MU-NLPC/Calc-aqua_rat huggingface dataset:
Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 2 muffins remained. How many guests did Monica plan on?
Choices:  A) 3.  B) 4.  C) 5.  D) 6.  E) 7.

Solution: Let x be the number of guests.   Number of muffins prepared = 5x + 2   Number of muffins eaten + Number of muffins remaining = Number of muffins prepared   6(x - 1) + 2 = 5x + 2   6x - 4 = 5x + 2   x = 6   Answer: 6.
Answer: D
The average weight of three men A, B and C is 84 Kg. The average weight becomes 80 Kg when D joins them. If E whose weight is 3 Kg more than D joins the group replacing A, then the average weight of B, C, D and E becomes 79 Kg. The weight of A is:	Choices.
A) 65kg B) 70kg C) 75kg D) 80kg E) 85kg

Solution: Wt of AB75kg = 84*3= 
84*3 = 252
252 kg   wt of AB75kgD= 80*4= 
80*4 = 320
320 kg   wt of D= 68 kg   wt of E = 71 kg   wt of AB75kgDE = 320+71= 
320+71 = 391
391 kg   wt of B75kgDE= 79*4= 
79*4 = 316
316 kg   wt of A= 391-316= 
391-316 = 75
75 kg   ANSWER:75kg
Answer: C
Choose the missing terms out of the given alternatives.
AD, EH, IL, ?, QT Select the correct option
A) MP B) LM C) MN D) OP E) OM

Solution: MP   MP   The letters move four steps forward.
Answer: A
A firm has 4 senior partners and 6 junior partners. How many different groups S of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)  Choose the most appropriate option
A) 48	B) 100	C) 120	D) 288	E) 600

Solution: What seems to work as well, though its tougher to come up with this solution:     (10*9*8) * 2/3 + (10*9*4)*1/3= 
  (10*9*8) * 2/3 + (10*9*4)*1/3 = 600
600. Divided by all possible permutations (=3!) yields 100.   Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.   Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.   Now you just need to divide the answer (600) by the number of different positions (=3!) and get S=600/6=100.100
Answer: B
In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 48%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass? Choose the correct choice:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: The tests scores are 4k, 5k, 6k, 7k, and 8k.   The sum of the test scores is 30k.   The average test score is 30k/5 = 48. Then k = 8.   The test scores are 32, 40, 48, 56, and 64.   The student passed 2 subjects.   The answer is 2.
Answer: B
Two numbers N and 12 have LCM = 54 and GCF = 8. Find N.	Pick:
A) 24
B) 34
C) 36
D) 54
E) 64

Solution: The product of two integers is equal to the product of their LCM and GCF. Hence.   12 × N = 54 × 8   N = 54 × 8 / 12 = 36   correct answer 36
Answer: C
Seats for Maths, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%,50% and 75%. What will be the ratio of increased seats?	Pick one:
A) 1:2:3 B) 2:3:4 C) 2:4:5 D) 3:6:7 E) 5:7:9

Solution: Let the number of seats of M,P,B be 5x,7x,8x   Number of increased seats are 140% of 5x , 150% of 7x , 175% of 8x   5x*140/100 , 7x*150/100 and 8x*175/100   i.e. 7x, 21x/2 and 14x   Required ratio = 7x:21x/2 : 14x = 14x:21x:28x = 2:3:4   Answer is 2:3:4
Answer: B
The Hobo Music Orchestra is comprised of, 3/5 wind instrument musicians, 1/4 string instrument musicians, and the rest are percussion instrument musicians. If half of the string instrument musicians are violinists, and the conductor doubles the number of violinists, what proportion of the orchestra are now wind instrument musicians?	Pick one.
A) 9/10	B) 6/11	C) 7/15	D) 1/2	E) 6/7

Solution: Wind = 3/5 = 12/20   String = 1/4 = 4/20   Percussion = 1 - (12/20 + 4/20) = 1 - 16/20 = 4/20   Violinists = (1/2)(4/20) = 2/20   If Violinists doubled => (2)(2) = 4; then, total = 12 + 6 + 4= 
12 + 6 + 4 = 22
22,   and 12 are Wind=> proportion = 12/22 = 6/11.   Answer: 6/11
Answer: B
A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?  Choose the correct option.
A) 120 kg	B) 240 kg	C) 360 kg	D) 480 kg	E) 520 kg

