MU-NLPC/Calc-aqua_rat huggingface dataset:
The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is  Choices:
A) 71.5	B) 11.5	C) 81.5	D) 11.5	E) 21.5

Solution: Explanation:   Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5.   Answer: 11.5
Answer: B
If 4 cats can kill 4 rats in 4 minutes, how long will it take 100 cats to kill 100 rats?
Choose the correct choice from the following answers:
A) 1 minutes
B) 2 minutes
C) 3 minutes
D) 4 minutes
E) 5 minutes

Solution: It will take 4 minutes for 100 cats to kill 100 rats.   1 cat can kill 1 rat in 4 minutes, so 100 cats can kill 100 rats in 4 minutes   Answer 4 minutes
Answer: D
The difference between the two digit number and the number obtained by interchanging its digits is 54. The difference between the digits is? Answers.
A) 5
B) 6
C) 7
D) 9
E) 11

Solution: Explanation:   (10x + y) – (10y + x) = 54   x – y = 6   6)
Answer: B
A housing society has been allotted a square piece of land measuring 2550.25 sq.m. What is the side of the plot? Select the correct option.
A) 50.25 m
B) 50.5 m
C) 50.65 m
D) 50.85
E) NONE

Solution: Solution   Side = √2550.25   = √255025 / 100   = 505 / 10= 
505 / 10 = 101/2 = around 50.5
50.5 m.   Answer 50.5 m
Answer: B
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ?  Choose the correct choice from the following options
A) 36 - x	B) 10 - x	C) x + 4	D) x - 4	E) x + 26

Solution: Original Digits=xy i.e. Number=10x+y   After reversing the digits:   Digits=yx i.e. Number=10y+x   10y+x is 36 more than 10x+y   10x+y+36=10y+x   10x-x+36=10y-y   9x+36=9y   x+4=y   OR   y=x+4   Ans:x + 4
Answer: C
Find the value of (45 + 23/89) × 89	Select the correct option:
A) 4028 B) 4026 C) 4248 D) 4538 E) 9028

Solution: =(45 + 23/89) × 89   =(4005 + 23)/89 × 89   =4028/89 × 89   =4028   4028nswer is 4028.
Answer: A
if log 3 = 0.47712, the number of digits in 3128 is	Choose the correct choice from the following choices.
A) 22	B) 39	C) 88	D) 28	E) 62

Solution: 62xplanation:   log(3128) = 128log(3) = 128 × 0.30103 ≈ 61.07   ie, its characteristic = 61   Hence, number of digits in 3128 = 61+1= 
61+1 = 62
62   Answer: Option 62
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? Choose one:  A) 40  B) 50  C) 60  D) 79  E) 80

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 5) km/hr.   x - 5 = 45 => x = 50 km/hr.   Answer: Option 50
Answer: B
A and B started a business investing Rs. 90,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? Choose the correct choice from the following answers
A) 9:2 B) 3:2 C) 18:20 D) 18:4 E) 17:4

Solution: 9:2: B = 90000 : 20000   = 90 : 20   = 18 : 4   = 9 : 2   9:2NSWER:9:2
Answer: A
A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?
Options:  A) 5.38 days  B) 9.38 days  C) 7.38 days  D) 3.38 days  E) 9.38 days

Solution: 7.38 days   7.38 days   A + B = 1/8   B + 7.38 days = 1/12   7.38 days + A = 1/16   -------------------------------   2(A + B +7.38 days) = 1/8 + 1/12 + 1/16 = 13/48   A + B +7.38 days = 13/96   96/13 = 7.38 days
Answer: C
Which of the following numbers is two more than the square of an odd integer?
Choose the correct choice from the following options:	A) 14,173	B) 14,361	C) 15,153	D) 15,737	E) 16,643

Solution: If a square has an odd unit's digit, then its ten's digit must be even.   Only 16,643-2 = 16,641 satisfies this condition.   The answer is 16,643.
Answer: E
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:	Choose the most appropriate option:
A) Rs. 2000
B) Rs. 10,000
C) Rs. 15,000
D) Rs. 18,000
E) Rs. 20,000

