 7 According to the question, x+x+1+x+2+x+3+x+4+x+5+x+6+x+7 = 4 8x 28 4+ = 8x 4 28= - 8x 24= - , x 3= -
3. If the sum of ten different positive integers is 100, then what is the greatest possible number among these 10 numbers?
- A. 45
- B. 91
- C. 55
- D. 64
Answer: 55
4. How many times digit '5' appears in the number from 1 to 100?
- A. 20
- B. 21
- C. 19
- D. 18
Answer: 20
Explanation: (a) Number of repetitions of digit 5 between 1 to 100- 5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 75, 85, 95 means 20 times
5. If the difference of squares of two consecutiv e odd number is 64, then what is the sum?
- A. 34
- B. 32
- C. 30
- D. 17
Answer: 32
6. Find the positive number which when decreased by 20 is equal to 2925 times the reciprocal of the number.
- A. 35
- B. 65
- C. 55
- D. 45
Answer: 65
Explanation: Let the number be x then According to the question, x-20 = 2925x x2 - 20x - 2925 = 0 x2 - 65x + 45x - 2925 = 0 x(x-65) +45(x-65) = 0 (x-65) (x+45) = 0 x - 65 = 0, x + 45 = 0 x = 65, x = - 45 Hence the required number is 65
7. There are five stations on a railway line. Wha t is the number of different journey tickets that are required for railway authorities?
- A. 20
- B. 30
- C. 25
- D. 35
Answer: 20
Explanation: Required number of journey tickets = n(n - 1) = 5 × 4 = 20
8. The difference between two numbers is 43 and their product is 50. Find the sum of their squares.
- A. 1947
- B. 1949
- C. 1948
- D. 1946
Answer: 1949
Explanation: Let that two number be a and b respectively ∴ a - b = 43 a × b = 50 (a - b) 2 = (43)2 ⇒ a 2 + b2 - 2ab = 1849 a 2 + b2 = 1849 + 2 × 50 = 1849 + 100 = 1949
9. If the sum of two numbers is 11 and the sum of their squares is 65, then the sum of their cubes will be
- A. 615
- B. 407
- C. 355
- D. 576
Answer: 407
Explanation: Let two numbers be x and y ∴ According to question x + y = 11 ____ (i) And x2 + y2 = 65 ____ (ii) x3 + y3 = ? ∴ (x+y)2 = x2 + y2 + 2xy ⇒ (11)2 = 65 + 2xy ⇒ 121 = 65 + 2xy ⇒ 2xy = 56 ⇒ xy = 28 ____ (iii) (x+y)3 = x3 + y3 + 3xy(x+y) Substituting values from equation (i), (ii) and (ii i) ⇒ (11)3 = x3 + y3 + 3×28×11 ⇒ 1331 = x3 + y3 + 924 ⇒ x3 + y3 = 407
10. The sum of two numbers is 47 and their product is 550. Find the sum of their squares.
- A. 1109
- B. 876
- C. 986
- D. 1209
Answer: 1109
Explanation: Let two numbers be a and b respectively QQ QQ a + b = 47, ab = 550 ∴ (a + b)2 = a2 + b2 + 2ab (47)2 = a2 + b2 + 2×550 2209 = a2 + b2 +1100 a2+b2 = 2209 - 1100 Hence a2 + b2 = 1109
11. The difference between two numbers is 3 and the difference between their cubes is 999. Find the difference between their square.
- A. 18
- B. 36
- C. 63
- D. 81
Answer: 63
Explanation: Let two numbers be a and b respectively According to question, a - b = 3 a3 - b3 = 999 ∴ (a - b)3 = a3 - b3 - 3ab (a - b) 33 = 999 - 3ab×3 27 = 999 - 9ab 9ab = 999 - 27 9ab = 972 ab = 108 ∴ (a-b)2 = (a+b)2 -4ab 32 = (a+b)2 - 4 × 108 (a+b)2 = 9 + 432 (a+b)2 = 441 a+b = 21 ∴ a2 - b2 = (a-b) (a+b) = 3 ×21 = 63
12. If the difference between two numbers is 6 and the difference between their squares is 60, what is the sum of their cubes?