Solution: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x. This must be equal to 360.   3x=360   x=3603   x=120   Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon.   correct answer 240 kg
Answer: B
A 10% stock yielding 8% is quoted at?  Choose the most appropriate option
A) 125
B) 170
C) 175
D) 180
E) 185

Solution: 125ssume that face value = Rs.100 as it is not given   To earn Rs.8, money invested = Rs.100   To earn Rs.10, money invested = 100×10/8 = Rs.125   ie, market value of the stock = Rs.125   125nswer is 125.
Answer: A
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?	Choose one
A) 270 m	B) 176 m	C) 197 m	D) 167 m	E) 187 m

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 27 * 10= 
27 * 10 = 270
270 m.   The length of the faster train= 270 m.   270 mnswer:270 m
Answer: A
how many square are there between 2001....2300 I don't remember the exact series.
Choose the correct choice from the following choices:
A) 1
B) 4
C) 2
D) 3
E) 5

Solution: series was from 2001 to 2300   45^2=2025   46^2=2116   47^2=2209   48^2=2304 (so exclude 48)   so ans is 3 (45,46 and 47)   ANSWER:3
Answer: D
A bag contains 7 green balls and 7 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour? Pick one.
A) 4/13	B) 6/13	C) 8/21	D) 11/21	E) 17/42

Solution: The total number of ways to draw two balls is 14C2 = 91   The number of ways to draw two green balls is 7C2 = 21   The number of ways to draw two white balls is 7C2 = 21   P(two balls of the same colour) = 42/91 = 6/13   The answer is 6/13.
Answer: B
If f(x) = ax^4 + x^3 + 2ax + 5, then f(b) – f(-b) will equal:	Choose the correct answer
A) 0 B) 2ab C) 2ab^4 – 8b^2 – 6 D) -2ab^4 + 8b^2 + 6 E) 2b^3 + 4ab

Solution: f(x)=ax^4 + x^3 + 2ax + 5   f(b) = ab^4 + b^3 + 2ab + 5   f(-b) = ab^4 - b^3 - 2ab + 5   f(b) - f(-b) = ab^4 + b^3 + 2ab + 5 - ab^4 + b^3 + 2ab - 5   =2b^3 + 4ab   Answer 2b^3 + 4ab
Answer: E
The profit obtained by selling an article for Rs. 56 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article?	Choose one
A) Rs. 40
B) Rs. 50
C) Rs. 49
D) Rs. 59
E) None of these

Solution: S.P 1- Rs. 49.P = Rs. 49.P – S.P 2   56 - Rs. 49.P = Rs. 49.P - 42   2 Rs. 49.P = 56 + 42;   Rs. 49.P = 98/2= 
98/2 = 49
49   ANSWER:Rs. 49
Answer: C
A can give B a start of 50 metres or 10 seconds in a kilometer race. How long does A take to complete the race?	Choose one:	A) 200 seconds	B) 140 seconds	C) 220 seconds	D) 190 seconds	E) None

Solution: Solution:   A can give B a start of 50 metres or 10 seconds in a 1000 m race.   That is, B takes 10 seconds to run 50 metres.   Therefore, B will take  (10/50) * 1000= 
 (10/50) * 1000 = 200
200 seconds to run 1000 metres.   A who can give B a start of 10 seconds will take 10 seconds lesser to run the 1000m.   Hence, the time taken by A= 190 seconds.   Answer 190 seconds
Answer: D
For which of the following does f(m)−f(n)=f(m−n) for all values of m and n? Choose the correct choice from the following answers
A) f(y)=y^2	B) f(y)=y/2	C) f(y)=y+5	D) f(y)=2y−1	E) f(y)=|y|

Solution: To solve this easiest way is just put the value and see that if it equals or not.   with option 1. f(m) = m^2 and f(n) = n^2   so L.H.S = m^2 - n^2   and R.H.S = (m-n)^2 ==> m^2 + n^2 -2mn.   so L.H.S not equal to R.H.S   with option 2. f(m) = m/2 and f(n) =n/2   L.H.S = m/2 - n/2 ==> 1/2(m-n)   R.H.S = (m-n)/2   so L.H.S = R.H.S which is the correct answer.   f(y)=y/2
Answer: B
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?
Choose the correct choice.
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

Solution: 70 + 65= 
70 + 65 = 135
135 * 5/18= 75/2 mps   D = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 2/75 = 20/3 - 6 2/3 sec   6 2/3 secnswer: 6 2/3 sec
Answer: A
Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is: Choose the correct option:  A) 36  B) 98  C) 34  D) 35  E) 62

Solution: (3x-9):(5x-9) = 9:17   x = 12 => 3x = 36   36nswer:36
Answer: A
The graph of a quadratic function and the graph of a linear function in the xy plane can intersect in at most how many points	Select the correct option:
A) one
B) Two
C) Three
D) Four
E) More than four

Solution: i also thought 2 but i think we need to consider linear function like y=|X| then it could intersect at 6 points.   More than four
Answer: E
A train traveling at 72 kmph crosses a platform in 33 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
Choose the correct choice from the following answers:	A) 240 meters	B) 360 meters	C) 420 meters	D) 300 meters	E) Cannot be determined

Solution: Speed of train = 72 * (5/18)= 
72 * (5/18) = 20
20 m/s   Lets consider the man as a stationery point on the platform.   Crossing the point gives us the length of the train.   Lt= 20 * 18= 
20 * 18 = 360
360 m.   Crossing the platform gives us the length of trainlength of platform.   L(t+p)= 20 * 33= 
20 * 33 = 660
660 m.   So, length of platform= 660 - 360= 
660 - 360 = 300
300 m   IMO, Answer   300 meters
Answer: D
What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?	Choose the correct choice from the following options.
A) 9800  B) 9600  C) 9400  D) 9200  E) 9300

Solution: Greatest number of four digits = 9999   LCM of 15, 25, 40 and 75 = 600   9999 ÷ 600 = 16, remainder = 399   Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75   = 9999 - 399= 
9999 - 399 = 9_600
9600 Answer: Option 9600
Answer: B
One-fifth of the apples produced by farm are defective and one-quarter of all apples produced are rejected by the quality control technician. If one-tenth of the non defective apples are rejected by mistake, and if all the apples not rejected are sold, then what percent of the apples sold by the farm are defective?	Choose the correct option.
A) 4%
B) 5%
C) 6%
D) 8%
E) 12%

Solution: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective. Correct answer is 4%.
Answer: A
In a Fish tank there are 8 fishes are there. In how many possibilities to choose 6 fishes from the tank?
Choose the correct choice:
A) 20
B) 21
C) 28 possibilities
D) 8
E) 30

Solution: The possible way to select 6 fishes out of 10 fishes in the tank is 8C6.   828 possibilities6=8!/2!*6!=8*7*6!/6!*2*1   828 possibilities6=28   There are 28 ways to select a 6 fishes from the tank.
Answer: C
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 sec. The length of each train is? Choose one
A) 50
B) 37.5
C) 27
D) 28
E) 21

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/27 = 25/9 => x = 37.5.   Answer: 37.5
Answer: B
Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability E that the new color will be one of theJaunecolors?
Choose one
A) 5/42 B) 37/42 C) 1/21 D) 4/9 E) 5/9

Solution: I get B.   Jaune Y = (4 choose 1)*(5 choose 2) = 4*10= 
4*10 = 40
40   Jaune X= (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4= 
6*5 + 4 = 34
34   Total combinations= 9 choose 3 = 84   Probability of Jaune E= (40 + 34)/84 = 37/42.37/42
Answer: B
Suppose you play a game where you role a single dice and whatever you roll you get that dollar amount. For example, if you roll a 1 you get $1. If you roll a 6 you get $6. If you are unhappy with the first roll, you can roll again. However, if you get lower the second time, you cannot take the first roll. If you are unhappy with the second roll you can roll a third and final time. Again, if you get lower on the third roll, you have to keep this roll and cannot take the first or second roll.
What is the expected value of this game?	Choose the correct choice:
A) 4250	B) 4500	C) 467	D) 512	E) 850