Solution: Principal = Rs. (100 x 5400)/(12X3) = Rs. 15000. Answer: Option Rs. 15,000
Answer: C
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:  Choose the correct answer: A) 15 B) 16 C) 18 D) 25 E) 28

Solution: Work done by Sakshi in 1 day = 1/20   Since Tanya is 25% efficient than Sakshi, she completes 25% more work in a day than Sakshi.   => Tanya's 1 day work = 120 + 120 * 25100 = 116   So time taken by Tanya to finish the work = 16 days answer 16
Answer: B
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly four elements each?	Answers
A) 126 B) 120 C) 110 D) 100 E) 118

Solution: nC2 = 36   => n*(n-1)/2 = 36 by middle term factor n can not be negative   => n = 9   nC3 = 9C4 = 126   So, 126nswer is 126.
Answer: A
Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long W would it take Victor to complete 10 jobs without any supervision?	Choose the most appropriate option
A) 34
B) 52
C) 60
D) 70
E) 92

Solution: Rate when supervised = (job)/(time) = 1/t.   Rate when unsupervised = (job)/(time) = 1/(t+3).   For  144/2= 
 144/2 = 72
72 days he is supervised and for  144/2= 
 144/2 = 72
72 days he is unsupervised and does 36 jobs:   72/t + 72/(t+3)= 36 --> t=3 days --> t+3 = 6 days.   Victor to complete 10 jobs without any supervision will need W 10(t + 3) = 60 days.   Answer: 60.
Answer: C
A box measuring 90 inches long by 45 inches wide by 9 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective? Choose the correct choice from the following answers:
A) 17  B) 18  C) 50  D) 108  E) 864

Solution: least number of cubes will be required when the cubes that could fit in are biggest.   9 is the biggest number that could divide all three, 90, 45 and 9.   Thus side of cube must be 9, and total number of cubes = 90/9 * 45/9*9/9= 
90/9 * 45/9*9/9 = 50
50   Ans 50 it is.
Answer: C
A car travels at a speed of 65 miles per hour. How far will it travel in 6 hours?  Choose the correct choice from the following options
A) 125 miles B) 225 miles C) 390 miles D) 425 miles E) 525 miles

Solution: During each hour, the car travels 65 miles. For 6 hours it will travel   65 + 65 + 65 + 65 + 65+ 65 = 6 × 65 = 390 miles   correct answer is 390 miles) 390 miles
Answer: C
A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 2 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 50 worth of diesel fuel?  Choose the correct choice from the following answers:	A) 50 seconds	B) 1 minute	C) 1 minute 20 seconds	D) 20 minutes	E) 1 hour 20 minutes

Solution: 2 gal / 5 sec   $2 / gal   $40/$2 = 20 gal   2 gal / 5 sec with 20 gal   40/ 2= 
  40/ 2 = 20
20 gal   2 gal / 5 sec with 20 gal= 50 sec   A. 50 seconds
Answer: A
Exactly 12% of the reporters for a certain wire service cover local politics in Country X. If 40% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?  Choose the correct choice from the following answers:  A) 20%  B) 42%  C) 44%  D) 80%  E) 84%

Solution: Let's assume there are 100 reporters --> 12 reporters cover local politics.   Now, as 40% of the reporters who cover all politics do not cover local politics then the rest 60% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 60% of them equal to 12 (# of reporters who cover local politics): 0.6x=12 --> x=20, hence 20 reporters cover politics and the rest 100-20= 
100-20 = 80
80 reporters do not cover politics at all.   Answer: 80%.
Answer: D
When two dice are rolled, what is the probability that the sum is either 7 or 11? Choose the correct choice from the following choices
A) 1/4	B) 1/9	C) 4/3	D) 3/9	E) 2/9

Solution: Total number of outcomes possible=36   Probability of getting sum of 7=6/36   Probability of getting sum of 11=2/36   probability that the sum is either 7 or 11=6/36+2/36=2/9   ANSW2/9R:2/9
Answer: E
A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
Select the correct option.
A) 15 litres B) 10 litres C) 30 litres D) 22 litres E) 18 litres