- A. 945
- B. 678
- C. 894
- D. 520
Answer: 520
Explanation: Let there be two numbers a and b respectively According to question, a - b = 6, ....................(i) a 2 - b2 = 60 ∵ a 2 - b2 = (a - b) (a + b) 60 = 6(a + b) a + b = 10 ...................(ii) From eq (i) & (ii), a = 8, b = 2 ∴ (a + b) 3 = a3 + b3 + 3ab(a + b) 10 3 = a3 + b3 + 3 × 8 × 2 (10) 1000 = a 3 + b3 + 480 a 3 + b3 = 1000 - 480 a 3 + b3 = 520 Hence the sum of cubes of numbers = 520
13. The sum of two numbers is 59 and their product is 840. Find the sum of their squares.
- A. 1754
- B. 1801
- C. 2961
- D. 1875
Answer: 1801
Explanation: Let the two numbers be a & b respectively then, a + b = 59, ab = 840 ∴ (a + b) 2 = a2 + b2 + 2ab (59) 2 = a2 + b2 + 2 × 840 3481 = a 2 + b2 + 1680 a 2 + b2 = 3481 - 1680 Hence a2 + b2 = 1801
14. When a two-digit number is multiplied by the sum of its digits, the product is 424. When the number obtained by interchanging its digits is multiplied by the sum of the digits, the result is 280. The sum of the digits of the given number is
- A. 9
- B. 8
- C. 7
- D. 6
Answer: 8
15. The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares ?
- A. 106
- B. 196
- C. 53
- D. 68
Answer: 106
16. If A = 0.abcabc....., then by what number A should be multiplied so as to get an integeral value ?
- A. 2997
- B. 1000
- C. 1998
- D. Both 2997 and 1998
Answer: Both 2997 and 1998
Explanation: A = 0.abc abc ....... A 0.abc= abcA 999= So, to get an integral value A should be multiply b y any multiple of 999. 2997 = 999 × 3 1998 = 999 × 2
17. In a two-digit number, its unit digit exceeds its tens digit by 2 and that the product of the given number and the sum of its digits is equal to 460. The number is
- A. 48
- B. 64
- C. 36
- D. 46
Answer: 46
Explanation: From option (d), Let two digit number = 46 Hence 46 ×10 = 460 ∴ number is 46
18. If three numbers are in the ratio 2 : 3 : 5 an d the twice of their sum is 200. The square of the largest of three numbers is
- A. 2500
- B. 1000
- C. 625
- D. 2250
Answer: 2500
Explanation: Let numbers be = 2x, 3x and 5x then, 2(2x + 3x + 5x) = 200 20x = 200 x = 10 then the square of the greatest number = (5x)2 = (5 × 10) 2 = 2500
19. The number 1563241234351 is
- A. divisible by both 3 and 11
- B. neither divisible by 3 nor by 11
- C. divisible by 3 but not by 11
- D. divisible by 11 but not by 3
Answer: neither divisible by 3 nor by 11
Explanation: Sum of digits number 1563241234351 = 40 (which is not divisible by 3) Hence the number will not divisible by 3 Again, Sum of digits of odd places ∼ Sum of digits of even places ⇒ (1 + 3 + 3 + 1 + 2 + 6 + 1) ~ (5 + 4 + 2 + 4 + 3 + 5) ⇒ 17 ~ 23 ⇒ 6 (which is neither divisible 11 nor zero) Hence the number is not divisible by 11
20. 13 a, b and c are four different numbers and the HCF of each pair of numbers (13, a); (13, b) and (13, c) is 13, where a, b, c each are less than 60, and a < b < c. What is the value of a + cb ?
- A. 2
- B. 3.5
- C. 5
- D. 4.5
Answer: 2
Explanation: Four numbers are 13, a, b and c HCF of (13, a) (13, b) (13, c) = 13 a, b, c < 60 ....... (I) a < b < c ....... (II) a, b, c should be multiple of 13 as the HCF is 13. So a = 26, b = 39, c = 52 These all satisfy the conditions. So, the numbers are 13, 26, 39 and 52 Hence, a c 26 52 78 2b 39 39+ += = =
21. If N = 1+11+111+1111+ .... + 111111111, then what is the sum of the digits of N ?
- A. 45
- B. 18
- C. 36
- D. 5
Answer: 45
Explanation: N = 1+11+111+1111+ .... + 111111111 Digits in N = 1+2+3+4+……….+9 ∴ Sum of digits of n(n +1) 9 10N = 45 2 2 ×= =
22. Two mixers and one T.V cost Rs 500, while two TVs and one mixer cost Rs 700. What is the cost of a TV ?
- A. ₹100
- B. ₹200
- C. ₹300
- D. ₹400
Answer: ₹300
Explanation: Let the cost of one mixer = ₹x and the cost of one TV = ₹y As per question :- 2 x + y = 500 ….(i) x + 2 y = 700 ….(ii) On multiplying equation (ii) by 2 and subtracting equation (i) 2x 4y 1400 2x y 500- - - 3y 900 + = + = = y = 300 So the cost of one TV is ₹300
23. How many composite numbers are there from 53 to 97.
- A. 35
- B. 36
- C. 37
- D. 38
Answer: 35
Explanation: Prime numbers from 53 to 97 are = 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 = 10 (total) Total numbers from 53 to 97 = 45 ∴ Composite number from 53 to 97 = 45-10 = 35
24. If the digits of the two digit number are reversed, the number is reduced by 36. Which of the following statements is correct regarding numbers? I. The difference of digits is 4 II. The number could be 84 III. Number is always a composite number
- A. II and III
- B. I and III
- C. I, II and III
- D. I and II
Answer: I and II
Explanation: Let the two digit number be 10x + y If the digits of the number are reversed then the n umber becomes 10y + x As per question , (10y + x) = 10x+y-36 9 (x-y) = 36 (x-y) = 4 ... (i) (I) From the above equation (i) it is clear that th e difference of digit is 4 ∴ statement (I) is correct.
25. If 2 x + 3y = 17 and 2x+2 - 3y+1 = 5 then
- A. x = 1, y = 2
- B. x = 1, y = 3
- C. x = 3, y = 3
- D. x = 3, y = 2
Answer: x = 3, y = 2
Explanation: Let, 2x = a, 3y = b Then, 2 x +3y = 17 a + b = 17 a = 17-b 2x+2 -3y+1 = 5 2x.22 -3y.31= 5 4a -3b = 5 4(17-b) -3b = 5 68-4b -3b = 5 63= 7b b = 9 a= 17-9 a= 8 Again, 2x = a 2x= 8 2x= 23 x = 3 3y = 9 3y = 32 y = 2 So, x= 3 y= 2
26. M is inversely proportional to N. If M is 20, then N is 70. If N is 50 then what is the value of M?
- A. 700
- B. 28
- C. 600
- D. 20
Answer: 28
27. Rohit Purchased 12 kg oranges for a total of Rs 480 and 18kg guavas at the rate of Rs 30 per kg. Find the average price of fruits purchased by Rohit ?
- A. ₹ 38.20
- B. ₹ 37.20
- C. ₹ 34.00
- D. ₹ 36.00
Answer: ₹ 34.00
Explanation: Rohit bought 12 kg oranges = ₹480 And 18kg guavas = 18×30= ₹540 Average price of fruits purchased by Rohit 540 + 480= 12 +18 1020= 30 = ₹ 34
28. The total cost of ten refrigerators and four mobiles phones is Rs. 210000, while the total cost of six refrigerators and 2 mobile phones is Rs 122000. What will be the cost of a refrigerator and 2 mobile phones ?
