MU-NLPC/Calc-aqua_rat huggingface dataset:
At 6′o a clock ticks 6 times. The time between first and last ticks is 40 seconds. How long does it tick at 12′o clock
Choose the correct choice from the following choices:
A) 47  B) 88  C) 28  D) 66  E) 11

Solution: Explanation:   For ticking 6 times, there are 5 intervals.   Each interval has time duration of   40/5= 
  40/5 = 8
8 secs   At 12 o'clock, there are 11 intervals,   So total time for 11 intervals= 11 × 8 = 88 secs.   Answer: 88
Answer: B
Distance between two stations A and B is 1108 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of train during the whole journey. Answers:	A) 60 km/hr	B) 30.5 km/hr	C) 57 km/hr	D) 67.2 km/hr	E) None of these

Solution: Explanation :   Average speed = (2xy)/(x+y) km/hr   = (28456)/(84+56) km/hr   = (28456)/140 km/hr   = 67.2 km/hr.   Answer : 67.2 km/hr
Answer: D
If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C:D
Choose the correct choice from the following choices:	A) 15:24:30:35	B) 16:24:30:35	C) 17:24:30:35	D) 18:24:30:35	E) NONE OF THE ABOVE

Solution: Explanation:   A:16:24:30:35=2:3   16:24:30:35:C=4:5=(4∗3/4:5∗3/4)=3:15/4   C:D=6:7=(6∗15/24:7∗15/24)=15/4:35/8   A:16:24:30:35:C:D=2:3:15/4:35/8=16:24:30:35=8:12:9   ANSWER IS 16:24:30:35
Answer: B
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?  Choose the correct choice from the following answers
A) 50/625  B) 2/625  C) 4/625  D) 25/625  E) 75/625

Solution: I think most of the answers are missing a point. Let me try to put it across:   Total number of possible numbers are : 5x5 = 25   Correct number =1   Case 1: When he gets it right in first attempt: P(E1) = 1/25   Case 2: He gets 1st attempt wrong and second right:   When he gets it wrong then the probability of getting wrong is 24/25.   Now there are 24 cases with him and he chooses the right one this time.   Probability of right case is 1/24   Thus, P(E2) = 24/25 x 1/24   =1/25   Probability of getting it right in at most two cases = P(E1) + P(E2)   = 1/25 + 1/25   = 2/25   = 50/625   Option (50/625) is therefore right as most of you mentioned but the method employed was wrong.
Answer: A
There are 10 teams in a soccer league and each team plays each of the other teams once. How many games will be played in total?  Choose the correct option
A) 33 B) 36 C) 39 D) 42 E) 45

Solution: 10C2=45   The answer is 45.
Answer: E
A train running at 25 km/hr takes 60 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
Answers.
A) a) 200/3m175/3m  B) b) 30m190m  C) c) 50m45m  D) d) 100/3 m200/3  E) e) none of these

Solution: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m   lets solve it   To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.   The man covered the distance during 12sec is  5*5/60*12= 
 5*5/60*12 = 5
5m so the train covered a distance in 12 sec= 25*5/60*12= 
25*5/60*12 = 25
25   so the length of the train(Lt) is  5+25= 
 5+25 = 30
30m   Now crossing the platform means length of train+length of platform(Lt+p)= 60*25*5/60= 
60*25*5/60 = 125
125m Now the length of platform (Lp) is= 125-30= 
125-30 = 95
95m   So answer is 30m and 95m Must beb) 30m190meven though its mentioned 30m and 190m thinking so typo mistake...........
Answer: B
50 square stone slabs of equal size were needed to cover a floor area of 98 sq.m. Find the length of each stone slab?
Pick
A) 140cm  B) 767cm  C) 88cm  D) 666cm  E) 776cm

Solution: 140cmrea of each slab   =98/50m2=1.96m2   Length of each slab √1.96=1.4m=140cm
Answer: A
In a 100 m race, A runs at 8km per hour. If A gives B a start of 5 m and still him by 15 seconds, what is the speed of B ?
Choose the correct choice from the following choices:	A) 5.56 km/hr.	B) 5.06 km/hr.	C) 5.70 km/hr.	D) 6.76 km/hr.	E) 5.72 km/hr.

