Practice MCQ Questions and Answer on Number System
631.
If (-1)n + (-1)4n = 0, then n is
(A) Any positive integer
(B) Any negative integer
(C) Any odd natural number
(D) Any even natural number
Solution:
Putting n = 1, 2, 3, 4, 5 . . . . n = 1 in the given equation (-1)1 + (-1)4 × 1 = 0 Or, -1 + 1 = 0 n = 2 (-1)2 + (-1)4 × 2 = 0 Or, 1 + 1 ≠ 0 n = 3, -1 + 1 = 0 We will see that the given condition will be satisfy only for ANY ODD NATURAL NUMBER.
632.
A boy appeared in CAT for four consecutive year years, but coincidentally each time his net score was 75. He told me that there was rd negative marking for every wrong answer and 1 mark was allotted for every correct answer. He has attempted all the questions every year, but certainly some answers have been wrong due conceptual problem. Which is not the total number of questions asked for CAT in any year, in that period?
(A) 231
(B) 163
(C) 150
(D) 123
Solution:
Option method: The best way to go through options. You will find that when you consider 150 questions you cannot get 75 marks anyhow. Alternatively: Since 75 is an integer, he must have to do (75 + 4x) problems, where x is a whole number. Now we put the value of x (0, 1, 2, 3, 4, 5 .........) to get the correct answer. As he gets the net marks in integer it means when he does 3n question wrong, he losses actually 4n marks.
633.
If you subtract - 1 from + 1, what will be the result ?
(A) - 2
(B) 0
(C) 1
(D) 2
Solution:
(+ 1) - (- 1) = (+ 1 + 1) = 2
634.
The number of prime numbers between 0 and 50 is :
(A) 14
(B) 15
(C) 16
(D) 17
Solution:
Prime numbers between 0 and 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47 Their number is 15
635.
The difference between the squares of any two consecutive integers is equal to :
(A) an even integer
(B) difference of given integers
(C) sum of given integers
(D) product of given integers
Solution:
Let the two consecutive integers be a and (a + 1). Then, (a + 1)2 - a2 = a2 + 1 + 2a - a2 = (2a + 1) = (a + a + 1) = sum of given integers
636.
What is the value of x so that the seven digit number 8439x53 is divisible by 99?
(A) 9
(B) 4
(C) 3
(D) 6
Solution:
8 + 4 + 3 + 9 + x + 5 + 3 = 9 or multiple of x + 5 = 9 x = 4
637.
What is the least value of x such that 517x324 is divisible by 12?
(A) 3
(B) 1
(C) 0
(D) 2
Solution:
Divisibility rule of 3 : The sum of all digit should be divide by 3
638.
252 m of pant cloth and 141 m of shirt cloth are available in a cloth store. To stitch one pant and one shirt, m and m of cloth are needed respectively. Then the approximate number of pants and shirts that can be made out of it are :
(A) (80, 100)
(B) (100, 80)
(C) (100, 90)
(D) (90, 80)
Solution:
Number of pants can be made = = 100 Number of shirts can be made = = 80 Number of pants and shirts = 100, 80
639.
On multiplying a number by 7, all the digits in the product appear as 3ÃÂÃÂÃÂâÃÂÃÂÃÂÃÂs. The smallest such number is :
(A) 47619
(B) 46719
(C) 48619
(D) 47649
Solution:
We keep on dividing 33333... by 7 till we get 0 as remainder. ∴ Required number = 47619
640.
If a and b are positive integers and ÃÂÃÂ = , then: