MU-NLPC/Calc-aqua_rat huggingface dataset:
A farmer has 3,000 seeds which is enough for him to plant seeds every day for 50 days. After 10 days he loses some of the seeds and the remaining seeds is now enough for him to plant for the same period of 50 days as before. How many seeds did he lose?
Select.
A) 200	B) 600	C) 1,000	D) 900	E) 700

Solution: 3,000 ---- 50   3,000 ---- 40   x = 50   x*50 = 3,000*40   x = 2,400   3,000   -------   600   Answer = 600
Answer: B
What will come in place of the x in the following Number series? 3, 6, 12, x , 33	Pick one
A) 33  B) 37  C) 39  D) 21  E) 43

Solution: (D)   The pattern is + 3, + 6, + 9, +12 â€¦â€¦â€¦..   So the missing term is = 12 + 9= 
12 + 9 = 21
21
Answer: D
$600 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
Choose the correct choice from the following answers:
A) $100	B) $150	C) $125	D) $200	E) $240

Solution: A:(B+C) = 2:3   A's share = 600*2/5= 
600*2/5 = 240
$240   Answer is $240
Answer: E
A sum of 14,800 amounts to 19,800 in 3 years at the rate of simple interest. What is the rate of interest? Choose the correct choice from the following.
A) 12%
B) 11%
C) 16%
D) 15%
E) 18%

Solution: B   11%   S.I. = (19800 - 14800)= 
(19800 - 14800) = 5_000
5000.   Rate= (100 x 5000)/(14800x3)% = 11%
Answer: B
A basket contains 8 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
Select
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6

Solution: The total number of ways to choose 2 apples is 81/42 = 28   The number of ways that include the spoiled apple is 71/41 = 7   P(the spoiled apple is included) = 7/28 = 1/4   The answer is 1/4.
Answer: C
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days will the project be completed?	Choose the correct choice from the following answers
A) 18 days
B) 27 days
C) 26.67 days
D) 15 days
E) 12 days

Solution: Let X = the number of days taken to complete the project.   The amount of work done by A is (x-10) * (1/20).   The amount of work done by B is (x) * (1/30).   (1/20)*(x-5) + (1/30)*(x) = 1   (x/20) + (x/30) - (5/20) = 1   5x/60 = 5/4   x = 60/4= 
60/4 = 15
15   Therefore, the answer is 15 days: 15.
Answer: D
The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they subtract an antenna with a height of z feet to the top?  Choose the correct choice from the following options:
A) (x+z)/2 + 37
B) 2x−(37+z)
C) (x−37)/2 + z
D) x/2 - 37 + z
E) (x−37)/2 + z

Solution: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:   h1 + h2 = x   and h1 = h2 + 37 =>   Q: h2 + z = ?   h2 + h2 + 37 = x => 2h2 = x-37 =? h2 = (x-37)/2   => h2 - z = (x-37)/2 + z, CORR(x−37)/2 + zCT ANSW(x−37)/2 + zR (x−37)/2 + z
Answer: E
There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 11 cans so that at least one red and at least one blue cans to remain the refrigerator.	Answers.
A) 4  B) 490  C) 493  D) 455  E) 445

Solution: Ways to pick 1 cans so that at least one red and at least one blue cans to remain the refrigerator =   total ways to pick 1 can out of 12 - ways to pick 1 red out of 7 red - ways to pick 1 blue out of 5 blue   12C1âˆ’7C1âˆ’5C1=12âˆ’7âˆ’1=4   4NSWER:4
Answer: A
What is the area of the given rectangle?
I.	Perimeter of the rectangle is 60 cm.
II.	Breadth of the rectangle is 12 cm.
III.	Sum of two adjacent sides is 30 cm.
Choose the most appropriate option:
A) I only
B) II only
C) I and II only
D) II and III only
E) II and either I or III

Solution: EXPLANATION   From I and II, we can find the length and breadth of the rectangle and therefore the area can be obtained.   So, III is redundant.   Also, from II and III, we can find the length and breadth and therefore the area can be obtained.   So, I is redundant.   Correct answer is “II and either I or III”.   Answer II and either I or III
Answer: E
How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 54 kmph?
Select the correct option.
A) 22 sec	B) 77 sec	C) 16.7 sec	D) 18 sec	E) 17 sec

Solution: D = 100 + 150= 
100 + 150 = 250
250   S= 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 250/15 = 16.7 sec   Answer:16.7 sec
Answer: C
If d + xy = d and x is not equal to 0, which of the following must be true?
Choose the correct answer.
A) x=0 B) x+y=0 C) x<y D) y=0 E) x=d