Solution: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.   B covers (100 - 5)= 
(100 - 5) = 95
95 m in (45 + 15)= 
(45 + 15) = 60
60 sec.   B's speed= (95 x 60 x 60)/(60 x 1000)km/hr = 5.7 km/hr.   Answer is 5.70 km/hr.
Answer: C
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
Choose the correct choice
A) 5/7 B) 5/9 C) 5/5 D) 5/3 E) 2/9

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 = 5/9.   Answer:5/9
Answer: B
What is the difference between the local values of 3 in the number 53403?
Choose the correct choice from the following choices
A) 2992  B) 2997  C) 2877  D) 2077  E) 1211

Solution: Explanation:   3000 â€“ 3 = 2997   Answer:2997
Answer: B
The average marks of a Suresh in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest?  Choices:
A) 55
B) 60
C) 62
D) 52
E) Cannot be determined

Solution: Total marks of 10 papers = 80 x 10 = 800   Total marks of 8 papers = 81 x 8 = 648   Total marks of two papers = (800 - 648)= 
(800 - 648) = 152
152   If highest total is 92, then the lowest total is    (152 - 92)= 
 (152 - 92) = 60
60.   ANSWER:60
Answer: B
If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between
Answers
A) 0 and 3/20	B) 3/20 and 1/5	C) 1/5 and 1/4	D) 1/4 and 3/10	E) 3/11 and 1/2

Solution: E. 3/11 and 1/2   Definitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation.   Now you have excellent explanantion byscthakur. In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it. 3/11 and 1/2
Answer: E
X and Y invest Rs.21000 and Rs.15000 respectively in a business. At the end of the year, they make a profit of Rs.25500. What is the share of X in the profit?
Choose the correct option.
A) Rs.14400  B) Rs.26400  C) Rs.12000  D) Rs.12500  E) Rs.14875

Solution: Ratio of the investment=21000:15000=7:5   Share of X in the profit=(25500×7)/12=14875   ANSWRs.14875R:Rs.14875
Answer: E
Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 70 more. What was his original selling price? Answers:	A) $770	B) $660	C) $700	D) $1100	E) $840

Solution: Let the original purchase price be X   So original selling price at 10% profit = 1.1X   If product is purchased at 10% less of original = 0.9X   Profit of 30% on this price = 1.3(0.9X)   He would have received $70 more in second scenario => 1.3(0.9X) - 1.1X = 70   => 0.07X = 70   => X = $1000   Original purchase price = $1000   Hence, original selling price (at 10% of profit) = 1.1(1000) = $1100   Option $1100
Answer: D
How many 6 digits no can be formed using 0,1,2,3,5,7 without repeatation?	Select.
A) 500  B) 600  C) 700  D) 800  E) 900

Solution: no. of words with all nos. is 6!   no. of words with 0 in 1st position is 5!   required no. 6!-5!=600   ANSWER:600
Answer: B
John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?	Choose the correct choice from the following answers: A) 26.5% B) 36.5% C) 46.5% D) 56.5% E) 66.5%

Solution: Let N be the total number of books sold. Hence   N = 75 + 50 + 64 + 78 + 135= 
75 + 50 + 64 + 78 + 135 = 402
402   Let M be the books NOT sold   M= 1200 - N = 1200 - 402= 
1200 - 402 = 798
798   Percentage   Books not sold / total number of books= 798/1200= 
798/1200 = 133/200 = around 0.665
0.665= 66.5%   correct answer 66.5%
Answer: E
When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?
Choose the correct answer
A) 30  B) 44  C) 42  D) 46  E) 50

Solution: Total # of students 20+28+18-(9+7+10)+4= 
20+28+18-(9+7+10)+4 = 44
44.   Answer: 44.
Answer: B
The combined salaries of three brothers is $270,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?	Pick one.
A) 45,000 B) 60,000 C) 55,000 D) 30,000 E) 40,000

