Page 14 - Arithmetic

Explanation:
1. The difference of two odd numbers: for example, 5 – 3 = 2; the result is even Sum of two even numbers = 2 + 4 = 6; the result is even
Product of two odd numbers = 3 × 7 = 21; the result is odd
Sum of two odd numbers = 3 + 9 = 12; the result is even
Product of one even and odd = 3 × 4 = 12; the result is even Therefore, the product of two odd numbers is always odd
2. 2 is the smallest prime number because 0 and 1 are neither prime nor composite numbers.
3. Case I: k is even; 25 =32
Case II: k is odd; 35 = 243
If k5 is odd, k can never be even
k4 is odd, k can never be even Therefore, statements II and III are false
4. Let a = -1, b = -2
a + b = -1 + (-2) = -3; sum of two negative integers is always negative ab = -1 × -2 = 2; product of two negative integers can never be negative a – b; the answer depends upon whether a>b or a<b
ab= -1 × -2 = 2; product of two negative integers is always positive Therefore, ab is positive will always hold true
5. Prime numbers less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 There are 15 prime numbers which are less than 50
6. 2 is the only even prime number
7. The largest digit in the options is 997
32 >√997
List of prime numbers less than 32
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
997 is not divisible by anyone. So, 997 is the largest 3-digit prime number.
8. 215: The number ends in 5, which means it’s divisible by 5. So, this is not a prime number. 507: The sum of the numbers is divisible by 3. So, it’s not a prime number
14 >√191
List of prime numbers less than 14
2, 3, 5, 7, 11, 13
191 is not divisible by any number. So, it’s a prime number
Page 13 of 55
Arithmetic Concept