Number System Level 1 (Foundation) -Part 1 and Part 2

https://youtu.be/Q2NLTZo68bY

https://youtu.be/KcbLCwLe0jE

1. Which of the following pairs of numbers is co-prime but NOT prime individually?  (F)

(a) 7, 11

(b) 8, 15

(c) 9, 12

(d) 6, 10

2. Is 456,732 divisible by 12?  (F)

(a) Only by 3, not by 4

(b) No

(c) Only by 4, not by 3

(d) Yes

3. Find the smallest digit to replace in 4523 so that the number is divisible by 9.  (F)

(a) 7

(b) 5

(c) 4

(d) 2

4. Is 3,900,847 divisible by 7?  (F)

(a) Yes

(b) No, remainder is never 0 for numbers ending in 7

(c) Yes, remainder is always 0 for numbers ending in 7

(d) No

5. Find the greatest 4-digit number exactly divisible by 88.  (F)

(a) 9988

(b) 9900

(c) 9944

(d) 9955

6. What is the smallest number that leaves a remainder of 1 when divided by each of 2, 3, 4, 5, and 6?  (F)

(a) 60

(b) 121

(c) 31

(d) 61

7. How many factors does 1,800 have?  (F)

(a) 32

(b) 40

(c) 24

(d) 36

8. Find the sum of all factors of 720.  (F)

(a) 2160

(b) 2016

(c) 2418

(d) 2480

9. Of the factors of 2² × 3³ × 5², how many are odd?  (F)

(a) 8

(b) 6

(c) 12

(d) 18

10. Find the HCF and LCM of 84, 126, and 210.  (F)

(a) HCF = 42, LCM = 1260

(b) HCF = 42, LCM = 2520

(c) HCF = 21, LCM = 2520

(d) HCF = 14, LCM = 1260

11. The HCF of two numbers is 12 and their LCM is 336. If one number is 84, find the other.  (F)

(a) 42

(b) 64

(c) 48

(d) 56

12. Find the HCF of 1,071 and 1,029.  (F)

(a) 42

(b) 7

(c) 14

(d) 21

13. Of 2⁴ × 3³ × 5², how many factors are perfect squares?  (F)

(a) 18

(b) 9

(c) 15

(d) 12

14. Three bells ring at intervals of 15, 20, and 25 minutes. If they ring together at 7:00 AM, at what time will they next ring together?  (F)

(a) 12:30 PM

(b) 11:00 AM

(c) 12:00 PM

(d) 1:00 PM

15. Find the remainder when 2⁴⁰ is divided by 7.  (F)

(a) 4

(b) 6

(c) 1

(d) 2

16. Find the remainder when 3²⁵⁰ is divided by 7.  (F)

(a) 4

(b) 2

(c) 5

(d) 1

17. Find the remainder when 7¹⁰⁰ is divided by 12 (F)

(a) 11

(b) 1

(c) 5

(d) 7

18. Find the remainder when 9⁵⁰ is divided by 10.  (F)

(a) 9

(b) 5

(c) 0

(d) 1

19. A number, when divided by 39, leaves a remainder of 17. What is the remainder when the same number is divided by 13?  (F)

(a) 0

(b) 8

(c) 4

(d) 17

20. Find the remainder when 15! is divided by 17  (F)

(a) 15

(b) 0

(c) 16

(d) 1

21. Find the unit digit of 7⁹⁵.  (F)

(a) 3

(b) 7

(c) 9

(d) 1

22. Find the unit digit of 234⁵⁶⁷.  (F)

(a) 4

(b) 2

(c) 8

(d) 6

23. Find the last two digits of 23²³.  (F)

(a) 67

(b) 87

(c) 43

(d) 23

24. Find the unit digit of 4¹⁷ + 9²³.  (F)

(a) 5

(b) 1

(c) 9

(d) 3

25. Convert 135 (base 10) to base 5.  (F)

(a) 1002

(b) 1200

(c) 1020

(d) 1010

26. Convert 10110 (base 2) to base 10.  (F)

(a) 26

(b) 22

(c) 20

(d) 18

27. If 421 in base 5 equals x in base 10, find x.  (F)

(a) 106

(b) 116

(c) 111

(d) 121

28. Find the number of trailing zeros in 40!.  (F)

(a) 7

(b) 10

(c) 8

(d) 9

29. Find the highest power of 3 that divides 50!.  (F)

(a) 24

(b) 16

(c) 22

(d) 20

30. Find the highest power of 6 that divides 30!.  (F)

(a) 15

(b) 26

(c) 14

(d) 10

Scroll to the bottom for answer key and refer embedded part 1 and part 2 videos for entire end to end concept as well as solutions or visit @iimwalabanda YouTube page

Q.No	Correct Option	Q.No	Correct Option
Q1	B (8, 15)	Q16	A (4)
Q2	D (Yes)	Q17	B (1)
Q3	C (4)	Q18	D (1)
Q4	D (No)	Q19	C (4)
Q5	C (9944)	Q20	D (1)
Q6	D (61)	Q21	A (3)
Q7	D (36)	Q22	A (4)
Q8	C (2418)	Q23	A (67)
Q9	C (12)	Q24	D (3)
Q10	A (HCF =42, LCM =1260)	Q25	C (1020)
Q11	C (48)	Q26	B (22)
Q12	D (21)	Q27	C (111)
Q13	D (12)	Q28	D (9)
Q14	C (12:00 PM)	Q29	C (22)
Q15	D (2)	Q30	C (14)