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively   4x/(3x+9)=4/5   20x=4(3x+9)   8x=36   x=4.5   Quantity of alcohol = (4 x 4.5) litres = 18 litres.   Answer is 18 litres
Answer: E
If a^x = b^4y, then  Choose the correct choice.
A) log a/b= x/y	B) log a/ log b = x/y	C) log a/ log b = 4y/x	D) log b/a = x/y	E) log b/a = y/x

Solution: a^x = b^4y => log a^x = log b^4y => x log a = 4y log b   => log a/ log b = 4y/x   ANSWER:log a/ log b = 4y/x
Answer: C
A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.150. Find the unknown rate of two towels? Pick one.
A) 400
B) 450
C) 500
D) 550
E) 600

Solution: 10 * 150= 
10 * 150 = 1_500
1500   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1500 – 1050= 450   450
Answer: B
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder S of Y divided by 5?  Pick.
A) S=1.  B) S=2.  C) S=3.  D) 4.  E) 5.

Solution: X divided by 10 gives reminder of 2. X can be 2/12/22....   X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....   If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2   Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2   Hence the answer must be 2 (B)   Also....   x+y=5m+4 and x=10K+2   hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is S=2.
Answer: B
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 98 cookies, what is the minimum number of chocolate chip cookies he makes?	Choose the correct choice: A) 7 B) 14 C) 21 D) 28 E) 56

Solution: 7C+6P=98   We need to maximize P to minimize C so that the eq is also satisfied   Try substitution for CP to solve so that eqn is satisfied   The least value of C for which equation gets satisfied is 5   i.e. 7*2+6*14=14+84= 
14+84 = 98
98   Hence 14 is the answer
Answer: B
Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is:
Choose the correct choice
A) 0.20887  B) 0.3887  C) 0.33487  D) 0.20833  E) 0.38222

Solution: Explanation:   Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x   \therefore Cultivated land of village = 384000x   \therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833   Answer: 0.20833
Answer: D
Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/3 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?  Choose the most appropriate option
A) 1/32
B) 7/8
C) 9/64
D) 5/64
E) 3/64

Solution: P(Xavier will solve)=1/4   P(Yvonne will solve)=1/2   P(Zelda will NOT solve) = 1- 5/8 = 3/8.   Now, we need to multiply all this Ps to find an answer:   p= (1/4)*(1/3)*(3/8) = 1/32.   Ans. 1/32.
Answer: A
The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 72 metres, what is its area?  Choices
A) 315 sq.metres	B) 260 sq.metres	C) 280 sq.metres	D) 380 sq.metres	E) None of these

Solution: Let the length and breadth be 7x and 5x respectively.   Then, P = 2(7x + 5x) = 72 â‡’ x = 3   Area = 7 Ã— 3 Ã— 5 Ã— 3 = 315 sq.m.   315 sq.metresnswer 315 sq.metres
Answer: A
If the area of circle is 616 sq cm then its circumference?	Select
A) 21	B) 88	C) 66	D) 16	E) 12

Solution: 22/7 r2 = 616 => r = 14   2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88   Answer: 88
Answer: B
A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
Pick:  A) 20  B) 25  C) 27  D) 22  E) 91

Solution: Let the son's present age be x years.   Then, man's present age = (x + 22) years.   (x + 22) + 2 = 2(x + 2) x + 24 = 2x + 4 => x = 20.   20nswer: 20
Answer: A
Albert invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit?	Choose one:
A) Rs. 8600
B) Rs. 8620
C) Rs. 8800
D) Rs. 8840
E) None of these

Solution: Amount = [8000 * (1 + 5/100)2]   = 8000 * 21/20 * 21/20   = Rs. 8820   ANSWNone of theseR:None of these
Answer: E
1/2 + [(2/3 * 3/4)/4] - 9/16 =
Select
A) 1/16  B) 19/16  C) 15/16  D) 9/13  E) 0

