question: Find the largest 5 digit number which is exactly divisible by 88?
Options:
(A) 98765
(B) 98907
(C) 99944
(D) 99954
(E) 99968
answer: Stream of consciousness: Largest 5 digit number is 99999
After doing 99999 ÷ 88 we get remainder 31
Hence largest 5 digit number exactly divisible by 88 = 99999 - 31 = 99968 The answer is (E).


q: The average of first four prime numbers greater than 10 is?
Options:
(A) 10
(B) 20
(C) 15
(D) 40
(E) 50
a: Stream of consciousness: 11 + 13 + 17 + 19 = 60/4 = 15 The answer is (C).


question: Find a a prime number from below options?
Options:
(A) 84
(B) 97
(C) 98
(D) 100
(E) 102
answer: Stream of consciousness: Clearly, 97 is a prime number. The answer is (B).


q: There are 10person 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) 7!*1!
(B) 7!*2!
(C) 6!*2!
(D) 8!*2!
(E) 6!*2!
a: Stream of consciousness: Total number of ways = 7!*2!. The answer is (B).


question: In how many ways can you seat 4 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
(A) 720
(B) 1720
(C) 2880
(D) 6
(E) 10080
answer: Stream of consciousness: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6. The answer is (D).


question: If L is the least positive integer that is divisible by every integer from 1 to 9 inclusive, then L/2 is =
Options:
(A)  5040
(B)  2520
(C)  1890
(D)  1260
(E)  630
answer:

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: The integer should be divisible by: 2, 3, 4, 5, 6, 7, 8 and 9, that is 2, 3, 2^2, 5, 2*3, 7, 2^3 and 3^2. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, L/2 is (7 * 5 * 3^2 * 2^3)/2 = 7*5*9*4 = 1260. The answer is (D).