MU-NLPC/Calc-aqua_rat huggingface dataset:
Truck P and Truck Q drive on the highway in the same direction at respective rates of 70 kph and 77 kph. If Truck Q is 4 km behind Truck P, by how much does Truck P need to increase the speed to catch up with Truck P in 15 minutes?	Choose the correct choice from the following:
A) 1 kph	B) 3 kph	C) 5 kph	D) 7 kph	E) 9 kph

Solution: Truck Q needs to gain 4 km in 15 minutes.   The relative speed difference needs to be 4 km / 15 minutes = 16 km/hour   Truck Q needs to increase up to 86 kph, thus an increase in 9 kph.   The answer is 9 kph.
Answer: E
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%. Their gross income from sales for one month increases by what percent?  Choose the correct answer:
A) 2%
B) 4%
C) 5%
D) 8%
E) 12%

Solution: Let List price of an item = 100   8%iscount on each item = 10%   8%iscounted price of an item = .9*100= 
.9*100 = 90
90   If they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%   Originally if 10 items were sold in a month , with the new discount 12 items will be sold   Original revenue= No of items* Price of an item = 10 * 100= 
10 * 100 = 1_000
1000   New revenue= 12 * 90= 
12 * 90 = 1_080
1080   Increase in gross income= 1080 - 1000= 
1080 - 1000 = 80
80   % increase in gross revenue= 80/1000 * 100= 
80/1000 * 100 = 8
8%   Answer 8%
Answer: D
Mohit sold an article for Rs. 18000. Had he offered a discount of 22% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?  Answers:
A) 13000	B) 27767	C) 16688	D) 26678	E) 19987

Solution: Let the CP be Rs. x.   Had he offered 22% discount, profit = 8%   Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 22/100(18000) = Rs. 14040   => 1.08x = 14040   => x = 13000   \13000nswer: 13000
Answer: A
50 men can complete a work in 65 days.Five days after started the work, 20 men left the group. In how many days can the remaining work be completed?
Pick one:
A) 767 days B) 666 days C) 555 days D) 5126 days E) 100 days

Solution: After 5 days, the following situation prevails.   50 men can complete the work in 60 days.   30 men can complete the work in ? days.   M1 D1 = M2 D2   => 50 * 60 = 30 * D2   => D2 = (50 * 60)/30= 
(50 * 60)/30 = 100
100 days.   Answer:100 days
Answer: E
The average age of three persons is 52 years. Their ages are in the proportion of 1:5:7. What is the age in years of the oldest one among them. Choose the correct choice:
A) 9 years B) 12 years C) 60 years D) 70 years E) 80 years

Solution: Explanation:   Let the age of three persons be x, 5x, 7x   = 13x/3 = 52   x= 12 years   Answer: Option 70 years
Answer: D
The cost of 10 kg of apples is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is Rs.20.50. Find the total cost of 4 kg of apples, 3 kg of rice and 5 kg of flour?	Choose the correct choice from the following answers
A) 777.4
B) 877.4
C) 577.4
D) 477.4
E) 177.4

Solution: Let the costs of each kg of apples and each kg of rice be Rs.a and Rs.r respectively.   10a = 24r and 6 * 20.50 = 2r   a = 12/5 r and r = 61.5   a = 147.6   Required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5   = 590.4 + 184.5 + 102.5 = Rs.877.40   Answer: 877.4
Answer: B
If A is thrice as fast as B and together can do a work in 21 days. In how many days A alone can do the work?
Select
A) 36 B) 42 C) 28 D) 54 E) 45

Solution: A’s one day’s work= 1/X   B’s one day’s work= 1/3x   A + B’s one day’s work= 1/x + 1/3x = 1/21   = 3+1/3x = 4/3x = 1/21   x = 21*4/3= 
21*4/3 = 28
28   ANSWER:28
Answer: C
When n is divided by 5 the remainder is 3. What is the remainder when (n + 3)^2 is divided by 5?	Choose the correct choice from the following options.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: n = 5x+3, for some integer x   (n+3)^2=(5x+6)^2=5y+36, for some integer y   When we divide this by 5, the remainder is 1.   The answer is 1.
Answer: B
A team scored a total of 126 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team?	Choose the correct choice from the following answers:
A) A)6 B) B)7 C) C)8 D) D)9 E) E)10

