Number System (Part-6)​​​

1. If ³√N lies between 6 and 7, where N is an integer then how many values N can take? [SSC CGL Tier II (08/08/2022)]

(a) 126
(b) 127
(c) 128
(d) 125

Correct Answer: (a) 126

Solution:

2. If the digits of a two digit number is reversed, then the number is decreased by 36. Which of the following. is correct regarding the number? [SSC CGL Tier II (08/08/2022)]

I. The difference of the digits is 4.
II. The value of number can be 84.
III. Number is always a composite number.

(a) I, II and III
(b) II and III
(c) I and III
(d) I and II

Correct Answer: (d) I and II

Solution:

3. x, y and z are distinct prime numbers where x<y<z. If x + y + z = 70 then what is the value of z? [SSC CGL Tier II (08/08/2022)]

(a) 29
(b) 43
(c) 31
(d) 37

Correct Answer: (d) 37

Solution:

4. How many numbers are there from 400 to 700 in which the digit 6 occur exactly twice? [SSC CGL Tier II (08/08/2022)]

(a) 19
(b) 18
(c) 21
(d) 20

Correct Answer: (d) 20

Solution:

5. What is the sum of the first 20 terms of the following series? [SSC CGL Tier II (08/08/2022)]

1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 .......

(a) 3160
(b) 2940
(c) 3240
(d) 3080

Correct Answer: (d) 3080

Solution:

6. What is the value of 7/2 + 11/2 + 7/6 +11/15 + 7/12 + 11/35 +......+ 7/156 + 11/575 ? [SSC CGL Tier II (08/08/2022)]

(a) 3917/355
(b) 3816/325
(c) 3714/345
(d) 3216/315

Correct Answer: (b) 3816/325

Solution:

7. Which of the following is not a pair of co-prime numbers? [Graduate Level 01/08/2022 (Shift-4)]

(a) 22, 24
(b) 1,4
(c) 3,7
(d) 21, 22

Correct Answer: (a) 22, 24

Solution:

8. The sum of three prime numbers is 90. If one of them exceeds another by 30, then one of the numbers is: [Graduate Level 05/08/2022 (Shift-3)]

(a) 41
(b) 67
(c) 47
(d) 59

Correct Answer: (d) 59

Solution:

9. If 608xy0 is divisible by both 3 and 11, the nonzero digit in the hundred's place and ten's places, respectively, are: [Higher Secondary 02/08/2022 (Shift-2)]

(a) 5 and 6
(b) 5 and 8
(c) 8 and 5
(d) 6 and 5

Correct Answer: (c) 8 and 5

Solution:Divisibility of 3 :- A number is divisible by 3 if the sum of the number is divisible by 3.
Divisibility of 11 :- A number is divisible by 11 if the difference of sum of odd places values and even places values is equal to 0 or multiple of 11.
Given no. = 608xy0
Sum of no. = 6 + 0 + 8 + x + y + 0
= 14 + x + y
x + y = 1, 4, 7, 10, 13 and so no. --------(i)
Difference between Sum of the odd place
value and even place value
= (6 +8 + y) - (x)
= 14 + y - x ⇒ 14 + y - x = 0
⇒ x - y = 14 or 3 -------(ii)
From (i) and (ii)
x + y = 13 , x - y = 3
2x = 16 ⇒ x = 8 and y = 5
So, 608850 is divisible by both 3 and 11.

10. If the 5-digit number 743pq, is divisible by 90, then q/p = 7 [Higher Secondary 05/08/2022 (Shift-2)]

(a) 0
(b) 5
(c) 10
(d) 1

Correct Answer: (a) 0

Solution:

Number System (Part-6)​​​

1. If ³√N lies between 6 and 7, where N is an integer then how many values N can take? [SSC CGL Tier II (08/08/2022)]

2. If the digits of a two digit number is reversed, then the number is decreased by 36. Which of the following. is correct regarding the number? [SSC CGL Tier II (08/08/2022)]

3. x, y and z are distinct prime numbers where x<y<z. If x + y + z = 70 then what is the value of z? [SSC CGL Tier II (08/08/2022)]

4. How many numbers are there from 400 to 700 in which the digit 6 occur exactly twice? [SSC CGL Tier II (08/08/2022)]

5. What is the sum of the first 20 terms of the following series? [SSC CGL Tier II (08/08/2022)]

6. What is the value of 7/2 + 11/2 + 7/6 +11/15 + 7/12 + 11/35 +......+ 7/156 + 11/575 ? [SSC CGL Tier II (08/08/2022)]

7. Which of the following is not a pair of co-prime numbers? [Graduate Level 01/08/2022 (Shift-4)]

8. The sum of three prime numbers is 90. If one of them exceeds another by 30, then one of the numbers is: [Graduate Level 05/08/2022 (Shift-3)]

9. If 608xy0 is divisible by both 3 and 11, the nonzero digit in the hundred's place and ten's places, respectively, are: [Higher Secondary 02/08/2022 (Shift-2)]

10. If the 5-digit number 743pq, is divisible by 90, then q/p = 7 [Higher Secondary 05/08/2022 (Shift-2)]

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Number System (Part-6)