- A. 35200
- B. 36000
- C. 34500
- D. 37000
Answer: 37000
Explanation: Let the cost of one refrigerator and mobile phone is x and y respectively According to the question, 10x + 4y = 210000 ........ (I) 6x + 2y = 122000 ....... (II) Eq. (II) ×2 → 12x + 4y = 244000 10x + 4y = 210000 - - - 2x = 34000 x = ₹17000 Now form eq. (II) 6×17000+2y = 122000 2y = 20000 So, the cost of one refrigerator and 2 mobile phone s is = x+2y = 17000+20000 = ₹37000
29. What is the least, number multiplied to 200, s o that the obtained number becomes a multiple of 600?
- A. 5
- B. 15
- C. 3
- D. 8
Answer: 5
Explanation: (c) Let the number be = x Then x × 200 = 600 x = 3 Hence, on multiplying the number 200 by 3, the numb er obtained will be a multiple of 600.
30. In an office, There are 216 tables and 264 chairs. If 16 of tables and 14 of chairs are broken, then how many people can work in the office if each person needs one table and one chair?
- A. 180
- B. 186
- C. 100
- D. 198
Answer: 180
Explanation: According to the question, Number of tables = 216 Number of tables which are not broken 216= 216 - = 216 - 366 = 180 Number of chairs = 264 Number of chairs which are not broken 264= 264 - = 264 - 66 4 = 198 Since, each person needs one table and one chair, then the number of required person = 180
31. How many whole numbers are there between 112 and 122 ?
- A. 24
- B. 21
- C. 22
- D. 23
Answer: 22
32. A bag contains Rs 5 and Rs 10 coins such that the product of their numbers is 135 and the total amount of money in the bag is Rs 165. What is the total amount of all Rs 10 coins?
- A. ₹90
- B. ₹85
- C. ₹95
- D. ₹80
Answer: ₹90
Explanation: Let the number of coin of Rs 5 and Rs. 10 be x and y respectively. According to the question, x × y = 135 xy = 135 ……..(1) 135x y = 5x + 10y = 165 x + 2y = 33 …….(2) Put the value of (x = 135/y) from eq. (1) 135 2y 33y⇒ + = ⇒ 135+2y2= 33y ⇒2y2-33y +135 = 0 ⇒ 2y2-18y -15y+135= 0 ⇒ 2y (y-9) -15 (y-9) = 0 y= 9 then 135 135x = = =15y 9 Hence, the total amount of all Rs 10 coins = 10y = 10×9 = ₹90
33. What is the sum of the divisors of 484 which are perfect square ?
- A. 35
- B. 125
- C. 13
- D. 610
Answer: 610
Explanation: 484 = 22 × 22 = 2 × 11 × 2 × 11 = 11 2 × 22 Sum of divisors which are perfect numbers = (110 + 112) × (20 + 22) = (1 + 121) × (1 + 4) = 122 × 5 = 610° Method (2.) 484 → 1, 4, 121, 484 (required divisors) Sum → 1+ 4 + 121 + 484 = 610
34. The square of the sum of any two natural numbers is 784, while the product of the two given number is 192. What is the positive difference of square of both the numbers ?
- A. 112
- B. 122
- C. 512
- D. 400
Answer: 112
35. The sum of the cube of any two natural numbers is 9728, while the sum of both the number is 32. What will be the positive difference of the cube of both the numbers ?
- A. 4662
- B. 6272
- C. 5832
- D. 7904
Answer: 6272
36. The cube of the sum of any two numbers is 1728, while the product of the two given numbers is 32. Find the sum of the cube of two given numbers ?
- A. 260
- B. 512
- C. 640
- D. 576
Answer: 576
Explanation: Let the numbers are x and y. As per question :- (x + y)3 = 1728 (x + y) = 12 and xy = 32 (x-y)2 = (x+y)2 - 4xy (x-y)2 = 144-128 = 16 x-y = 4 x+y = 12 x= 8, y = 4 So, = x3 +y3 = 83 + 43 = 512 + 64 = 576
37. The average of 1088 real numbers is zero. At most how many of them can be negative?
- A. 544
- B. 1087
- C. 100
- D. 88
Answer: 1087
Explanation: Since the average of 1088 numbers is zero. Then maximum 1087 numbers can be negative For example Let (x1 +x2+……….x1087 = -400 That x1088 = 400 So, Average = Sum -400 400 N 1088 += = 0 (Proved)
38. While baking a cake for 15 people Jaya used 2.4 kg of flour. How much flour will be used to bake the same cake for 36 people?
- A. 5.56 kg
- B. 6.00 kg
- C. 5.76 kg
- D. 5.88 kg
Answer: 5.76 kg
Explanation: According to questions :- 15 People → 2.4 kg Then 36 people → 2.4 3615× kg → 5.76 kg. Hence, 5.76 kg flour will be required to bake the c ake for 36 people.
39. A group of college students had decided to complete a project in 10 days. The project was completed at the end of the 15th day due to 2 students dropping out each day. What was the number of students at the initial time of project?
- A. 45
- B. 40
- C. 35
- D. 42
Answer: 42
40. The difference of the cubes of two natural numbers 6272 while the positive difference of these two numbers is 8. What will be the product of these two numbers?
- A. 200
- B. 320
- C. 160
- D. 240
Answer: 240
Explanation: Let the natural numbers are x and y According to the question, x3 - y3 = 6272 & x - y = 8 ∴ x3 - y3 = (x - y)3 + 3xy (x - y) 6272 = 8 3 + 3xy (8) 3xy = 57608 xy = 7203 ∴ xy = 240
41. If the cost of a cloth of 120m is Rs 9600 the n what is the cost of the cloth of 147m ?
- A. ₹ 17,160
- B. ₹ 11,760
- C. ₹ 11,670
- D. ₹ 16,170
Answer: ₹ 11,760
Explanation: According to question:- 120m → ₹ 9600 then 9600 147147m 120×→ = 8×1470 = 11, 760 Hence, the cost of the cloth of 147m is ₹11760.
42. The square of the difference of any two natur al number is 324, while the product of the two given number is 144. Find the positive difference of the square of the given numbers?
- A. 630
- B. 360
- C. 540
- D. 450
Answer: 540
Explanation: As per question:- (a-b)2 = 324 (a-b)2= 182 (a-b) = 18 and ab = 144 (Given) (a+b)2= (a-b)2 + 4ab (a+b)2 = 182+4×144 = 324+576 (a+b)2 = 900 ⇒ (a+b) = 30 ⇒ (a-b) = 18 30+18a = , 2 30-18b 2= a= 24 b = 6 Hence, a2 -b2 = 242 -62= 576-36 = 540
43. The sum of cubes of two given numbers is 10234, while the sum of the given two number is 34. What is the positive difference between the cubes of the two given numbers ?
- A. 3484
- B. 8602
- C. 3356
- D. 3488
Answer: 3484
44. The cost of 2 pencils and 3 pens is Rs 55 and the cost of 7 pencils and 2 pens is Rs 65. What is the total cost of a pen and a pencil?
- A. 25
- B. 15
- C. 20
- D. 12
Answer: 20
Explanation: Let the cost of one pencil = x and the cost of one pen = y According to the question, 2x +3y = 55 ____(i) 7x + 2y = 65 ____(ii) From equation (i)× 2 and eq. (ii) ×3 Then, x = 5 From eq (i) 2×5+3y = 55 y = 15 Cost of one pencil = ₹5 And cost of one pen = ₹15 Total cost of a pen and a pencil = 5 +15 = ₹20
45. Rewa has some hens and some goats. If the total number of head of animals is 100 and the total number of feet of animals is 348. How many goats does rewa have?
- A. 74
- B. 80
- C. 76
- D. 55
Answer: 74
46. A T-shirt costs Rs 450 and a jeans costs Rs. 1650. If you buy three T-shirts and two jeans, what is the average price of each garments?
