question:How many common two-digit whole numbers are there which gives a remainder of 2 when divided by 9 and gives a remainder of 5 when divided by 8?
Options:
(A) Five
(B) Three
(C) One
(D) Two
(E) Four
answer:(C)
Stream of consciousness:Answer = C) One
Two digit numbers giving remainder 2 when divided by 9 = 11, 20, 29, 38, 47, 56, 65, 74, 83, 92
Two digit numbers giving remainder 5 when divided by 8 = 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93
Common Numbers = 29 = 1

question:If a 3-digit integer is selected at random from the integers 700 through 899, inclusive, what is the probability that the second digit is one greater then the first digit, and the third digit is one greater than the second digit?
Options:
(A) 2/225
(B) 2/200
(C) 8/700
(D) 1/50
(E) 1/200
answer:(E)
Stream of consciousness:Hundreds digit can be 7 or 8
If the hundreds digit is 7, then the tens digit has to be 8 and the units digit has to be 9
If the hundreds digit is 8, then the tens digit has to be 9 and the units digit has to be 10
A digit has to fall between 0 and 9, so 10 cannot be a digit
The number is 789
Total numbers between 700 and 899 = (899-700)+1 = 200
Probability = 1/200

question:In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is:
Options:
(A) 15
(B) 18
(C) 20
(D) 22
(E) 24
answer:
(C)
Stream of consciousness:Number = (35 * 12) = 420
Correct quotient = 420/21 = 20