Solution: Mr. Small = x;   Mr. Middle = 3/2*x;   Mr. Big = 2x.   x + 3/2*x + 2x = 270 --> x=60   Answer: 60,000
Answer: B
If Jake loses 29 pounds, he will weigh twice as much as his sister. Together they now weigh 99 pounds. What is Jake's present weight, in pounds? Choose the correct choice.
A) 69  B) 135  C) 139  D) 147  E) 188

Solution: J = Jake’s current weight, in pounds   S = Sister’s current weight, in pounds   We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:   J – 29 = 2S   J = 2S + 29 (Equation 1)   Next, we are told that “Together they now weigh 89 pounds.” We can also put this into an equation.   J + S = 89 (Equation 2)   To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:   2S + 29 = 89-S   3S = 60   S = 20   J + 20 = 89   J = 69   69nswer: 69
Answer: A
The value of x + x(xx) when x = 1 is:	Answers
A) 5
B) 8
C) 2
D) 1
E) 4

Solution: x + x(xx)   Put the value of x = 1 in the above expression we get,   =1 + 1(1)   = 1 + 1(1)   = 1 + 1= 
1 + 1 = 2
2 2ORRE2T ANSWER : 2
Answer: C
If a student loses 6 kilograms, he will weigh twice as much as his sister. Together they now weigh 132 kilograms. What is the student's present weight in kilograms? Answers.
A) 82 B) 84 C) 86 D) 88 E) 90

Solution: Let x be the weight of the sister.   Then the student's weight is 2x+6.   x + (2x+6) = 132   3x = 126   x = 42 kg   Then the student's weight is 90 kg.   The answer is 90.
Answer: E
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?  Choose the most appropriate option.
A) 5% B) 29% C) 10% D) 80% E) 90%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 70   2/3 SP1 = 70   SP1 = 105   100 --- 5 => 5%   5%nswer: 5%
Answer: A
A sum of Rs.312 was divided among 100 boys and girls in such
a way that each boy gets Rs.3.60 and each girl Rs.2.40. Select the correct option.
A) 45 B) 49 C) 52 D) 60 E) 74

Solution: Let number of boys = x   Then number of girls = (100-x)   3.60x +2.40(100-x) = 312 ¡ê 1.2x   = 312 - 240= 
312 - 240 = 72
72 ¡ê x= 60   answer :60
Answer: D
How many integers are divisible by 3 between 20! and 20! + 20 inclusive?	Answers:
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: B - 7   20! is divisible by 3   There are 6 numbers between 10! and 10!+20 that are divisible by 3.   Hence 7
Answer: B
The average age 8 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?  Options
A) 14 years  B) 16 years  C) 18 years  D) 12 years  E) 11 years

Solution: 2 * 2   = 16   Answer:16 years
Answer: B
If an object travels 200 feet in 2 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)  Choose the correct choice
A) 68 B) 54 C) 21 D) 48 E) 22

Solution: 1 mile = 5280 feet   => 1 feet = 1/5280 miles   If the object travels 200 feet in 2 sec   then it travels 200/2 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)   = 3600 * 100 feet in 1 hour   = 360000 feet in 1 hr   = 360000/5280 miles in 1 hour   = 36000/528 miles/hr ~ 68 miles/hr   68nswer - 68
Answer: A
A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?	Choose the correct choice from the following answers:
A) 1:5 B) 2:3 C) 4:9 D) 4:3 E) 6:2

Solution: Explanation:   12:9   = 4:3   Answer: 4:3
Answer: D
In a throw of dice what is the probability of geÆ«ng number greater than 3  Pick one
A) 1/2  B) 1/3  C) 1/5  D) 1/6  E) None of these

Solution: Explanation:   Number greater than 3 is 4, 5, 6, so only 3 number   Total cases of dice = [1,2,3,4,5,6]   So probability = 3/6 = 1/2   1/2nswer: 1/2
Answer: A
A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1406?	Choose the correct choice from the following answers:
A) s.109
B) s.108
C) s.100
D) s.95
E) s.102

