q: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
(A) 1
(B) 2
(C) 4
(D) 6
(E) 7
a: Stream of consciousness: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2 The answer is (B).


question: Two trains are moving at 65 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 6 2/3 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/9 sec
answer: Stream of consciousness: 70 + 65 = 135 * 5/18 = 75/2 mps
D = 150 + 100 = 250 m
T = 250 * 2/75 = 20/3 - 6 2/3 sec The answer is (A).


q: How many positive integers less than 50 have a reminder 01 when divided by 4?
Options:
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
a: Stream of consciousness: 1 also gives the remainder of 1 when divided by 4. So, there are total of 13 numbers. The answer is (A).


question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 7 ?
Options:
(A) 3
(B) 1
(C) 4
(D) 0
(E) 2
answer: Stream of consciousness: A number ending with 7 can never be a perfect square. The answer is (D).


q: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 28
(C) 26
(D) 27
(E) 21
a: Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec The answer is (A).


q: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:
(A) 229
(B) 108
(C) 278
(D) 126
(E) 112
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: S = 180/6 * 18/5 = 108 kmph The answer is (B).