Solution: Expected value for one roll is 1/6*(1+2+3+4+5+6)= 
1/6*(1+2+3+4+5+6) = 7/2 = around 3.5
3.5$. This part is easy.   Let's proceed: if it's 3.5$, when will I agree to continue the game and roll the second time? Well obviously if the first roll will give me the value less than 3.5 or 1, 2, 3. In other cases if I get 4, 5 or 6, it won't be clever to continue as I already have from my first roll the value higher than the expected value of the second. So what is the expected value of two rolls:   1/6*6+1/6*5+1/6*4+1/2*3.5=2.5+1.75= 
2.5+1.75 = 4.25
4.25   The same for the three rolls: if I know that expected value for two rolls is 4.25$, so I'll continue to roll if the first roll will give me the value less than 4.25 or 1,2,3,4. So for three rolls expected value must be:   1/6*6+1/6*5+2/3*4.25=1.833+2.833=~4.67$	467
Answer: C
A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
Select the correct option
A) $20,200	B) $20,500	C) $20,800	D) $21,000	E) $21,400

Solution: average = 2(19000)+(21000)+3(22000) / 6 = $20,833   The answer is $20,800.
Answer: C
The successive discounts 20% and 15% are equal to a single discount of?  Select.
A) 33
B) 77
C) 32
D) 77
E) 99

Solution: Let the CP of an article be Rs. 100   Given that successive discounts are 20% and 15%.   SP = 85% of 80% of 100 = (85/100)(80/100)(100)   => SP = Rs. 68   Clearly, single discount is 32%.   Answer:32
Answer: C
Product of two natural numbers is 7. Then, the sum of reciprocals of their squares is
Choose the correct answer:
A) 50/49  B) 1/289  C) 290/90  D) 290/19  E) None of these

Solution: Explanation:   If the numbers are a, b, then ab = 7,   as 17 is a prime number, so a = 1, b = 7.   1/a2+1/b2=1/1(2)+1/7(2)   1/ 2+1/ 2= 
1/ 2+1/ 2 = 1
1/1(2)+1/7(2)=50/49   Option 50/49
Answer: A
A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?
Choose the correct choice from the following options:
A) 7203  B) 2403  C) 3603  D) 4803  E) 5803

Solution: LCM of 16, 20, 25, 45 = 3600   1 * 3600 + 3= 
1 * 3600 + 3 = 3_603
3603 not divisible by 21   2 * 3600 + 3= 
2 * 3600 + 3 = 7_203
7203 is divisible by 21   7203NSWER:7203
Answer: A
The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 60 kmph. Find the speed of the boat in still water and the speed of the stream?
Choose the correct choice from the following answers
A) 10 B) 99 C) 15 D) 66 E) 23

Solution: Speed of the boat in still water = (30+60)/2= 
(30+60)/2 = 45
45 kmph. Speed of the stream= (60-30)/2= 
(60-30)/2 = 15
15 kmph. Answer:15
Answer: C
GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then BED?	Choose the correct choice from the following choices
A) 33  B) 34  C) 35  D) 32  E) 31

Solution: GOOD=(7+15+15+4)*4= 
(7+15+15+4)*4 = 164
164   BAD= (2+1+4)*3= 
(2+1+4)*3 = 21
21   UGLY= (21+7+12+25)*4= 
(21+7+12+25)*4 = 260
260   coding follows   (sum of position of alphabets)*(no. of letters in the given word)   so,   BED=(2+5+4)*3= 
(2+5+4)*3 = 33
33   33NSWER:33
Answer: A
Solve the given two equations and find the inequality of X and Y. (a) 225X^2-4 = 0 and (b) (225y)^(1/2) +2 = 0
Choose the correct choice from the following choices.
A) If x>y	B) If x>=y	C) If x < y	D) If x<=y	E) x=y or relationship cannot be established

Solution: Solution:-   X= +2/15 and -2/15   Y= 4/225   Comparing we get X>Y and X<y   Hence, no relationship can be established   x=y or relationship cannot be established)
Answer: E
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? Choose the correct choice from the following answers:
A) 40	B) 37	C) 32	D) 39	E) 28

