dr raju's problem/need clarification

[trisa120]

need clear explanation

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?

[Atreides]

1. (10^8 + 10^9 + 10^10 + 10^11 + 10^12) = 10^8( 1 + 10 + 100 + 1000 + 10000) = 10^8 * 11111.
10^8 can't be divided by 11, the same for 11111. Hence, the remainder is > 0. So, answer is A.

2. Let A = (7^6 + 7^7 + 7^8 + 7^9 + 7^10) = 14*m + k, where 0<=k<14
We are interested in finding k. What do we know about A? It is divisible by 7.
Hence, 14*m + k should be divisible by 7. It means that k is either 7 or 0.
But all 7^p, where p > 0 are odd and there are five of them. It means that A is odd, and, hence, k can't be zero.
Answer is 7.

[Atreides]

3. Let's calculate the opposite, how many number are divided by either 5 or 7.
For 5, there are 20 of them. For 7, 12 of them. But, there are two numbers 35 and 70 that are in both groups. Hence, the total number is 30.
And the X is 1000 - 30 = 70.
A is the answer.

[finix_regen]

3. the answer is C. following Atreides method- ..for 7 there are 14 of dem (7*14=98) so the total numbr is 20+14-2=32 hence num of elements,100-32=68
5. i think answer is 7 prts.

[green_bear]

Question 4, the answer should be 7. How can a digit be "24" ?

[mlkovach]

4) I get 7 as well...

soln: you know that it follows the pattern 3, 33, 333, ....and you want to sum 10 and find the hundreds digit. well, terms 3-10 all have at least 3 digits (hundreds place) so take ____333*8, and you have ___664, then add 33+3=36 and get ___700

(note, ___ indicates that there are other digits but they do not matter for our calculation)

I agree with finix_regen on
3) C

5) I'm skeptical about this...assuming the question means that each line cuts the circle at 2 places each...then it should be 7,

but why would they say this? If the line cut at more than two places, it would cease to be a line...(in Euclidean geometry, a line is a straight curve, so it could at most intersect twice) perhaps they are defining line?

if they mean the three lines can cut at exactly 2 points total on the circle, then all three lines would be the same line, and the answer would be 2 parts. what is the OA?

[green_bear]

Yes, mikovach. I was confused about qstn 5 as well. And I think the qstn means each of the line cuts the circle at 2 places (so not tangent).

I think for me the hardest part in Quantative is their use of words. Sometimes it can be very misleading

[hahahuhut]

5) It should be 7