Number System

26. If x is an odd integer and y is an even integer which of the statements is(are) always true? I. x + y is odd II. xy is odd III. 2x + y is even.

• ক. I only
• খ. II and III only
• গ. I and III only
• ঘ. III only

27. If the product of 3 consecutive integers is 120, then the sum of the integers is----

• ক. 9
• খ. 15
• গ. 12
• ঘ. 14

28. If m and n are positive integers, which of the following must be an even integer?

• ক. n(m - 1)
• খ. (n - 1)m
• গ. (m - 1)(n - 2)
• ঘ. n(n - 1)(m - 1)

29. If both x and y are integers and x = 24y + 12, then which of the following must be true?

• ক. x/12 is even
• খ. x/6 is even
• গ. (x + 4)/8 is odd
• ঘ. (x + 4)/8 is even

30. If n is a positive integer and k + 2 = 3n, which of the following could be a value of k?

• ক. 1
• খ. 4
• গ. 7
• ঘ. 25

31. If n and p are both odd numbers, which of the following must be an even number?

• ক. np + 2
• খ. n + p
• গ. n + p + 1
• ঘ. np

32. What is the least integer that is a sum of three different primes each greater than 20?

• ক. 69
• খ. 73
• গ. 75
• ঘ. 83

33. Sum of three different positive integeris the same as their product. Find the smallest of these three integers?

• ক. 5
• খ. 2
• গ. 3
• ঘ. 1

34. How many prime numbers are there between 45 and 72?

• ক. 5
• খ. 6
• গ. 8
• ঘ. 7

35. A student first reduced a number by 20 percent and then increased it again by 20 percent. If the difference between the two new numbers was 8, then what is the original number?

• ক. 40
• খ. 50
• গ. 96
• ঘ. 75

36. A two-digit number has 3 in its unit digit. The sum of its digits is one-seventh of the number itself. What is the number?

• ক. 73
• খ. 63
• গ. 53
• ঘ. 50

37. If x = 12, which of the following has the maximum value?

• ক. x - 3
• খ. (x - 7)(x - 9)
• গ. (x - 5)(x - 3)
• ঘ. (x - 8)(x - 7)

38. If x and (x + 11)/2 are integers, which of the following must be true? i. x is odd ii. x is a multiple of 9 iii. (x + 9)/2 is an integer

• ক. i only
• খ. ii only
• গ. iii only
• ঘ. i and ii

39. If n and p are both even number, which of the following number must be an odd number?

• ক. n +2p
• খ. np + 1
• গ. n + p
• ঘ. 2n + p

40. If the sum of four consicutive even integer is s, what is the greatest of the integers in terms of s?

• ক. (s + 12)/4
• খ. (s - 12)/4
• গ. (s + 6)/4
• ঘ. (s - 6)/4

41. If N and P are odd numbers then which of the following must be even number?

• ক. NP
• খ. 2N + P
• গ. N + P
• ঘ. NP + 2

42. What is the difference between the 6 digit largest and the smallest numbers?

• ক. 888889
• খ. 899999
• গ. 999888
• ঘ. 988888

43. The average of 3 numbers is 7. If 2 of the numbers are zero, then what is the 3rd number?

• ক. 15
• খ. 17
• গ. 19
• ঘ. 21

44. The value of - 3 - (- 10) is how much greater than the value of - 10 - (- 3)?

• ক. 0
• খ. 6
• গ. 7
• ঘ. 14

45. What are all values of x that satisfy the equation x2 + 4x + 3 = 0?

• ক. - 3
• খ. - 1
• গ. - 3 and - 1
• ঘ. 3 and 4

46. How many pupils can be seated in a room with N single chairs and B double seated benches?

• ক. nb
• খ. 2nb
• গ. 2(b + n)
• ঘ. 2b + n

47. A number consists of two digits. The sum of the digits is 10. If 72 is subtracted from the number, it's digits are interchanged. Find the number.

• ক. 82
• খ. 37
• গ. 55
• ঘ. 73

48. If k is an integer and .0010101×10k is greater than 1000, what is the least possible value of k?

• ক. 2
• খ. 3
• গ. 4
• ঘ. 5

49. If 18 is 15 percent of 30 percent of a certain number, what is the number?

• ক. 9
• খ. 36
• গ. 40
• ঘ. 81

50. Which of the following franctions has the smallest value?

• ক. 34.7/163
• খ. 125/501
• গ. 173/700
• ঘ. 10.9/42.7