MU-NLPC/Calc-aqua_rat huggingface dataset:
A man's speed with the current is 20 kmph and speed of the current is 4 kmph. The Man's speed
against the current will be	Choose the correct option
A) 11 kmph B) 12 kmph C) 14 kmph D) 17 kmph E) None of these

Solution: Explanation:   Speed with current is 20,   speed of the man + It is speed of the current   Speed in sƟll water = 20 - 4= 
20 - 4 = 16
16   Now speed against the current will be   speed of the man - speed of the current= 16 - 4= 
16 - 4 = 12
12 kmph   Answer: 12 kmph
Answer: B
At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:50. At this university, what is the maximum number of students possible in a course that has 4 teaching assistants? Choose the correct choice from the following answers.
A) 63 B) 64 C) 65 D) 66 E) 67

Solution: (4/3)*50=66 plus remainder   The answer is 66.
Answer: D
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?	Choose the correct option:
A) 482
B) 268
C) 260
D) 480
E) 632

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer: 480
Answer: D
Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 8 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 8 questions did Zachary answer correctly?
Choose the correct choice from the following answers.
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: i got two equations:   3x-2y=25   x+y=8   3x-2(8-x)=25   3x-16+2x=25   5x=41   x=8.2 or between 8 and 9. 9ANS 8)
Answer: C
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?  Choose the correct choice from the following answers.
A) 625	B) 298	C) 269	D) 200	E) 267

Solution: Let the sum be Rs. x. Then,   [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x   S.I. = (x * 4 * 2)/100 = 2x/25   51x/625 - 2x/25 = 1 or x = 625.625nswer: 625
Answer: A
What is the probability that a man flipping ten fair coins flips at least two heads?
Choose the correct choice from the following options.
A) 1	B) 1/2	C) 1/512	D) 1013/1024	E) 1023/1024

Solution: There is a 1/1024 chance of flipping no heads, and a 10/1024 chance of flipping 1 head. This means the chance of flipping two or more heads is 1 - (1/1024 + 10/1024) = 1013/1024, so the answer is 1013/1024.
Answer: D
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
Choose the correct choice from the following choices
A) 5/6	B) 5/9	C) 5/3	D) 5/1	E) 5/2

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
If k,m ,and n are positive real numbers such that k(m+n) = 152, m(n+k) =162 , and n(k+m) = 170, then kmn is  Choices
A) a) 672  B) b) 688  C) c) 704  D) d) 720  E) e) 750

Solution: km+kn = 152 --------------------------------------1)   mn+mk = 162---------------------------------------2)   kn+nm = 170---------------------------------------3)   Re-writing equation 3 as follows: kn+nm = 162 + 8 kn+nm= mn+mk + 8   kn = mk + 8 ............... (4)   Adding (1)(4)   2kn = 160   kn = 80   kmn has to be multiple of 80, only 720 fits in   Answer = d) 720
Answer: D
Arjun started a business with Rs. 5,000 and is joined afterwards by Anoop with Rs.10, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?	Pick one.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: Suppose Anoop joined after 3 months.   Then, 5000 * 12 = 10000 * (12 – x)   => x = 6.   ANSWER:6
Answer: D
The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers? Choose the correct choice:
A) 9
B) 8
C) 5
D) 4
E) 3

Solution: A + B + 5 = 48   B + 5 + D = 45   A + D = 13   A – D = 3   A + D = 13   2D = 10   D = 5   Answer: 5
Answer: C
The ratio of the volumes of two cubes is 216 : 343. What is the ratio of their total surface areas? Choose the correct answer
A) 81:12  B) 31:36  C) 81:22  D) 8:19  E) 1:11

Solution: Ratio of the sides = ³√216 : ³√343   = 6 : 7   Ratio of surface areas = 62:72   = 31:36   Answer: 31:36
Answer: B
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Five years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?	Select the correct option.
A) Can't be determined
B) 40
C) 27
D) 24
E) None of these

Solution: Explanation:   Let the present ages of Sameer and Anand be 5x years and 4x years respectively.   Then, (5x+5)/(4x+5)=11/9   ⇒ 45x + 45 = 44x + 55⇒ 9(5x + 5) = 11(4x + 5)   ⇒ 45x - 44x = 55 - 45= 
55 - 45 = 10
10.   Anand's present age= 4x = 40 years.   Answer: 40
Answer: B
If n is an integer, f(n) = f(n-1) - n and f(4)=14. What is the value of f(6)?
Select the correct option.
A) 3	B) 0	C) 1	D) 2	E) 4