Solution: d + xy = d --> xy=0. Since x is not equal to 0, thus y = 0.   Answer: y=0.
Answer: D
(1-1/n)+( 1-2/n)+(1-3/n)+…… up to n terms=?	Choose the correct choice from the following:
A) 1/2n B) 1/2(n-1) C) 1/2n(n-1) D) none of these E) cannot be determined

Solution: Solution: Given sum=(1+1+1+…. to n terms)-(1/n+2/n+3/n+…. to n terms)   = n-(n(n+1)/2)/n   = n-(n+1)/2=1/2(n-1).   Answer 1/2(n-1)
Answer: B
In a fraction, if numerator is added by 2 and denominator by 1 it results 1, and if numerator added again by 4 and denominator by 2 it results 1/2. Find the fraction?	Select the correct option
A) 3/4 B) 5/4 C) 7/4 D) 9/4 E) 11/4

Solution: x+2/y+1 =1 i.e, x-y+1=0;--------(1)   x+4/y+2 =1/2 i.e., 2x-y+6=0;---------(2)   solving 1 and 2...we get x= -5 and y= -4   answer is 5/4...   ANSWER:5/4
Answer: B
LCM of two numbers is 7700 and HCF is 11. If one number is 308 then other number is
Answers
A) 269 B) 285 C) 300 D) 275 E) None of these

Solution: Option 275
Answer: D
There are two numbers whose sum is 72. One number is twice the other. What are the
numbers? Choose the correct choice from the following answers:
A) 32-55	B) 24-48	C) 35-42	D) 20-40	E) 33-55

Solution: Read the problem. It is about numbers.   The question at the end asks, “What are the numbers?”   Create a let statement.   Let x smaller number   2x= larger number   Reread the problem. It states that the sum of the two numbers is 72.   Translate the problem into an equation and solve.   x+2x=72   3x=72   x=24   2x=48   The answers are: The smaller number is 24 and the larger number is 48.   Is this sensible? Yes, because the sum of 24 and 48 is 72.   correct answer 24-48
Answer: B
In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 100 bricks in the wall, how many bricks does the bottom row contain ?  Select:
A) 18  B) 16  C) 17  D) 15  E) 19

Solution: The bottom row has x bricks   x+x-1+x-2+x-3+x-4 = 100   5x-10=100   5x=90   x= 18   18nswer:18
Answer: A
In track last week, the boys ran 15 laps. The girls ran 5 more
laps. Each lap is a one-fifth of a mile. How many miles did the girls run?	Choose the correct choice from the following choices:	A) 2 miles	B) 3 miles	C) 4 miles	D) 5 miles	E) 6 miles

Solution: The girls ran 15 + 5= 
15 + 5 = 20
20 laps. 20 x 1/5= 20/5, which reduces to 4.   The girls ran 4 miles   correct answer 4 miles
Answer: C
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was?
Choices: A) 16 years B) 14 years C) 18 years D) 19 years E) 15 years

Solution: Let the son's present age be x years.   Then, (38 - x) = x   2x = 38 => x = 19   Son's age 5 years back = (19 - 5)= 
(19 - 5) = 14
14 years.   Answer: 14 years
Answer: B
P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?	Choose the correct choice
A) 4/5	B) 2/7	C) 8/15	D) 7/5	E) 2/8

Solution: Explanation :   Amount of work P can do in 1 day = 1/15   Amount of work Q can do in 1 day = 1/20   Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60   Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15   Fraction of work left = 1 – 7/15= 8/15   ANSWER:8/15
Answer: C
A man can row upstream at 25 kmph and downstream at 37 kmph, and then find the speed of the man in still water? Choose the correct choice from the following options
A) 86 B) 67 C) 31 D) 15 E) 17

Solution: US = 25   DS = 37   M = (37 + 25)/2= 
(37 + 25)/2 = 31
31   Answer: 31
Answer: C
A number exceeds 20% of itself by 40. The number is  Choose the correct option:
A) 50
B) 60
C) 80
D) 320
E) None

Solution: Explanation:   Let the answer be 'a'   Then a−20/100a=40⇒5a−a=200   ⇒a=50⇒a=50   Correct Option: 50
Answer: A
Calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length, if the speed of the train is 40 km/hour ?
Choose the correct choice from the following answers:	A) 21.2 seconds	B) 25.2 seconds	C) 29.2 seconds	D) 35.2 seconds	E) 11.2 seconds