- A. ₹ 920
- B. ₹ 900
- C. ₹ 910
- D. ₹ 930
Answer: ₹ 930
Explanation: As per question, Price of 1 T-shirt = ₹ 450 Then price of 3 T-shirt = 450 × 3 = ₹1350 ∵ Price of 1 jeans = ₹1650 Then price of 2 jeans = 1650× 2 = ₹ 3300 ∴ Required Average = 1350+33005 = 46505 = ₹ 930
47. How many multiples of 6 are there from 1 to 200 which are not multiple of 4 ?
- A. 16
- B. 17
- C. 19
- D. 15
Answer: 16
Explanation: (b) Multiples of 6 from 1 to 200 (n6) = 198 6 16- + = 192 16 + = 32 + 1 = 33 L.C.M of 6 and 4 which means number of multiples of 12 (n12) = 192 12 112- + 180 112= + = 15 + 1 = 16 Numbers of multiples which are multiples of 6 but n ot multiple of 4 = n6 - n12 = 33 - 16 = 17
48. What is the average of all the natural numbers from 49 to 125?
- A. 85
- B. 87
- C. 88
- D. 86
Answer: 87
Explanation: Given 49, 50, 51, 52 .................. 125 first terms (a) = 49 common difference (d) = 50 - 49 = 1 last term (l) = 125 From, a (n 1) d= + - ×l 125 49 (n 1) 1= + - × (n 1) 76⇒ - = n 77⇒ = Hence sum of natural numbers from 49 to 125 n (a )2= + l 77 (49 125)2= + 77 1742= × 77 87= × Average of natural number from 49 to 125 77 87 8777×= =
49. How many multiples of 5 are there from 1 to 200 which are not multiples of 4.
- A. 40
- B. 30
- C. 25
- D. 35
Answer: 30
Explanation: Trick: 200 405 = which denotes the total number of factors of 5 from 1 to 200. In 40 numbers, the numbers which are multiples of 4 , and 5 both L.C.M of 4 and 5 = 20 200 1020 = Hence required numbers = (40 - 10) = 30
50. How many numbers less than 350 are multiples of both 4 and 3?
- A. 29
- B. 31
- C. 30
- D. 28
Answer: 29
Explanation: L.C.M of 3 & 4 = 12 Numbers less than 350 which are multiples of 3 & 4 12, 24, 36, 48 ..............348 In AP a =12 d =12 T n = 348 Number of terms = n ∴ a + (n-1).d = Tn 12 + (n-1).12 = 348 12 + 12n - 12 = 348 12n = 348 n = 29 Hence the number of such terms = 29 Trick: L.C.M of 4 & 3 = 12 35012 = quotient = 29 Hence required number of numbers = 29
51. What is the sum of first 40 terms of 1+3+4+5+7+7+10+9+ .....?
- A. 1010
- B. 1115
- C. 1030
- D. 1031
Answer: 1030
52. How many multiple of 6 are there between 1 and 200, which are not multiple of 4?
- A. 16
- B. 17
- C. 19
- D. 15
Answer: 16
Explanation: (b): Number of multiple of 6 between 1 and 200 = 198 6 16- + = 192 16 + = 32 + 1 = 33 Number of multiple of LCM of 4 and 6 i.e. 12 192 - 12= +1 12 180= +1 12 = 16 Hence, number of multiples of 6 but not of 4 = 33-16= 17
53. What is the sum of all the natural number between 1 and 200 which are multiple of 5?
- A. 3900
- B. 4100
- C. 4155
- D. 4235
Answer: 3900
54. Find the sum of 6 + 8 + 10 + 12 + 14 +....... + 40.
- A. 424
- B. 1600
- C. 400
- D. 414
Answer: 414
55. How many numbers are there from 400 to 700 in which the digit 6 occurs exactly twice ?
- A. 20
- B. 19
- C. 18
- D. 21
Answer: 20
Explanation: There are '20' numbers from 400 to 700 in which the digit 6 occurs exactly twice. Numbers are → 466, 566, 606, 616, 626, 636, 646, 656, 660, 661, 6 62, 663, 664, 665, 667, 668, 669, 676, 686, 696 Note:- The number 666 cannot be count because in this number 6 occurs thrice not twice
56. What is the sum of the first 20 terms of the given series ? 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ........