Solution: 126/14= 
126/14 = 9
9 plus remainder.   The answer is 9.
Answer: D
The sale price sarees listed for Rs.400 after successive discount is 20% and 15% is?	Pick
A) 297	B) 272	C) 342	D) 762	E) 269

Solution: 400*(80/100)*(85/100)= 
400*(80/100)*(85/100) = 272
272   Answer: 272
Answer: B
The diameter of the wheel of a car is 120m. How many revolution/min mustthe wheel makeing order to keep a speed of 60 km/hour approximately? Choose the correct choice from the following answers: A) 140 B) 160 C) 220 D) 250 E) 265

Solution: Distance to be covered in 1 min. = (60 X 1000)/(60) m = 1000 m.   Circumference of the wheel = (2 x (22/7) x 0.60) m = 3.77 m.   Number of revolutions per min. =(1000/3.77) = 265   265
Answer: E
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women? Pick
A) 11760 B) 266 C) 5040 D) 3000 E) 2000

Solution: Req no of ways = 8C5 * 10C6   =11760   11760NSWER 11760
Answer: A
P is three times as fast as Q and working together, they can complete a work in 14 days. In how many days can Q alone complete the work? Choose the correct choice from the following answers
A) 18 1/2 days  B) 17 1/2 days  C) 19 1/2 days  D) 14 1/4 days  E) 10 1/2 days

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 14 days, which means Q can do the work in 48 days.   Hence, P can do the work in 18 1/2 days.   18 1/2 daysnswer:18 1/2 days
Answer: A
If an investor puts $800 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?	Choose the correct choice from the following options:
A) $878
B) $880
C) $882
D) $884
E) $886

Solution: 1.05*1.05*800= 
1.05*1.05*800 = 882
$882   The answer is $882.
Answer: C
There are 3 bags, in 1st there are 9 Mangoes, in 2nd 8 apples & in 3rd 6 bananas. There are how many ways you can buy one fruit if all the mangoes are identical, all the apples are identical, & also all the Bananas are identical?  Select:
A) 648 B) 432 C) 23 D) 2 to the power(23)-1 E) 25

Solution: Since bags are different so it should be 9+8+6= 
9+8+6 = 23
23   ANSWER:23
Answer: C
How many three digits number can be formed by using the digits 1,2,3,4,5?
Choices:
A) 152	B) 125	C) 225	D) 325	E) 252

Solution: Here the repetition of digits allowed. The unit place of the number can be filled in by any of the given numbers in 5 ways. Simillarly each one of the ten's and the hundred's place can be filled in 5 ways. Therefor the total number of required numbers =5*5*5= 
5*5*5 = 125
125 Answer : 125
Answer: B
One out of every 250 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?  Options:
A) 2,000
B) 5,000
C) 10,000
D) 50,000
E) 25,000

Solution: 20 broken glasses indicates that  10*10= 
 10*10 = 100
100 defected bulbs are present.   100 defected bulbs indicates that 100*250= 25,000 light bulbs are present.   25,000 is the answer
Answer: E
Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-5# = 6, what is the value of #5#? Choose the correct answer: A) 5 B) 0 C) -8 D) -3 E) -5

Solution: #p# = ap^3 + bp - 1   #-5# = 6   putting p = -5 in above equation   -125a -(5b +1) = 6 or   #-5# = (125a+5b+1) = -6   therefore 125a+5b = -7 .....(1   now putting p = 5   #5# = 125 a+5b - 1   using equation 1(125a+5b = -7)   #5# = -7-1 = -8   hence -8
Answer: C
Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?  Pick one.
A) 81.6  B) 81.7  C) 81.0  D) 281.6  E) 81.2

Solution: SI = 40 + 40   CI = 40 + 40 + 1.6 = 81.6.81.6nswer: 81.6
Answer: A
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?  Choose the correct choice from the following choices
A) 3.34 sq m B) 3.38 sq m C) 3.24 sq m D) 3.36 sq m E) 5.34 sq m