Solution: Speed = 40 Km/hr = 40*(5/18) m/sec = 11.1111 m/sec   Total distance = 120+160= 
120+160 = 280
280 meter   Time= Distance/speed   = 280 * (1/11.1111) = 25.2 seconds   Answer: 25.2 seconds
Answer: B
The least value of expression 2log10 x - logx (1/100) for x>1 is: Choose the correct option:	A) 2	B) 3	C) 4	D) 5	E) 6

Solution: 2log10 x = logx1/100 x = log10 10^-2/log10 x   =2log10 x + 2/log10 x   =2[log10 x - 1/log10 x]   since x>1=>log10 x >0   log10 x+ 1/log10^x>=2=> for x = 10, 2[log10 x + 1/log 10 x] > 4   Hence least value is 4   ANSWER 4
Answer: C
A person covered one-fourth of the total distance at 22 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Choose the correct choice from the following choices
A) 21 (1/8)
B) 21 (1/15)
C) 23 (7/15)
D) 29 (1/15)
E) 21 (4/15)

Solution: Let the total distance be x km   total time taken = (x/4)/22 + (3x/4)/24 = 15x/352   Average speed = x/(15x/352) = 23 (7/15)kmph.   Answer: 23 (7/15)
Answer: C
24 oz of juice P and 25 oz of juice E are mixed to make smothies X and Y . The ratio of p to E in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X? Pick
A) 5  B) 10  C) 15  D) 20  E) 25

Solution: Easy way to solve this question is start from the answer and then conform the information provided in the question.   we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to E ratio is 4:1   this gives us that quantity of juice P in X = 20 therefore quantity of Juice E will be 5 ... hence ratio = 4:1   This will lead to quantity of juice P in X = 4 and quantity of Juice E = 20 ... hence ratio 1:5   if we calculate total Juice P = 24 and total of juice V = 25   it fits because totals are same as what mentioned in the question ...   thus ans is 20
Answer: D
Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability T that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls? Choices:
A) T=8/28	B) T=9/28	C) T=10/28	D) T=10/18	E) T=11/18

Solution: (3c2*2c1*3c2)/8c5   =(3*2*3)/ (8*7*6/3*2)   =18/56   =9/28   T=9/28
Answer: B
How many different subsets of the set {10, 14, 13, 24} are there that contain an odd number of elements? Select the correct option.
A) 3 B) 6 C) 8 D) 10 E) 12

Solution: Answer = 8 = 8   {10}   {14}   {13}   {24}   {10, 14, 13}   {14, 13, 24}   {10, 13, 24}   {10, 14, 24}
Answer: C
Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 12 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?	Choose the correct choice from the following answers:
A) 4  B) 4.5  C) 6  D) 8  E) 6.5

Solution: Work done by AB in a day = xy respectively.   When A starts:   No. of days when A works = 6No. of days when B works = 6 → 6x + 6y = 1   When B starts:   No. of days when A works = 6.5No. of days when B works =5.5 → 6.5x +5.5y = 1   Solving the above two equations for xy   x = 1/12 y = 1/12   → Total work done by AB in a day = 1/12 + 1/12 = 2/12 =1/6   → No. of days to complete the work when both work together = 6   Answer: 6
Answer: C
How many possible positive integer values are there for k if -24 < 9k – 6 ≤ 3?	Options.
A) Zero B) One C) Two D) Three E) Four

Solution: -24 < 9k – 6 ≤ 3   Add 6: -18 < 9k ≤ 9   Divide by 9: -2< k ≤ 1.   k can take only one positive integer value: 1.   Answer: One.
Answer: B
hree number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:  Choose the correct choice from the following:
A) 40
B) 50
C) 60
D) 70
E) 80

Solution: Let the numbers be 3x, 4x and 5x.   Then, their L.C.M. = 60x.   So, 60x = 2400 or x = 40.   The numbers are (3 x 40), (4 x 40) and (5 x 40).   Hence, required H.C.F. = 40.   40NSWER :40
Answer: A
John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4125. What is the difference between Rose ’s and Tom ’s share in the profit?  Pick one:
A) s.340
B) s.362
C) s.375
D) s.382
E) s.390

Solution: John : Rose : Tom   Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8   = 6 : 3: 2   The difference between Rose’s and Tom’s share = 1 share   :.i.e. = Rs. 4125 × 1/11 = Rs.375.   s.375)
Answer: C
By travelling at 80 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Choose the correct choice from the following answers:
A) 25 kmph B) 40 kmph C) 35 kmph D) 46 kmph E) 50 kmph

Solution: Let the time taken to reach the destination be 3x hours. Total distance = 80 * 3= 
80 * 3 = 240
240x km   He covered 2/3 * 240= 
2/3 * 240 = 160
160x km in 1/3 * 3x= x hours So, the remaining 80x km, he has to cover in 2x hours. Required speed = 80x/2x   =40 kmph.   Answer: 40 kmph80 /2= 
80 /2 = 40
40 kmph.   Answer: 40 kmph
Answer: B
On a particular mathematics exam, the student has 5 answers to choose from. If the student guesses at the answers, the probability of the student getting a correct answer on each question is 1/5. What is the least number of times that the student should guess in order to take the probability of getting a correct answer at least once to more than 50%. Answers
A) 4	B) 1	C) 2	D) 5	E) 6

Solution: Rule of Subtraction: P(A) = 1 - P(A')   Rule of Multiplication: P(A ∩ B) = P(A) P(B)   The probability that the student gets a correct answer at least once in 2 guesses is 1- (4/5)^2 = 1 - 16/25 = 9/25 < 50%.   The probability that the student gets a correct answer at least once in 3 guesses is 1- (4/5)^3 = 1 - 64/125 = 61/125 < 50%.   The probability that the student gets a correct answer at least once in 4 guesses is 1- (4/5)^4 = 1 - 256/625 = 369/625 > 50%.   4nswer: 4
Answer: A
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 8 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?	Options:
A) R-4
B) R/(R+4)
C) R/(R-16)
D) 8/(R-8)
E) 2R - 4

Solution: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.   In T hours Alex will cover 4T miles;   Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);   We want the distance covered by Brenda to be twice as much as that of Alex: 2*8T=R(T-1) --> 16T=RT-R --> T=R/(R-16).   Answer: R/(R-16).
Answer: C
The ratio between the presents of the A and B is 2:3. If B is 5 years older than A, what will be the ratio of the ages of A and B after 5 years?  Choose the correct choice from the following options:  A) 3:4  B) 1:2  C) 2:3  D) 5:6  E) 1:3

Solution: Let 3:4 and B ages will be 2x and 3x   3x - 2x = 5   x = 5   Required ratio = 2x+5 : 3x+5 = 15:20 = 3:4   3:4nswer is 3:4
Answer: A
If a randomly selected non-negative single digit integer is added to {2, 3, 6, 8}. What is the probability that the median of the set will increase but the range still remains the same? Choose the correct choice from the following choices.
A) 0.2 B) 0.3 C) 0.4 D) 0.5 E) 0.6

Solution: We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.   Hence, the total number of outcomes is 10.   We need to find the probability that the median of the set will increase but the range still remains the same.   The median of the set is  (3 + 6)/2= 
 (3 + 6)/2 = 9/2 = around 4.5
4.5, thus the number selected must be 5 or greater.   For the range to remain the same, the number must be between 2 and 8 inclusive.   To satisfy both conditions, the number selected must be 5, 6, 7, or 8.   The probability is  4/10= 
 4/10 = 2/5 = around 0.4
0.4   The answer is 0.4.
Answer: C
A cubic object 3'' x 3'' x 3'' is painted blue on all the outside surfaces, including the top and bottom. If the cube is cut into 27 cubes of 1'' x 1'' x 1'' , how many 1" cubes do have any painted surfaces?	Select the correct option:
A) 15
B) 22
C) 26
D) 33
E) 44

Solution: 26   26   Only the box in the very centre of the stack will not suffer the strokes of the paint brush, whereas all the other 26 boxes will have at least one side painted.
Answer: C
Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
Choices:
A) 22.5 years  B) 24.5 years  C) 12.5 years  D) 28.5 years  E) 29.5 years

Solution: Let Rahul's age be X years.   Then, Sachin's age = (X - 7) years.   Therefore (X - 7) / X	=	7/9   9X - 63 = 7X   2X = 63   X = 31.5   Hence, Sachin's age =(X - 7) = 24.5 years.   ANSWER:24.5 years
Answer: B
If x is a sum of all even integers on the interval 13...55 and y is their number, what is the GCD (x, y)? Pick one
A) 1
B) 21
C) 26
D) 52
E) 1014

Solution: x = 14 + 16 + ... + 54 = (largest + smallest)/2 *(# of terms) = (14 + 54)/2*21= 34*21.   GCD of 21 and 34*21 is 21   Answer: 21.
Answer: B
If one-third of one-fourth of a number is 15, then three-tenth of that number is: Choose one
A) 45  B) 65  C) 54  D) 34  E) 44

Solution: Let the number be x.   Then,1/3 of 1/4 of x = 15 <=> x = 15 x 12 = 180.   So, required number =3/10 x 180= 54.   ANSWER:54
Answer: C
A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 380 miles apart, at what time will the trains pass each other?  Answers
A) 12:40pm  B) 12:49pm  C) 12:55pm  D) 1:01pm  E) 1:05pm

Solution: Train A: going from K to T   Train B: going from T to K   First I calculated how far Train A will have travelled by the time Train B starts at 12:10:   10 minutes at 240 mph    1/6*240= 
 1/6*240 = 40
40miles   They have 380-40= 
380-40 = 340
340 miles to travel to meet each other.   I found the combined rate of the two trains   Rate(A) + Rate(B)= 400mph   1:01pmivide 1:01pmistance/Rate to find total time each will travel:   340/400>>> 51 Minutes to meet   12:10+51 minutes = 1:01 or Answer 1:01pm
Answer: D
On taking delivery of a consignment of eggs the market stall owner was furious to find that several were cracked. In fact, on counting them up in order to assess the damage he found that 72 were cracked, which was 12 percent of the total consignment. How many eggs in total were in the consignment?	Choose the most appropriate option.
A) 500  B) 600  C) 800  D) 200  E) 900

Solution: 600   600   72 ÷ 12 × 100 = 600.
Answer: B
A man walks at certain place and rides back in 10 hours. He could ride both ways in 8 hours. The time taken by him to walk both ways?
Select the correct option.
A) 10	B) 12	C) 14	D) 16	E) None of above

Solution: W + R = 10and 2R = 8, R = 4so, W = 6 so, walking both sides, he will take = 12 hours Answer: 12
Answer: B
In Arun's opinion, his weight is greater than 66 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 69 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?  Select:
A) 86.5 kg	B) 67.5 kg	C) 46.5 kg	D) 26.5 kg	E) 16.5 kg

Solution: Let Arun's weight be X kg.   According to Arun, 66 < X < 72.   According to Arun's brother, 60 < X < 70.   According to Arun's mother, X < 69.   The values satisfying all the above conditions are 67 and 68.   Required average = (67 + 68) / 2= 
(67 + 68) / 2 = 135/2 = around 67.5
67.5 kg   Answer: 67.5 kg
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
Pick one:
A) 356
B) 250
C) 127
D) 279
E) 150

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 15= 
50/3 * 15 = 250
250 m   Answer: 250
Answer: B
For integers x, y, and z, if (3^x) (4^y) (5^z) = 838,860,800,000 and x + y + z = 19, what is the value of xy/z? Choose the correct choice from the following:	A) 0	B) 2	C) 4	D) 6	E) 8

Solution: The number 838,860,800,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)   Thus x = 0 and xy/z = 0.   The answer is 0.
Answer: A
The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 60.5. When one student dropped the class, the average of the remaining scores increased to 64.0. What is the quiz score of the student who dropped the class?	Choose one:  A) a) 8  B) b) 25  C) c) 40  D) d) 55  E) e) 70

Solution: Total Score of 16 students is  16*60.50= 
 16*60.50 = 968
968   Total Score of 15 students is  15*64= 
 15*64 = 960
960   So, the score of the person who left is 8 ( 968 - 960 )   a) 8nswer will be (a) 8
Answer: A
At the beginning of 2011, Company X created a list of n charities, and committed to donating 10% of its prots for the year to these charities, donating an equal amount to each charity. However, during the year, Company X removed a charities from this list, and donated 10% of its prot in equal amounts to each of the remaining charities on the list. If the Wesley Homeless Shelter was one of the charities on the list which received a donation from Company X, which of the following represents, in terms of n and a, the percent increase in the amount the Wesley Homeless Shelter received because the a charities were removed from the list?  Pick:	A) 100n/a	B) 100a/(n-a)	C) 100(n-a)/n	D) 100n/(n-a)	E) 100(n-a)/a

Solution: Sol:   Let profit be "P"   for n charities - each get p/n   when a charities are removed - each get p/(n-a)   increase will be (p/(n-a)) - (p/n) = pa/(n-a)*n   Increase % will be (pa/(n-a)*n) / (p/n) multiplied by 100.   result will be 100a/(n-a)   ANSW100(n-a)/aR:100(n-a)/a
Answer: E
8 points are marked on a straight line and another 9 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points? Choose the correct choice:
A) 91  B) 105  C) 196  D) 20  E) 14

Solution: assuming that the top line can have either 2 points or 1 point...   8! / 1!7! - 8! / 2! 6! yields 20.   20
Answer: D
When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.50 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?	Select.
A) $255 B) $275 C) $510 D) $1,250 E) $2,550

Solution: Total no. Of boxes = 3060000/(20×20×15) = 510   Total cost = 510×$0.5=$255   $255nswer $255
Answer: A