 # Problems on Numbers System : Level 02

1. Which of the following numbers is divisible by 2?
1. 178653
2. 164857
3. 176485
4. 178560

A number is divisible by 2 if the last digit of the number is 0 or a multiple of 2. Therefore only 178560 is divisible by 2. So, answer is option 4.
2. Simplify the expression using BODMAS rule:: (3/2) of (4/7) {(10 × 3) – (8 × 2)}
1. 6
2. 12
3. 18
4. 14

Applying BODMAS rule = (3/2) of (4/7) {30 – 16} = (12/14) × 14=12
Therefore, the correct answer is option 2.
3. The product of 40 odd numbers is
1. even
2. odd
3. 625
4. Can’t say

The product of 40 odd numbers will give an odd number. So answer is option 2.
4. The six digit number 54321A is divisible by 9 where A is a single digit whole number. Find A.
1. 0
2. 2
3. 4
4. 3

A number is divisible by 9, when the sum of its digits is divisible by 9. Here, 5 + 4 + 3 + 2 + 1 + A = 15 + A should be divisible by 9. Therefore, A = 3 gives 15+ 3 = 18 as the sum of digits, which is divisible by 9. So, answer is option 4.
5. The seven digit number 43567X is divisible by 3, where X is a single digit whole number. Find X.
1. 2
2. 5
3. 8
4. All of these

A number is divisible by 3 when sum of its digits is divisible by 3. Here, sum of digits = 4 + 3 + 5 + 6 + 7 + X = 25 + X. So, X can be 2, 5, 8 which gives the sum 27, 30 and 33 respectively. Therefore, X has 3 values here, for which the number is divisible by 3. So, the answer is option 4.
1. Find the greatest three number which is multiple of 7.
1. 993
2. 995
3. 994
4. None of these

Greatest three digits number = 999. When 999 is divided by 7, the remainder will be 5. Required number= 999 – 5 = 994.
2. Find the greatest 6-digit number, which is a multiple of 12.
1. 999980
2. 999990
3. 999984
4. None of these

Greatest six-digit number is 999999. Divide this number by 12 and get remainder as 3. Since the remainder is 3, if you subtract 3 from the number, the remaining number will be a multiple of 12. So the greatest such number will be 999999 – 3 =999996.
3. Find the smallest three number which is a multiple of 7.
1. 103
2. 105
3. 98
4. None of these

Smallest three digit number =100. Divide this number by 7 and get the remainder as 2. If you subtract 2 from the number the remaining number will be a multiple of 7, 100 - 2 = 98 which is two digit number. Now if we add 7 so that we get the smallest three digit number which is a multiple of 7. Required number = 98 + 7 = 105.
4. Simplify the expression using BODMAS rule (3/7) of (4/5) of 20 (252 - 242)
1. 336
2. 168
3. 84
4. None of these