Solution: We need to simplify the expression using PEMDAS.   Parentheses   Exponents   Multiplication andDivision   1/16ddition andSubtraction   The calculation of an equation or expression must be carried out in the following order:   1) Operations within parentheses (or absolute value bars or radicals)   2) Exponents   3) Multiplication and division from left to right   4) 1/16ddition and subtraction from left to right   The answer is 1/16.
Answer: A
If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {3,4,5}, what`s the probability that xy will be even?  Options:	A) 1/6	B) 2/3	C) 1/2	D) 1/3	E) 5/6

Solution: The product to be even either one or both must be even, so:   P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;   Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.   Answer: 2/3.
Answer: B
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 5 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) + 3 = 5x + 2   6x - 5 = 5x + 2   x = 7   Answer: 7.5  + 2= 
5  + 2 = 7
7   Answer: 7.
Answer: E
The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
Select: A) 13√2 B) 15 C) 48 D) 75 E) 23

Solution: xplanation:   4a = 48 4a = 20   a = 12 a = 5   a2 = 144 a2 = 25   Combined area = a2 = 169 => a = 13   d = 13√2   13√2nswer: 13√2
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is? Options:
A) 22 B) 77 C) 36 D) 88 E) 21

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer: 36
Answer: C
The simple interest on a sum of money is Rs. 50. What is the sum?
I.The interest rate is 10% p.a.
II.The sum earned simple interest in 10 years.
Choose the correct option
A) I alone sufficient while II alone not sufficient to answer	B) II alone sufficient while I alone not sufficient to answer	C) Either I or II alone sufficient to answer	D) Both I and II are not sufficient to answer	E) Both I and II are necessary to answer

Solution: EXPLANATION   Explanation:   Given : S.I. = Rs. 50.   I gives, R = 10% p.a.   II gives, T = 10 years.   Sum =(100 x S.I/ T x R) = Rs. (100x50/10x10) = Rs.50   Thus, I and II together give the answer.   answer is (Both I and II are necessary to answer).
Answer: E
Kant and Jaya started a business by investing a certain amount, Jaya’s share is Rs.1400, out of annual profit of Rs.3800, then what is the ratio of investments of Kant and Jaya respectively ?
Choose the correct choice from the following options
A) 3:4 B) 18:21 C) 12:7 D) 6:11 E) 4:3

Solution: otal profit = Rs.3800.   Jaya share = Rs.1400.   Kant share = Rs.3800 - Rs.1400 = Rs.2400.   Kant : Jaya = 2400 : 1400 => 12 : 7   Option 12:7
Answer: C
Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
Answers:
A) 4 hrs 29 min  B) 4 hrs 24 min  C) 4 hrs 84 min  D) 3 hrs 24 min  E) 7 hrs 24 min

Solution: 1/4 + 1/5 = 9/20   20/9 = 2 2/9   9/20 * 2 = 9/10 ---- 4 hours   WR = 1 - 9/10 = 1/10   1 h ---- 1/4   ? ----- 1/10   2/5 * 60= 
2/5 * 60 = 24
24= 4 hrs 24 min   Answer:4 hrs 24 min
Answer: B
The sum of 3 consecutive numbers is definitely:
Select.
A) Positive  B) Divisible by 2.  C) Divisible by 3  D) Divisible by 4.  E) Divisible by 5

Solution: If 1st term is x:   x+(x+1)+(x+2)=3x+3--->Always divisible by 3   If 2nd term is x:   (x-1)+x+(x+1)  +( +1)+( +2)= 
  +( +1)+( +2) = 3
3x+3--->Always divisible by 3   If 2nd term is x:   (x-1)+x+(x+1)=3x--->Always divisible by 3   If 3rd term is x:   (x-2)+(x-1)+x=3x-3--->Always divisible by 3   Answer: Divisible by 3
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 answer:
A) 5/5	B) 5/9	C) 5/3	D) 5/8	E) 5/1

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
Which of the following options must be true given the equation p=-q^6
I. If q is negative then p is negative.
II. q is negative.
III. q is non-negative. Choose the correct choice:  A) I only  B) II only  C) III only  D) II and III only  E) I and III only