Solution: 3.34 sq mrea of the path = 3.34 sq mrea of the outer circle - 3.34 sq mrea of the inner circle   = ∏{4/2 + 25/100}2 - ∏[4/2]2   = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }   = (3.14)(1/4)(17/4)   = 53.38/16   = 3.34 sq m   3.34 sq mnswer:3.34 sq m
Answer: A
If the gross salary for first year is Rs. 45000 and an employee has two options to choose from for increment .Either he can opt for 4% yearly increase or Rs. 25000/- yearly increase on the gross salary. If an employee choose the first option, after how many years his salary will be more than the option two ?  Choose one.
A) 15 years B) 16 years C) 17 years D) 18 years E) 19 years

Solution: if initial annual gross salary = Rs. 450000/-   check when   450000+25000*n = 450*(1+4/100)^n   After 18 years   ANSWER:18 years
Answer: D
A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?  Pick one:
A) 33
B) 37
C) 41
D) 45
E) 49

Solution: 5/7*P are ponies with horseshoes, so P is a multiple of 7.   2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21.   The minimum value of P is 21. Then H = P+3 = 24.   The minimum number of horses and ponies is 45.   The answer is 45.
Answer: D
An empty wooden vessel weighs 14% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
Choose the correct choice from the following answers:
A) 3/5	B) 5/9	C) 1/24	D) 4/9	E) 7/13

Solution: An empty wooden vessel weighs 14% of its total weight when filled with paint:   Vessel = 0.1(Vessel + Paint);   14V = V + P (so the weight of completely filled vessel is 10V)   P = 13V (so the weight of the paint when the vessels is completely filled is 9V).   The weight of a partially filled vessel is one half that of a completely filled vessel:   V + P' = 1/2*14= 
1/2*14 = 7
7V (so the weight of the paint when the vessels is partially filled is 7V).   What fraction of the vessel is filled?   So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:   P'/P= 7V/13V = 7/13.   Answer: 7/13.
Answer: E
In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?  Choose the correct choice from the following.
A) 16 2/3 %	B) 25 %	C) 33 1/3 %	D) 50%	E) 75%

Solution: 1986; 2/3   1988; 1/2   % decrease = change/original*100   2/3−1/2 / 2/3∗100   1/6∗3/2∗100=14∗100=25   Answer: "25 %"
Answer: B
A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values Q are within three standard deviations of the mean?
Choose the correct choice from the following options.
A) 0  B) 1  C) 3  D) 6  E) 7

Solution: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.   With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.1
Answer: B
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:	Choose the correct option:
A) 70 km/hr	B) 75 km/hr	C) 80 km/hr	D) 87.5 km/hr.	E) 97.5 km/hr.

Solution: Let the speed of two trains be 7x and 8x km/hr.   Then, 8x = 400/4= 
400/4 = 100
100   Let the speed of two trains be 7x and 8x km/hr.   x= 100/8= 
100/8 = 25/2 = around 12.5
12.5   Speed of first train= (7 x 12.5) km/hr = 87.5 km/hr.   Answer : 87.5 km/hr..
Answer: D
Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 60% problems right. How many more questions he would have to answer more to get
passed  Choose the correct choice from the following options: A) 5 B) 6 C) 7 D) 8 E) 9

Solution: Explanation:   Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)   = 7 + 12 + 21= 
7 + 12 + 21 = 40
40.   Questions to be answered correctly for 60%= 60% of total quations   = 60 % of 75 = 45.   He would have to answer 45 - 40= 
45 - 40 = 5
5   5nswer: Option 5
Answer: A
A wheel that has 6 cogs is meshed with a larger wheel of 9 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: Pick one.
A) 49
B) 4
C) 12
D) 14
E) 27

Solution: Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   9 : 6 :: 21 : x 9 * x = 6 x 21   x =	(6 x 21)/9   x = 14.   Answer is 14.
Answer: D
A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?
Choose the correct choice from the following options
A) 60  B) 80  C) 90  D) 115  E) 170

Solution: b+c=250_______(1)   1.5b+0.75c=315   2b+c=420_______(2)   (2)-(1)   b=170   c=80   b-c=170-80= 
170-80 = 90
90   ANSWER:90
Answer: C
The probability that a visitor at the mall buys a pack of candy is 10%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy? Choose the correct answer:
A) 0.009
B) 0.015
C) 0.027
D) 0.036
E) 0.054