Solution: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.   As given that f(4)=14 then f(5)=14-5= 
14-5 = 9
9 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=9-6= 
9-6 = 3
3.   Answer: A.   Questions on funtions to practice:
Answer: A
Two men Amar and Bhavan have the ratio of their monthly incomes as 6:5. The ratio of their monthly expenditures is 3:2. If Bhavan saves one-fourth of his income, find the ratio of their monthly savings?
Choose the most appropriate option
A) 3:17
B) 3:10
C) 3:26
D) 3:19
E) 3:16

Solution: Let the monthly incomes of Amar and Bhavan be 6x and 5x respectively.   Let the monthly expenditures of Amar and Bhavan be 3y and 2y respectively.   Savings of 3:10havan every month = 1/4 (5x)   =(his income) - (his expenditure) = 5x - 2y   => 5x = 20x - 8y => y = 15x/8   Ratio of savings of Amar and 3:10havan   = 6x - 3y : 1/4 (5x) = 6x - 3(15x/8) : 5x/4   = 3x/8 : 5x/4 => 3:10   Answer: 3:10
Answer: B
If the area of a square with sides of length 9 centimeters is equal to the area of a rectangle with a width of 3 centimeters, what is the length of the rectangle, in centimeters?	Choose the correct choice from the following
A) 4	B) 27	C) 12	D) 16	E) 18

Solution: Let length of rectangle = L   9^2 = L*3   => L = 81/3= 
81/3 = 27
27   Answer 27
Answer: B
Last year Department Store X had a sales total for December that was 6 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
Choose the correct choice from the following
A) 6/17 B) 4/15 C) 1/3 D) 4/11 E) 4/5

Solution: Let avg for 11 mos. = 10   Therefore, Dec = 60   Year total = 11*10 + 60= 
11*10 + 60 = 170
170   6/17nswer= 60/170 = 6/17 = 6/17
Answer: A
If r is even and s is odd, which of the following is odd?  Choose the most appropriate option:
A) rs B) 5rs C) 6(r^2)s D) 5r + 6s E) 6r + 5s

Solution: Just checking options (In case you have difficulty then choose values of r=2 and t=1)   r = even   s= Odd   A. rs = Even*Odd = EvenINCORRECT   B. 5rs = Odd*Even*Odd = EvenINCORRECT   C. 6(r^2)s = 6*(Even^2)*Odd = EvenINCORRECT   D. 5r + 6s = 5*Even + 6*Odd = Even+Even = EvenINCORRECT   E. 6r + 5s = 6*6r + 5sven + 5*Odd = 6r + 5sven+Odd = OddCORR6r + 5sCT   Answer: option 6r + 5s
Answer: E
During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 100 percent. Which of the following is the percent change in the stock's value during those two years? Options.
A) 60 percent decrease B) 40 percent decrease C) 20 percent increase D) 60 percent increase E) 140 percent increase

Solution: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-80/100)=100*0.2= 
100*0.2 = 20
20 and in 2002 its value would be   20*(1+100/100)= 
  20*(1+100/100) = 40
40. Hence during those two years the value of the stock decreased from 100 to 40, so by 60%.   60 percent decreasenswer: 60 percent decrease.
Answer: A
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?	Pick:
A) 20  B) 33 1/3  C) 35  D) 40  E) 80

Solution: Consider total # of rooms to be 100;   As 3/5 of the rooms are air conditioned then # of rooms that are air conditioned is 3/5*100= 
3/5*100 = 60
60;   3/4 rooms were rented --> 1/4*100=25 were NOT rented;   2/3 of air conditioned rooms were rented --> 1/3*60 --  1/4*100= 
 --  1/4*100 = 25
25 were NOT rented;   2/3 of air conditioned rooms were rented --> 1/3*60=20 air conditioned room were NOT rented;   20/25  --  1/3*60= 
  --  1/3*60 = 20
20 air conditioned room were NOT rented;   20/25=4/5=80%.   Answer: 80.
Answer: E
In Town X, 64 percent of the population are employed, and 46 percent of the population are employed males. What percent of the employed people in Town X are females?
Choose the correct choice from the following answers
A) 16% B) 27% C) 32% D) 40% E) 52%

Solution: answer b   male-employed - 64%   female-employed-18%   Total employed 64%   means total unemployed = 36%   therefore d and e are not correct because female unemployed has to be less than 36%   female-unemployed = 32% male unemployed = 4%   48% + 4% = 52%   16% + 32%  48  + 4= 
 48  + 4 = 52
52%   16% + 32% = 48%   plug in a and b in place of 32% and the sum is not 100%   18/64  16  + 32= 
 16  + 32 = 48
48%   plug in a and b in place of 32% and the sum is not 100%   18/64=27 27%
Answer: B
The age of father 6 years ago was four times the age of his son. Five years hence, father's age will be twice that of his son. The ratio of their present ages is:	Options:  A) 55 : 23  B) 43 : 23  C) 51 : 23  D) 53 : 23  E) 56 : 23

Solution: Let the ages of father and son 6 years ago be 3x and x years respectively.   Then, (4x + 6) + 5= 2[(x + 6) + 5]   4x + 11 = 2x + 22   x = 5.5.   Required ratio = (4x + 6) : (x + 6) = 28 : 11.5 =56 : 23.   Answer: Option 56 : 23
Answer: E
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?  Pick:
A) 1
B) 2
C) 3
D) 4
E) None

Solution: Let the ten's digit be x and unit's digit be y.   Then, (10x + y) - (10y + x) = 36   9(x - y) = 36   x - y = 4.   Option 4
Answer: D
Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 205 barrels of oil?  Answers
A) 2	B) 3	C) 4	D) 18	E) 180

Solution: Well A produces 1/2 a barrel per minute.   Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.   So all three wells combined produce a little more than 1 barrel per minute.   So for 205 barrels they will take a bit less than 205 mins which will be more than 3 hrs but less than 4 hrs.   Answer (4)
Answer: C
A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained
2 hours by riding both ways. The time he would take to walk both ways is  Select:  A) 11 hrs  B) 8 hrs 45 min  C) 7 hrs 45 min  D) 9 hrs 20 min  E) 10 hrs

Solution: Given that time taken for riding both ways will be   2 hours lesser than the time needed for waking one way and riding back.   Therefore,   time needed for riding one way = time needed for waking one way -   2 hours   Given that time taken in walking one way and riding back   =5 hours 45 min   Hence, the time he would take to walk both ways   5 hours 45 min + 2 hours =7 hours 45 min   ANSWER 7 hrs 45 min
Answer: C
four mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the four arrange themselves in line such that Frankie’s requirement is satisfied?
Choose the most appropriate option.
A) 24 B) 28 C) 32 D) 36 E) 42

Solution: 4 mobsters can stand in 4! ways = 24   in half of the cases one person will be ahead and in the other person in the other half.   thus 24 cases.   24
Answer: A
What amount does Kiran get if he invests Rs.4500 at 10% p.a. compound interest for three years, compounding done annually?
Choose the correct answer.
A) 2999	B) 2787	C) 2097	D) 5989	E) 2886

Solution: A= P{1 + R/100}n   => 4500{1 + 10/100}3   = Rs.5989   Answer: 5989
Answer: D
Radha started a business, investing 75,000. After 3 months, Sunidhi joined her with an amount of 1,25,000 and after another six months Neha joined them with an amount of 1,50,000. Profit earned at the end of three years from when Radha started the business should be distributed in what ratio among Radha, Sunidhi and Neha respectively?	Choose the correct choice from the following answers:
A) 36 : 55 : 54	B) 18 : 28 : 27	C) 35 : 54 : 55	D) Cannot be determined	E) None of these

Solution: Ratio of their profits (Radha’s : Sunidhi’s : Neha’s)   = 75 × 36 : 125 × 33 : 150 × 27   = 3 × 36 : 5 × 33 : 6 × 27   = 3 × 12 : 5 × 11 : 6 × 9   = 36 : 55 : 54   36 : 55 : 54nswer 36 : 55 : 54
Answer: A
A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?	Choose the correct choice from the following options.
A) 37 B) 39 C) 42 D) 44 E) 45

Solution: Let the original number be 'a'   Let the divisor be 'd'   Let the quotient of the division of aa by dd be 'x'   Therefore, we can write the relation as a/d = x and the remainder is 24.   i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.   We know that a=dx+24. Therefore, 2a = 2dx + 48   The problem states that (2dx+48)/d leaves a remainder of 11.   2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.   The remainder of 11 was obtained by dividing 48 by d.   When 48 is divided by 37, the remainder that one will obtain is 11.   Hence, the divisor is 37.   37
Answer: A
A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 3300. What is the share of B ? Choices.
A) 1100
B) 800
C) 1400
D) 600
E) None of them

Solution: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x   A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.   Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.   Hence, B's share = Rs. ( 3300 x (2/11))= Rs.600   Answer is 600.
Answer: D
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 24 seconds. What is the length of the goods train? Choose one
A) 230 m  B) 240 m  C) 260 m  D) 270 m  E) None of these

Solution: Explanation:   Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.   Time = 24 sec.   Let the length of the train be x metres.   Then,[ (x+250)/24 ]= 20   => x + 250 = 480   => x = 230. 230 mnswer: 230 m
Answer: A
The ratio of two numbers is 3:4 and their sum is 49. The greater of the two numbers is?	Choose the most appropriate option:  A) 12  B) 14  C) 16  D) 17  E) 28

