Number System (Part-4)​​​

11. 6²⁵+6²⁶+6²⁷+6²⁸ is divisible by: [Higher Secondary 25/06/2024 (Shift-2)]

(a) 254
(b) 259
(c) 256
(d) 255

Correct Answer: (b) 259

Solution:

12. If a car covers 90 km using 4 litres of petrol, how much distance (in km) will it cover using 32 litres of petrol? [Higher Secondary 25/06/2024 (Shift-4)]

(a) 720
(b) 710
(c) 680
(d) 650

Correct Answer: (a) 720

Solution:

13. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 12, then what is the dividend? [Higher Secondary 25/06/2024 (Shift-4)]

(a) 368
(b) 372
(c) 386
(d) 352

Correct Answer: (b) 372

Solution:

14. Which of the following numbers will completely divide 4¹²+4¹³+4¹⁴+4¹⁵ [Higher Secondary 25/06/2024 (Shift-4)]

(a) 17
(b) 11
(c) 3
(d) 7

Correct Answer: (a) 17

Solution:

4¹²+4¹³+4¹⁴+4¹⁵
⇒ 4¹² (1 + 4¹ + 4² + 4³)
⇒ 4¹² (1 + 4 + 16 + 64) ⇒ 4¹² (85)
85 is divisible by 17 and hence 17 is the answer.

15. Without actual division, find the remainder when 379843 is divided by 3. [Higher Secondary 26/06/2024 (Shift-2)]

(a) 4
(b) 1
(c) 3
(d) 2

Correct Answer: (b) 1

Solution:

16. If the six-digit number 15x1y2 is divisible by 44, then the minimum value of (x + y) is equal to:

(a) 5
(b) 6
(c) 8
(d) 7

Correct Answer: (d) 7

Solution:

17. If a 9-digit number 389x6378y is divisible by 72, then the value of 6x+7y is:

(a) 64
(b) 32
(c) 16
(d) 28

Correct Answer: (a) 64

Solution:

18. Which of the following numbers is divisible by 9? [Graduate Level 20/06/2024 (Shift-3)]

(a) 553986
(b) 350846
(c) 941201
(d) 132490

Correct Answer: (a) 553986

Solution:

19. The five-digit number 725yz is divisible by 15. What is the maximum possible value of the product of y and z ? [Graduate Level 21/06/2024 (Shift-3)]

(a) 45
(b) 30
(c) 35
(d) 40

Correct Answer: (d) 40

Solution:

20. If the 6 digit number 70024 is completely divisible by 8, then the smallest integer in place of will be [Graduate Level 24/06/2024 (Shift-3)]

(a) 0
(b) 2
(c) 4
(d) 6

Correct Answer: (b) 2

Solution:

Number System (Part-4)​​​

11. 6²⁵+6²⁶+6²⁷+6²⁸ is divisible by: [Higher Secondary 25/06/2024 (Shift-2)]

12. If a car covers 90 km using 4 litres of petrol, how much distance (in km) will it cover using 32 litres of petrol? [Higher Secondary 25/06/2024 (Shift-4)]

13. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 12, then what is the dividend? [Higher Secondary 25/06/2024 (Shift-4)]

14. Which of the following numbers will completely divide 4¹²+4¹³+4¹⁴+4¹⁵ [Higher Secondary 25/06/2024 (Shift-4)]

15. Without actual division, find the remainder when 379843 is divided by 3. [Higher Secondary 26/06/2024 (Shift-2)]

16. If the six-digit number 15x1y2 is divisible by 44, then the minimum value of (x + y) is equal to:

17. If a 9-digit number 389x6378y is divisible by 72, then the value of 6x+7y is:

18. Which of the following numbers is divisible by 9? [Graduate Level 20/06/2024 (Shift-3)]

19. The five-digit number 725yz is divisible by 15. What is the maximum possible value of the product of y and z ? [Graduate Level 21/06/2024 (Shift-3)]

20. If the 6 digit number 7002*4 is completely divisible by 8, then the smallest integer in place of * will be [Graduate Level 24/06/2024 (Shift-3)]

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Number System (Part-4)

20. If the 6 digit number 70024 is completely divisible by 8, then the smallest integer in place of will be [Graduate Level 24/06/2024 (Shift-3)]