- A. 3080
- B. 3160
- C. 3240
- D. 2940
Answer: 3080
57. When 200 is divided by a positive integer x, t he remainder is 12. How many values of x are possible?
- A. 2
- B. 3
- C. 6
- D. 8
Answer: 3
Explanation: 200x ⇒Q remainder = 12 ∴x > 12 Then, 188 12x+ ⇒ [All values of x which exactly divided 188] 188 = 2 2 × 471 Total factors of 188 = (2 + 1) × (1 + 1) = 6 which means number of total values of x = 6 (but x > 12) ∴ x ≠ 1,2,4 The number of total values = (6 - 3) = 3
58. The ratio of two positive numbers is 9:11. The ir product is 6336. What is the smallest number?
- A. 32
- B. 72
- C. 88
- D. 48
Answer: 32
Explanation: (b) Let two positive numbers be 9x and 11x ∴∴ ∴∴ 9x × 11x = 6336 99x2 = 6336 2 6336x 99= x2 = 64 x = 8 ∴ Number = 9 × 8 = 72 and 11 × 8 = 88 ∴ The smallest number = 72
59. When 732 is divided by a positive integer x, then remainder is 12. How many values of x are there?
- A. 19
- B. 18
- C. 16
- D. 20
Answer: 20
Explanation: Number divisible by x = 732-12 = 720 = 2 4 × 32 × 51 The value of x will always be greater than 12 Number of factors of 720 = (4+1) × (2+1) × (1+1) = 30 But in these factors 1, 2, 3, 4, 5, 6, 8, 9, 10 and 12 are included or it is less than 12 Hence, possible values of x = 30-10 = 20
60. When an integer n is divided by 8, the remainder is 3. What will be the remainder if 6n - 1 is divided by 8?
- A. 4
- B. 1
- C. 0
- D. 2
Answer: 1
Explanation: ∵ On dividing n by 8, the remainder is 3. ∴ we can take n = 8 + 3 = 11 On putting n = 11 in 6n -1 65 1 (remainder)8 =
61. What will be the remainder when (401 + 402 + 403 + 404) is divided by 4?
- A. 10
- B. 2
- C. 6
- D. 3
Answer: 10
Explanation: (b) 401+ 402+ 404 = 1610 on dividng 1610 by 4
62. What will be the remainder when 421 is divided by 11?
- A. 3
- B. 5
- C. 7
- D. 4
Answer: 3
63. What is the largest two digit number which when divided by 6 and 7 gives remainder 3 and 4 respectively?
- A. 81
- B. 94
- C. 83
- D. 84
Answer: 81
64. A number when divided by 16 leaves a remainder 4. When the square of the number is divided by 16, what will be the remainder ?
- A. 1
- B. 2
- C. 3
- D. 0
Answer: 0
65. What will be the remainder when (631 × 632 × 633) is divided by 5?
- A. 6
- B. 1
- C. 4
- D. 3
Answer: 6
Explanation: (b) 631 632 633 5 × ×= 1 2 3 5 × ×= 65= Remainder = 1
66. What is the remainder when 622 is divided by 13?
- A. 2
- B. 11
- C. 9
- D. 17
Answer: 11
Explanation: Hence on dividing 622 by 13 will give the remainder 11.
67. A number when divided by 36 leaves remainder 25. What is the remainder when the same number is divided by 6?
- A. 0
- B. 1
- C. 2
- D. 4
Answer: 0
Explanation: (b) Let assume that on dividing number by 36, K is obtained the quotient and 25 is the remainder ∴ Dividend = 36 × K + 25 = 6 × 6K + 6 × 4 + 1 = 6 (6K + 4) + 1 Hence on dividing by 6, 1 is left as remainder
68. If a number is divided by 30 then it leaves 17 as a remainder. What will be the remainder when the same number is divided by 10?
- A. 7
- B. 3
- C. 1
- D. 2
Answer: 7
Explanation: (a) Let number be x and quotient be P dividend = divisor × quotient + remiander x = 30 × P + 17 on dividing by 10 30P 1710+ = 7 (remainder)
69. In a division question, the divisor is 6 times the quotient and 3 times the remainder. If the remainder is 40, then find the dividend.
- A. 2455
- B. 2440
- C. 2450
- D. 2445
Answer: 2440
70. When an integer n is divided by 5, then remainder is 3. What is the remainder if 8n is divided by 5?
- A. 4
- B. 2
- C. 3
- D. 1
Answer: 4
Explanation: According to question, Number in first condition (n) = 5K + 3 ( QK = quotient) Number in 2nd condition (8n) = 40K + 24 Required remainder 24 45= =
71. If a number is divided by 899, then remainder is 63. If the same number is divided by 29, then remainder will be
- A. 10
- B. 2
- C. 4
- D. 5
Answer: 5
Explanation: ∵ 899 is divisible by 29. ∴ ) (29 63 2 58 5 Remainder
72. The remainder when 75 × 73 × 78 × 76 is divided by 34 is
- A. 15
- B. 18
- C. 22
- D. 12
Answer: 12
73. If r is the remainder when each of 4749, 5601 and 7092 is divided by the greatest possible number (d >1), then the value of (d + r) will be
- A. 298
- B. 276
- C. 282
- D. 271
Answer: 276
74. When 2388, 4309 and 8151 are divided by a certain 3-digit number, then remainder in each case is the same. The remainder is
- A. 15
- B. 39
- C. 23
- D. 19
Answer: 15
Explanation: Let remainder be r Factor of 1921 = 113 × 17 Hence the three digit number = 113 ∴ 2388 113 ⇒ remainder = 15
75. If 14331433 × 1422 × 1425 is divided by 12, then what is the remainder?
- A. 9
- B. 3
- C. 6
- D. 8
Answer: 6
76. The remainder when 72 × 73 × 78 × 76 is divided by 35 is
- A. 12
- B. 15
- C. 22
- D. 8
Answer: 8
77. When a number is successively divided by 3, 4 and 7, the remainders obtained are 2, 3 and 5, respectively. What will be the remainder when 84 divides the same number?
- A. 71
- B. 53
- C. 48
- D. 30
Answer: 71
Explanation: When number is divided by 7 then the remainder obtained 5 so number = 7x+5 On dividing the same number by 4 is obtained as remainder 3, so number = 4(7x+5)+3 On dividing the same number by 3 the remainder obtained is 2 So number = 3[4(7x+5)+3]+2 ∴ Number = 3[28x + 23] +2 = 84x + 69 + 2 = 84x + 71 Hence on dividing the number by 84, 71 is obtained as remainder.
78. If 14331433×1422×1425 is divided by 10, then what is the remainder?
- A. 0
- B. 8
- C. 9
- D. 3
Answer: 0
Explanation: Given- Number = 14331433× 1422 × 1425 ∵ Last digit of number = 3×2×5 = 30 ∵ Last digit is 0 Hence on dividing by 10 the remainder obtained will be zero
79. What is the least number multiplied to 300, so that number becomes multiple of 105?
- A. 35
- B. 7
- C. 21
- D. 3
Answer: 35
Explanation: (b) The least number which is multiple of 300 and 105 both = L.C.M. of 300 and 105 = 2100 The number multiplied to 300 so that number become 2100 7300= = So, The required answer = 7
80. N is the largest two digit number, which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when N is divided by 5?
- A. 4
- B. 2
- C. 0
- D. 1
Answer: 4
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