Exams › SSC CGL (Prelims) › Maths › Number System
26 questions with worked solutions.
Q1. The number 4,29,714 is divisible by:
Answer: 3 and 6
For divisibility by 3, the sum of digits is 4+2+9+7+1+4=27, which is divisible by 3. For divisibility by 6, the number must be divisible by 2 and 3; it is even and already divisible by 3, so it is divisible by 6.
Answer: 11: 8
The mean proportional of 1.21 and 0.09 is $\sqrt{1.21\times 0.09}=\sqrt{0.1089}=0.33$. The mean proportional of 0.16 and 0.36 is $\sqrt{0.16\times 0.36}=\sqrt{0.0576}=0.24$. Their ratio is $0.33:0.24=33:24=11:8$.
Q3. Replace * by the smallest digit so that 723*56* is divisible by 6.
Answer: 2
For divisibility by 6, the number must be even and its digit sum must be divisible by 3. The last star must be an even digit, and testing the smallest possible digit that satisfies the sum condition gives 2. Hence, the number is divisible by 6 when the digit is 2.
Answer: 4 and 0
For divisibility by 5, the last digit must be 0 or 5. Since the number must also be divisible by 8, the last three digits must be divisible by 8; only 840 works here. So * = 4 and # = 0.
Q5. Which of the following is the largest 5-digit number divisible by 47?
Answer: 99969
The largest 5-digit number is 99999. Dividing by 47 gives a quotient of 2127 with remainder, so the greatest multiple not exceeding 99999 is \(47\times 2127=99969\).
Answer: 28
For two numbers a and b, a × b = LCM × HCF. So the product is 84 × 7 = 588. If one number is 21, the other is 588 ÷ 21 = 28.
Q7. What is the HCF of 60 and 48?
Answer: 12
The HCF is the greatest number that divides both 60 and 48 without leaving a remainder. The common factors are 1, 2, 3, 4, 6, and 12, so the greatest is 12.
Q8. If the average of five consecutive even numbers is 34, what is the second number in the series?
Answer: 32
For five consecutive even numbers, the average is the middle number. So the numbers are 30, 32, 34, 36, 38, and the second number is 32.
Q9. Which of the following numbers is divisible by both 3 and 5?
Answer: 30
A number divisible by both 3 and 5 must be divisible by 15. Among the options, 30 is divisible by 15, so it satisfies both conditions.
Answer: 343
The cube of a number is the number multiplied by itself three times. So, $7^3 = 7 \times 7 \times 7 = 343$.
Answer: 8
If a number leaves remainder 3 when divided by 5, it can be written as 5k + 3. For the same number to leave remainder 8 when divided by 10, it must be of the form 10m + 8, which also gives remainder 3 on division by 5.
Q12. What is the smallest prime number?
Answer: 2
A prime number is a number greater than 1 with exactly two factors: 1 and itself. The smallest such number is 2.
Q13. Find the square root of 1225.
Answer: 35
The square root of a number is the value that, when multiplied by itself, gives the original number. Since 35 × 35 = 1225, the square root is 35.
Q14. Find the LCM of 12, 15 and 20.
Answer: 60
The prime factors are 12 = $2^2 \times 3$, 15 = $3 \times 5$, and 20 = $2^2 \times 5$. Taking the highest powers gives $2^2 \times 3 \times 5 = 60$.
Q15. What is the cube root of 64?
Answer: 4
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. Since $4^3=64$, the cube root is 4.
Q16. What is the value of \(\pi\) up to two decimal places?
Answer: 3.14
The value of \(\pi\) is approximately 3.14159. Rounded to two decimal places, it becomes 3.14.
Q17. Find the square root of 625.
Answer: 25
The square root of a number is the value that, when multiplied by itself, gives the original number. Since $25 \times 25 = 625$, the square root is 25.
Q18. What is the HCF of 24 and 36?
Answer: 12
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest common factor is 12.
Q19. What is the square root of 900?
Answer: 30
The square root of a number is the value that, when multiplied by itself, gives the original number. Since 30 × 30 = 900, the square root of 900 is 30.
Answer: 50
Compute each square: $3^2=9$, $4^2=16$, and $5^2=25$. Their sum is $9+16+25=50$.
Answer: 6
The cube root of 216 is the number that when multiplied by itself three times gives 216. Since $6^3 = 216$, the cube root is 6.
Answer: 343
The cube of a number is the number multiplied by itself three times. So, $7^3 = 7 \times 7 \times 7 = 343$.
Q23. What is the square root of 289?
Answer: 17
The square root of a number is the value that, when multiplied by itself, gives the original number. Since $17 \times 17 = 289$, the square root of 289 is 17.
Q24. What is the cube root of 512?
Answer: 8
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. Since $8 \times 8 \times 8 = 512$, the cube root of 512 is 8.
Q25. What is the HCF of 18 and 24?
Answer: 6
The factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest common factor is 6.
Q26. What is the LCM of 12 and 18?
Answer: 36
The prime factors are 12 = $2^2 \times 3$ and 18 = $2 \times 3^2$. Taking the highest powers of each prime gives LCM = $2^2 \times 3^2 = 36$.