q: Find the smallest number which should be multiplied with 520 to make it a perfect square.
Options:
(A) 30
(B) 120
(C) 55
(D) 35
(E) None of these
a: Stream of consciousness: 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5
Required smallest number = 2 * 13 * 5 = 130
130 is the smallest number which should be multiplied with 520 to make it a perfect squar The answer is (E).

question: John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
Options:
(A) 201
(B) 301
(C) 401
(D) 101
(E) 501
answer: Stream of consciousness: The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't. The answer is (B).

q: What is the sum of all the prime numbers greater than 30 but less than 50?
Options:
(A) 126
(B) 199
(C) 198
(D) 188
(E) 122
a: Stream of consciousness: Required sum = (31 + 37 + 41 + 43 + 47) = 199
Note: 1 is not a prime number The answer is (B).

question: There are 250men and 150 women in a committee, if all will work they will complete 12 units per day, if all men work they will complete 15 units per day, how many units will women complete per day?
Options:
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
answer: Stream of consciousness: I think there is a mistake in this question. If all men and women together complete 12 units, how only men can do 15 Units of work a day?
Forgetting about the reality, Women can do -3 units a day. The answer is (B).

q: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
Options:
(A) 1875
(B) 2000
(C) 2375
(D) 2500
(E) 3875
a: Stream of consciousness: Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375 The answer is (C).

q: Select Odd number:
6, 9, 15, 21, 24, 28, 30
Options:
(A) 20
(B) 21
(C) 24
(D) 28
(E) 30
a:
Stream of consciousness: Each of the numbers except 28, is a multiple of 3. The answer is (D).