Solution: 3x 4x 5x   6 9 4   18x + 36x + 20x = 1406   74x = 1406 => x = 19   5x = 95 Rs.   Answer:s.95
Answer: D
The value of x + x(xx) when x = 4 is:
Choose the correct choice from the following options.
A) 8	B) 10	C) 64	D) 14	E) 16

Solution: x + x(xx)   Put the value of x = 4 in the above expression we get,   4 + 4(4*4)   = 4 + 64= 
4 + 64 = 68
68   ANSWER : 64
Answer: C
A man traveled a total distance of 1800 km. He traveled one-third of the whole trip by plane and the distance traveled by train is two-thirds of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?	Answers:	A) 660	B) 680	C) 720	D) 760	E) 800

Solution: total distance traveled = 1800 km.   distance traveled by plane = 600 km.   distance traveled by bus = x   distance traveled by train = 2x/3   x + 2x/3 + 600 = 1800   5x/3 = 1200   x = 720 km   The answer is 720.
Answer: C
Find the average of first 40 natural numbers.
Pick one.
A) 20.5	B) 18	C) 19.5	D) 19	E) 17

Solution: Exp. Sum of first n natural numbers = n( n+1)/2   So, sum of first 40 natural numbers = 40*41/2= 
40*41/2 = 820
820   Required average=820/40= 
820/40 = 41/2 = around 20.5
20.5   20.5nswer:20.5
Answer: A
The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 950 per sq. metre.
Select:
A) s. 20,550
B) s. 15,600
C) s. 20,900
D) s. 17,600
E) s. 17,900

Solution: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.   Cost of paving = Rs. (950 Ã— 22) = Rs. 20900   Answer: Option s. 20,900
Answer: C
Employees of a certain company are each to receive a unique 8-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, and 7 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?  Options:
A) 1220 B) 1840 C) 2160 D) 2480 E) 2760

Solution: There are 6! ways to make codes starting with 12.   There are 6! ways to make codes starting with 24.   There are 6! ways to make codes starting with 36.   The number of codes is 3*6! = 2160.   The answer is 2160.
Answer: C
A train 140m long is running at 60kmph. In how much time will it pass a platform 260m long?
Choose the correct choice from the following options.
A) 15 seconds
B) 24 seconds
C) 28 seconds
D) 30 seconds
E) 35 seconds

Solution: Distance travelled = 140 + 260= 
140 + 260 = 400
400m   Speed= 60 * 5/8 = 50/3m   Time = 400 * 3/50= 
400 * 3/50 = 24
24 Second   Answer : 24 seconds
Answer: B
A reading list for a certain course consists of 10 books, of which 5 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?
Choose the correct option
A) 90
B) 115
C) 130
D) 144
E) 155

Solution: Ans: B   Solution: Selection requires at most 2 novels, means=   0N4P + 1N3P + 2N2P   5c0*5c4+ 5c1*5c3 + 5c2*5c2   = 5+ 50 + 100= 
5+ 50 + 100 = 155
155   Ans: 155
Answer: E
A thief steals at a car at 2.30 p.m. and drives it at 40 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?  Pick one:
A) 6:34 p.m B) 9:34 p.m C) 3:34 p.m D) 2:34 p.m E) 3:41 p.m

Solution: :   Suppose the thief is overtaken x hrs after 2.30 p.m.   Then, distance covered by the owner in (x - 1/2) hrs.   40x = 75(x - 1/2) => x = 15/14hrs.   So, the thief is overtaken at 3:34 p.m.'   Answer: 3:34 p.m
Answer: C
Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers l did Carl drive each way?	Choose the correct choice from the following answers:
A) 350 B) 345 C) 320 D) 280 E) 240

Solution: Let us backsolve here.   The answer option has to be divisible by 7 to give us 1/2.   Let us try l=280 km. Time taken will be 3.5 hours and 4 hours.   Hence 280 is the answer.
Answer: D
How many different letter arrangements can be made from the letters of the word RECOVER?
Choose one:	A) 1210	B) 5040	C) 1260	D) 1200	E) None of these