Solution: One case is: candy - candy - no candy   The probability is 1/10*1/10*9/10 = 9/1000   There are 3 such cases, so we should multiply this probability by 3.   P(exactly 2 buy candy) = 9/1000 * 3 = 27/1000= 
27/1000 = 27/1_000 = around 0.027
0.027   The answer is 0.027.
Answer: C
Two years ago, Ram put $1,000 into a savings account. At the end of the first year, his account had accrued $100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 20%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of $1,000 ?
Pick:
A) 40%	B) 25%	C) 35%	D) 30%	E) 32%

Solution: investment 1000 dollars   1 st year total gained = 100   total amount end of first year = 1100   second year account increased by 20 % = 1100*0.2= 
1100*0.2 = 220
220   therefore total amount by second year end= 1320   so total percentage increase in money = (1320-1000)*100/1000= 
(1320-1000)*100/1000 = 32
32 %   Correct Answer 32%=32%
Answer: E
A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?  Choose one
A) 1222
B) 1289
C) 1210
D) 1129
E) 1123

Solution: π (232 – 122)   = 1210   Answer:1210
Answer: C
A number increased by 40% gives 1680. The number is? Pick:
A) 1680  B) 1600  C) 1200  D) 1500  E) 600

Solution: Formula = TOTAL=100% ,IN1200REASE = "+" DE1200REASE= "-"   A number means = 100 %   That same number increased by 40 % = 140 %   140 % -------> 1680 (140 Ã— 12= 1680)   100 % -------> 1200 (100 Ã— 12 = 1200)   Option '1200'
Answer: C
A dishonest dealer professes to sell his goods at Cost Price but still gets 40% profit by using a false weight. What weight does he substitute for a kilogram?	Choose the correct answer:
A) 714 1/7 grams	B) 714 2/7 grams	C) 714 8/3 grams	D) 714 1/3 grams	E) 732 1/3 grams

Solution: If the cost price is Rs.100, then to get a profit of 40%, the selling price should be Rs.140.   If 140kg are to be sold, and the dealer gives only 100kg, to get a profit of 40%.   How many grams he has to give instead of one kilogram(1000 gm).   140 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/140 = 714 2/7 grams.   Answer:714 2/7 grams
Answer: B
Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?	Select:  A) 1500  B) 3100  C) 4400  D) 6200  E) 7400

Solution: Each term in set B is 60 more than the corresponding term in set A.   The difference of the sums = 25 * 60= 
25 * 60 = 1_500
1500.   The answer is 1500.
Answer: A
Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 3 books, how many shelves does the bookcase have?	Choose the correct answer:
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Let x be the number of shelves.   12x - 21 = 8(x-1) + 3   4x = 16   x= 4   The answer is 4.
Answer: A
Lanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?  Choices:	A) 1/24	B) 1/8	C) 1/4	D) 1/3	E) 3/8

Solution: Total Lanya# of ways - 4! = 24.   1/3esired:   A-Mapped to the only correct address----------x 1 way only   B-Mapped to other two incorrect addresses - x 2 ways   C-Mapped to other two incorrect addresses - x 2 ways   1/3-Mapped to other two incorrect addresses - x 2 ways   Therefore, 1*2*2*2/24 = 1/3.?
Answer: D
If x is a randomly chosen integer between 1 and 20, inclusive, and y is a randomly chosen integer between 21 and 40, inclusive, what is the probability that xy is a multiple of 4?
Select the correct option.
A) 1/4 B) 1/3 C) 3/8 D) 7/16 E) ½

Solution: There are two ways that I see of getting a multiple of 4   1) x and/or y is a multiple of 4   2) x is a multiple of 2 and y is a multiple of 2   for 1 we have   P(option 1) = (5/20)(20/20) + (5/20)(20/20) - (5/20)(5/20) = 1/2 - 1/16   since 5 of the numbers in each range are divisible by 4, and if either x or y is selected to be divisible by 4 the selection of the other variable does not matter. Notice the last subtraction term which corrects the fact that we have counted the possibility of both being divisible by 4 twice (e.g. P(A union B) = P(A) + P(B) - P(A and B)).   Notice at this point that the probability of option one is already 7/16, the second largest available option. If we can come up with any other possibilities for getting xy divisble by 4 we must go with option E.   Of course this is the case because if we select a multiple of 2 that is not a multiple of 4 from both ranges of numbers, the product is divisible by 4.   We can formally compute this as:   P(option 2) = (5/20) * (5/20) = 1/16   since we do not wish to double count possibilities that fall into category 1, we only count the probability of selecting even numbers from each set that are not divisible by 4 (e.g. the other 5 even integers in each set).   Total probability is then P(option 1) + P(option 2) = 1/2
Answer: E
10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is ?
Options:
A) 1
B) 7
C) 3
D) 9
E) 2

