q: A card shop contains 5 birthday cards, 4 holiday cards, and 3 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be graduation cards?
Options:
(A) 1/33
(B) 6/264
(C) 1/44
(D) 1/264
(E) 1/1320
a: Stream of consciousness: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 3/12
Probability of choosing 2nd card of the same type: 2/11
Probability of choosing 3rd card of the same type: 1/10
Multiply and you get 1/264 The answer is (D).


question: The inverse ratio of 4: 2: 1 is?
Options:
(A) 2:4:8
(B) 2:3:9
(C) 2:3:2
(D) 2:3:6
(E) 2:3:1
answer: Stream of consciousness: 1/4: 1/2: 1/1 = 2:4:8 The answer is (A).


q: There are 9 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
Options:
(A) 90
(B) 120
(C) 540
(D) 180
(E) 200
a: Stream of consciousness: Number of ways of selecting 2 fiction books = 9C2
Number of ways of selecting 2 non fiction books = 6C2
9C2 * 6C2 = 36 * 15 = 540 The answer is (C).


question: There are 13person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
Options:
(A) 4!*2!
(B) 7!*2!
(C) 6!*1!
(D) 10!*2!
(E) 5!*1!
answer: Stream of consciousness: Total number of ways = 10!*2!. The answer is (D).


q: Which of the following is not divisible by 3?
Options:
(A) 10,395
(B) 41,714
(C) 15,354
(D) 30,708
(E) 29,313
a: Stream of consciousness: Divisibility rule of 3: The sum of the digits of the number should be divisible by 3
Option A: 10395, Sum = 18. Divisible by 3
Option B: 41714, Sum = 17, Not divisible by 3. Hence the number 41714 is also not divisible by 3
Option C: 15354, Sum = 18, Divisible by 3
Option D: 30708, Sum = 18, Divisible by 3
Option E: 29313, Sum = 18, Divisible by 3 The answer is (B).


q: Find the 100th place digit of a number forming from digits 1 to 9 without repeatation and number passes the divisibility test of 11 means difference of sum of alternative digits is 0 or divisible by 11.
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: Largest no is 987652413
So digit will be 4 The answer is (D).