q: 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
a: Stream of consciousness: A number ending with 7 can never be a perfect square. The answer is (D).

question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 240 feet in circumference.After how many minutes are the three of them together again?
Options:
(A) 4 mins
(B) 10 mins
(C) 15 mins
(D) 3 mins
(E) 7 mins
answer: Stream of consciousness: Answer will be A
The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 4 mins. The answer is (A).

q: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 10 minutes, how much time will she spend doing yoga? (rounded to minutes)
Options:
(A) 10 min.
(B) 41 min.
(C) 17 min.
(D) 23 min.
(E) 25 min.
a: Stream of consciousness: The ratio is 2:3 = gym:ride, so (10)(3/2) = 15 minutes at the gym, and 15 + 10 = 25 minutes exercise, so (2/3)(25) = 17 minutes yoga. The answer is (C).

question: There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights?
Options:
(A) 8300
(B) 14500
(C) 7700
(D) 13000
(E) 5900
answer: Stream of consciousness: Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700 The answer is (C).

q: How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.
Options:
(A) 22
(B) 34
(C) 73
(D) 26
(E) 11
a: Stream of consciousness: Single digit numbers = 4
Double digit numbers = 4 x 3 = 12
Three digit numbers = 3 x 3 x 2 x 1 = 18
Total = 34 The answer is (B).

q: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 46
(B) 82
(C) 45
(D) 43
(E) 53
a:
Stream of consciousness: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46. The answer is (A).