Solution: Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.   Total age of 4 members now = [96 + (10 x 4)] years = 136 years.   Total age of 6 members now = (24 x 6) years = 144 years.   Sum of the ages of 2 children = (144 - 136)= 
(144 - 136) = 8
8 years.   Let the age of the younger child be years.   Then, age of the elder child= years.   So,   Age of younger child = 3 years.   Answer: 3
Answer: C
In a sample of graduate students in a program, 20 percent are second-year students, and 80 percent are not first-year students. What percentage of the students at the law firm have been there for more than two years?
Choices:
A) 20
B) 30
C) 40
D) 50
E) 60

Solution: 80 percent are not first-year students --> This means 80 percent of students are either two or more than two years   Already, we know % of second-year students = 20 %   So, % of students there for more than two years = 80 % - 20 % = 60 % .. => (60)
Answer: E
If x+y=25 and x2y3 + y2x3=25, what is the value of xy?  Choose one
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: xy=1   1s x+y=25   x2y3+y2x3=25   x2y2(y+x)=25   Substituting x+y   x2y2=1   xy=1   1NSWER:1
Answer: A
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? Choose one:
A) 79.4 B) 79.0 C) 79.5 D) 79.2 E) 79.1

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   Answer:79.2
Answer: D
If 12 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?  Choose the correct choice.
A) 10•9•8•7•6•5•4•3•2•1  B) 10•10  C) 10•9  D) 66  E) 36

Solution: We got #12 people who shake each other's hands once ==> a pair of 2   12!/10!2! = 12*11 / 2*1= 
12*11 / 2*1 = 66
66.   Hence answer 66.
Answer: D
A pupil's marks were wrongly entered as 79 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
Choose the correct option:
A) 30
B) 80
C) 20
D) 68
E) 26

Solution: Let there be x pupils in the class.   Total increase in marks = (X*1/2) = X/2.   X/2 = (79 - 45)   => X/2 = 34   => X = 68.   ANSWER:68
Answer: D
A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?  Choose the correct choice
A) days B) days C) days D) 1/2 days E) days

Solution: Explanation:   10/40 + 10/30 + 10/x = 1   x = 24 days   daysnswer: days
Answer: A
What will be the day of the week 15th August, 2010? Choose the most appropriate option:
A) Sunday
B) Monday
C) Tuesday
D) Thursday
E) Friday

Solution: 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)   Odd days in 1600 years = 0   Odd days in 400 years = 0   9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.   Jan. Feb. March April May June July Aug.   (31 + 28 + 31 + 30 + 31 + 30 + 31 + 15)= 
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227
227 days   227 days= (32 weeks + 3 days) 3 odd days.   Total number of odd days = (0 + 0 + 4 + 3)= 
(0 + 0 + 4 + 3) = 7
7 0 odd days.   Given day is Sunday.   Sundaynswer: Option Sunday
Answer: A
What must be added to each of the numbers 7, 11 and 19, so that the resulting numbers may be in continued proportion? Select
A) 3	B) 5	C) 4	D) -3	E) -2

Solution: Let X be the required number, then   (7 + X) : (11 + X) :: (11 +X) : (19 + X)   (7 + X) (19 + X) = (11 + X)2   X2 + 26X + 133 = X2 + 22X + 121   4X = - 12 or X = - 3   ANSWER:-3
Answer: D
Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent E of all the possible subcommittees that include Michael also include Anthony?  Choose the correct choice from the following
A) 20%  B) 30%  C) 40%  D) 50%  E) 60%

Solution: The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability E= 1/5+4/5*1/4 = 2/5.40%
Answer: C