need clear explanation

[trisa120]

1.Col A: The remainder when (10^8 + 10^9 + 10^10 + 10^11 + 10^12) divided by 11
Col B: 0
answer: A

2. What is the remainder, when (7^6 + 7^7 + 7^8 + 7^9 + 7^10) is divided by 14?
answer: 7

3. Given ‘X’ as a set of elements that has numbers between 1 and 100 inclusive and are not divisible by either 5 or 7.
Col A: Number of elements in X
Col B: 68

4. Given a series 3, 33, 333 ………. find the hundreds digit of the sum of first 10 numbers of the series?
answer:24

5. In how many maximum parts can a circular region be divided by using 3 lines which cut the circle at exactly 2 places?

[finsisher]

for 1st question( -1^8 + -1^9 ....... + -1^12) = 0+1 =1 so answer should be 1 and not zero

[ahsan400]

I think these Column Questions are from GRE. So finsisher's answer, which is A, is correct. Column A has bigger value.

finsisher: Can you please explain how you've resolved it?

[ahsan400]

Originally Posted by ahsan400

I think these Column Questions are from GRE. So finsisher's answer, which is A, is correct. Column A has bigger value.

finsisher: Can you please explain how you've resolved it?

Q:3 We've total numbers = 100
Numbers that are divisible by 5 = 20
Numbers that are divisible by 7 = 14
Numbers that are divisible by both 5 & 7 = 2
Total Numbers that are NOT divisible by 7 & 5 = 100 - (20 + 14 - 2) = 68
IMO Answer is C

[3Gs]

10^0 mod 11 = 1
10^1 mod 11 = 10
10^2 mod 11 = 1
10^3 mod 11 = 10
10^4 mod 11 = 1

(10^8 + 10^9 + 10^10 + 10^11 + 10^12) mod 11
= (1 + 10 + 1 + 10 + 1) mod 11
= (23) mod 11
= 1

[3Gs]

(7^6 + 7^7 + 7^8 + 7^9 + 7^10) is divided by 14

for n > 0, 7^n mod 14 = 7

7^6 + 7^7 + 7^8 + 7^9 + 7^10 = (7*5) mod 14 = 35 mod 14 = 7