Solution: Possible arrangements are :   7!/2!×2!=1260 [division by 2 times 2! is because of the repetition of E and R]   Answer 1260
Answer: C
In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?  Choose the correct choice from the following answers:
A) 200
B) 300
C) 600
D) 700
E) 100

Solution: E   100   Let the number of students be x.   Then, Number of students above 8 years of age = (100 - 20)= 
(100 - 20) = 80
80% of x.   80% of x= 48 + 2/3 of 48   80/100x = 80   x = 100.
Answer: E
Mr. Jones sold two pipes at $2.50 each. Based on the cost, his profit one was 30% and his loss on the other was 20%. On the sale of the pipes. Find the amount of his profit or loss?	Choose the correct choice from the following choices
A) gain 0.25 cents
B) lost 4 cents
C) broke even
D) gained 4 cents
E) gained 10 cents

Solution: 30 % profit on $ 2.50   = $ 30/100 × 2.50   = $ 0.30× 2.50   = $ 0.75   Similarly, 25 % loss on $ 2.50   = $ 20/100 × 2.50   = $ 0.20× 2.50   = $ 0.50   Therefore, in one pipe his profit is $ 0.75 and in the other pipe his loss is $ 0.50   So profit by amount 0.25 cents   gain 0.25 centsnswer is gain 0.25 cents.
Answer: A
Parents spend an estimated $200 at the fair every year, and the fair typically wants to reach a goal of bringing profits at $150,000. To achieve that goal, how many parents need to be attending the fair for the 5 days it is open? The amount of parents need to be rounded to whole numbers.  Pick.
A) 130 people per day B) 145 people per day C) 200 people per day D) 175 people per day E) 150 people per day

Solution: To find out our answer, we must think about how much the fair could make in the time allotted.   So, we divide 150,000 by 5 to get 30,000   We then divide 30,000 by 200 to get our answer.   This is possible since we are following rules of division for 5 and 200.   Correct Option: 150 people per day
Answer: E
The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$420 per month. The salary of the new supervisor is:	Options.
A) 233	B) 600	C) 287	D) 780	E) 191

Solution: Explanation:   Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870   Now total salary of 8 workers = 3870 âˆ’ 870 = 3000   Total salary of 9 workers including the new supervisor = 9 Ã— 420 = 3780   Salary of the new supervisor = 3780 âˆ’ 3000 = 780   Answer: 780
Answer: D
In one hour, a boat goes 19 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
Choose one
A) 2 B) 4 C) 7 D) 12 E) 15

Solution: Sol.   Speed in still water = 1/2 (19+5) kmph = 12 kmph.   Answer 12
Answer: D
A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 40 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period? Choose the correct choice
A) 79	B) 89	C) 95	D) 72.72	E) 97.2

Solution: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6   A1+A2+A3+A4+A5+A6 = 100*6= 
100*6 = 600
600   The year before , the 5 courses be B1, B2 , B3 , B4 , B5   B1+B2+B3+B4+B5= 40*5= 
40*5 = 200
200   Student's average= (600+200)/11 = 72.72   Answer 72.72
Answer: D
The bankerâ€™s discount on Rs. 1600 at 12% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
Pick.
A) 2 months  B) 4 months  C) 5 months  D) 7 months  E) None

Solution: Sol.   S.I. on Rs. 1600 = R.D. on Rs. 1680.   âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 12%.   âˆ´ Time = [100 * 80 / 1600 * 12] year = 3/7 year = 5 months.   Answer 5 months
Answer: C
Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 110000 and 1100000 ? Choose the correct answer
A) 10  B) 11  C) 101  D) 1011  E) 10001

Solution: Binary Divison can provide a quick answer if you are comfortable with it.   as option E is the biggest binary number we try with it first :   100010000/ 11 =10000   1000100000/ 11 =100000   so answer is option is 11
Answer: B
Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 30 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 12 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?  Choose the correct choice from the following answers
A) 52 B) 67 C) 71 D) 73 E) 64

Solution: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)   n(E or F or I) = 26 + 26 + 30 - 0 - 12 - 6 + 0   Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.   n(64 or F or I) = 64   Answer (64)
Answer: E