Solution: I. p is negative --> not necessarily true, if q=0 then p=-q^6=0;   II. q is non-negative. q can take ANY value: positive, negative, zero. We don't have any restrictions on its value;   III. If q is negative then p is negative. p is negative means that q is not zero.   I onlynswer: I only (I only).
Answer: A
5670/(28*13.5) = ?	Choices
A) 11
B) 15
C) 16
D) 19
E) 18

Solution: 15   15   ? = 5670/378= 
5670/378 = 15
15
Answer: B
What is next in series
J F M A M ? ? Pick: A) MS B) SS C) FJ D) JJ E) DD

Solution: D   JJ   Series is the name of months . January, February ...   Therefore June and July is the answer. Hence J J is correct option
Answer: D
The HCF of two numbers is 62 and the other two factors of their LCM are 11 and 12. What is the largest number. Choose the correct choice from the following options.
A) 462	B) 744	C) 480	D) 504	E) 555

Solution: Explanation:   HCF of the two numbers = 62   HCF will be always a factor of LCM   62 is factor of LCM   other two factors are 11 & 12   Then the numbers are (62 *11) and (62 x 12)   = 682 and 744   Answer: Option 744
Answer: B
A can finish a work in 18 days B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?  Choose the correct answer
A) 5  B) 5 1/2  C) 6  D) 8  E) 9

Solution: Explanation:   B's 10 day's work = 1/15 * 10 = 2/3   Remaining work = (1 - 2/3) = 1/3   Now, 1/18 work is done by A in 1 day.   1/3 work is done by A in  (18 * 1/3)= 
 (18 * 1/3) = 6
6 days.   ANSWER IS 6
Answer: C
A speaks truth in 75% case and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?  Choose the correct answer.
A) 40 B) 23 C) 35 D) 60 E) 21

Solution: P( A)=75/100, P(B)=80/100   P( A’)=1/4   P(B’)=1/5   P( A and B contradict each other)=P(A).P(B’)+P(A’).P(B)   =35%   ANSWER 35
Answer: C
Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the
week is today?	Choose the correct answer:
A) Wednesday  B) Saturday  C) Friday  D) Sunday  E) None of these

Solution: Explanation :   Clearly it can be understood from the question that 9 days ago was a Thursday   Number of odd days in 9 days = 2 (As 9-7= 
9-7 = 2
2, reduced perfect multiple of 7 from total days)   Hence today= (Thursday + 2 odd days) = Saturday   Answer : Option Saturday
Answer: B
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:  Choose the correct option
A) Rs. 2000
B) Rs. 10,000
C) Rs. 15,000
D) Rs. 20,000
E) Rs. 22,000

Solution: Principal = Rs. 100 x 5400   --------------- = Rs. 15000.   12 x 3   Answer: Option Rs. 15,000
Answer: C
There are 11 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 choice from the following options:
A) 40
B) 45
C) 50
D) 55
E) 60

Solution: 11C2=55   The answer is 55.
Answer: D
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number T and the smallest possible number of students that could have taken both geometry and biology?	Choose the correct choice from the following choices:
A) 144
B) 119
C) 113
D) 88
E) 31

Solution: OFFICIAL SOLUTION:   First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.   {Total} = {geometry} + {biology} - {both} + {neither};   232 = 144 + 119 - {both} + {neither};   {both} = 31 + {neither}.   {both} is minimized when {neither} is 0. In this case {both} = 31.   The greatest possible number T of students that could have taken both geometry and biology, is 119.   Thus, the answer is 119 - 31= 
119 - 31 = 88
88.   Answer: 88.
Answer: D
Consider a quarter of a circle of radius 81. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.  Select the correct option
A) 86*(sqr2 -1)	B) 88*(sqr3 -1)	C) 4*(sqr7 - 1)	D) 81* (sqr2 -1)	E) None of these

Solution: I got 81/(sqr2 +1) and just forgot to multiply by (sqr2 -1).   Answer is 81* (sqr2 -1)
Answer: D