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40nswer: 40
Answer: A
Jar X is 1/2 full of water. Jar Y, which has half the capacity of Jar X, is 1/4 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?  Choose the correct choice from the following:
A) 3/4 B) 5/8 C) 7/8 D) 5/12 E) 7/12

Solution: Let P be the capacity of Jar X.   The amount of water in Jar Y is 1/4*P/2=P/8   Then the total amount in Jar X is P/2+P/8=5P/8   The answer is 5/8.
Answer: B
Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in three times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 36 minutes, then how many minutes does it take pump X alone to fill the tank?  Choose the correct choice from the following:
A) 18
B) 24
C) 26
D) 28
E) 30

Solution: Let V be the volume of the tank.   Let R be the rate per minute that pump X fills the tank.   Let T be the time it takes pump X to fill the tank.   The rate at which pump Y empties the tank is V/36 per minute.   (R - V/36)*3T=V=RT.   (R-V/36)*3=R   2R=V/12.   R=V/24.   It takes pump X 24 minutes to fill the tank.   The answer is 24.
Answer: B
If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?	Choose one:	A) 2	B) 8	C) 7	D) 62	E) 21

Solution: Explanation:   96% ---- 12   144% ---- ?     96/144 * 12= 
  96/144 * 12 = 8
8   Answer: 8
Answer: B
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?	Choose the most appropriate option
A) 1/166 B) 1/186 C) 1/196 D) 2/106 E) 1/126

Solution: Out of nine, five are good and four are defective. Required probability   = 4C4/9C4   = 1/126   Answer:1/126
Answer: E
How much 60% of 50 is greater than 40% of 30?	Pick
A) 18	B) 27	C) 26	D) 29	E) 21

Solution: (60/100) * 50 – (40/100) * 30   30 - 12= 
30 - 12 = 18
18   18nswer: 18
Answer: A
Two friends A and B are running up hill and then to get down! length of road is 440 yards. A on his return journey met B going up at 20 yards from top, A has finished the race 5 minutes earlier than B, then how much time A had taken to complete the race. Choose the correct choice from the following options
A) 51.5minutes	B) 52.5minutes	C) 53.5minutes	D) 54.5minutes	E) 55.5minutes

Solution: When A travels 460m (=440+20), B travels 420m (=440-20). So, ratio of speed = 460:420 = 23:21. Let A's speed be 23x, and that of B's be 21x.   23x = ((2*440) / t) which implies 23t = 880/x;   21x = ((2*440) / (t+5)) which implies 21(t+5) = 880/x.   From these two equations, 23t = 21(t+5). Solving, t = 52.5minutes   ANSWER:52.5minutes
Answer: B
If pq = p^5 + q^2 – 2pq, for what value of q is pq equal to p^5 for all values of p? Select.
A) -2  B) -1  C) 0  D) 1  E) 2

Solution: C   p5 + q2 â€“ 2pq = p5   => q2 - 2= 
2 - 2 = 0
0=> q (q - 2p) = 0   => q = 0 or q = 2p   im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI   0
Answer: C
A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 380 dollars, and, in a third, loses 70. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ? Answers: A) 80 B) 60 C) -60 D) -70 E) None

Solution: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.   Let x = the sum required.   Then according to the statement x + 380 - 70 = 250   And x = -60.   Answer -60
Answer: C
The editor of an anthology of short stories will select authors from a pool of 11 authors, of which 5 are female. If the anthology is to include the work of 6 authors of which at least 2 are female, in how many ways can the editor select the authors? Select.
A) 420 B) 431 C) 442 D) 453 E) 464

Solution: 11C6 = 462   The number of ways to select 6 males is 6C6 = 1   The number of ways to select 5 males and 1 female is 6C5*5C1 = 30   462 - 1 - 30= 
462 - 1 - 30 = 431
431   The answer is 431.
Answer: B
A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Choose the most appropriate option.
A) 81 B) 83 C) 85 D) 86 E) 89

Solution: Overall, there can be 81 minuses. Tus, it is 81.
Answer: A
The area of a triangle is with base 4m and height 5m?  Choose the correct choice from the following options:
A) 11 m2
B) 10 m2
C) 18 m2
D) 19 m2
E) 12 m2

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer: 10 m2
Answer: B