Solution: 3:4   Total parts = 7   = 7 parts --> 49 (7 Ã— 7 = 49)   = 1 part ---->7 (1 Ã— 7 = 7)   = The greater of the two number is = 4   = 4 parts ----> 28 (7 Ã— 4 = 28)   28
Answer: E
The unit digit in the product (624 * 708 * 913 * 463) is:
Pick.
A) 2
B) 5
C) 6
D) 8
E) 10

Solution: Explanation:   Unit digit in the given product = Unit 8igit in (4*8*3*3) = 8   ANSWER: 8
Answer: D
(51+ 52 + 53 + ... + 100) = ?  Choices
A) 3775	B) 3795	C) 3800	D) 3900	E) 4000

Solution: This is an A.P. in which a = 51, l = 100 and n = 50.   Sum = n (a + l) = 50 x (51 + 100) = (25 x 151) = 3775.   2 2   3775)
Answer: A
In an electric circuit, two resistors with resistances A and B are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of C is equal to the sum of the reciprocals of A and B. What is C in terms of A and B? Answers:
A) (A-B)/AB
B) (A+B)/AB
C) A+B
D) AB
E) AB/(A + B)

Solution: The wording is a bit confusing, though basically we are told that 1/C= 1/A + 1/B, from which it follows that C=AB/(A + B).   Answer: AB/(A + B)
Answer: E
A library has an average of 570 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is: Choose the correct choice.
A) 250	B) 276	C) 280	D) 295	E) None

Solution: Since the month begins with sunday,to there will be five sundays in the month   Average required = (570x5 + 240x25) /30) = 295   Answer: Option 295
Answer: D
If x-y=8, which of the following must be true?
I. If x is negative, y must be negative
II. Both x and y are positive
III. If x is positive, y must be positive	Choose the correct choice:
A) I only	B) II only	C) III only	D) I and II	E) II and III

Solution: If x-y=8, which of the following must be true?   I. Both x and y are positive   II. If x is positive, y must be positive   III. If x is negative, y must be negative   1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D   2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E   I only) I only   B) II only   C) III only   D) I and II   E) II and III   I onlynswer I only
Answer: A
Ajay had purchased a second hand scooter for 18,000 and spent Rs.1800 for repairs. After one year he wanted to sell the scooter. At what price should he sell it to gain 100/9%, if 100/11% is to be deducted at the end of every year on account of deprecation? Choose the correct answer: A) Rs.18000 B) Rs.19800 C) Rs.20000 D) Rs.22500 E) Rs.23500

Solution: Cost Price =Rs.18000.   Cost on Reparing = Rs. 1800.   So, Total cost = 18000 +1800= 
18000 +1800 = 19_800
19800.   Depreciation= 100/11% = 9.09%.   Gain = 100/9% = 11.11%.   After depreciation, the cost price would be = 19800 - 9.09% of 19800 = Rs. 18000   SP to gain 11.11% = 18000 + 11.11% of 18000 = 18000 + 1999.8 = Rs. 20,000.   ANSWER : Rs.20000
Answer: C
Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually  Choose the correct choice from the following choices:  A) 3358  B) 8952  C) 3309  D) 3109  E) 3528

Solution: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]=Rs. [8000 * (23/20) * (23/20) * (21/20)]= Rs. 11109. .:. C.I. = Rs. (11109 - 8000) = Rs. 3109. Answer : 3109
Answer: D
At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 45 other employees of Company K, how many employees does Company K have? Choose the correct choice from the following answers:
A) 160
B) 180
C) 190
D) 200
E) 400

Solution: Secretaries = 15 %   Salespeople = 60%   Percentage of employee other than Secretaries and Salespeople = 25%   Let total number of employees of company K = N   (25/100)* N = 45   =>N=180   Answer 180
Answer: B
A ship 77 km from the shore, springs a leak which admits to 9/4 tonnes of water in 11/2 minutes. 92 tonnes of water would sink it. But the pumps can throw out 12 tonnes of water per hour. Find the average rate of sailing so that the ship may just reach the shore as it begins to sink.	Choose the most appropriate option:
A) 10.5 B) 11 C) 12 D) 13 E) 15

Solution: Leak admits 9/4 tonnes water in 11/2 min   =11/2 * 4/9 = 22/9   leak admits 9/22 tonne of water in 5 min   in 1 min in thrws 1/5 tonne of water = 9/22 - 1/5 = 23/110   92/23/11 min = 440 min   22/3 min=7/22/22/3 => 10.5 km/hr   10.5NSWER 10.5
Answer: A
On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?  Pick one.
A) 4  B) 5  C) 6  D) 8  E) 9

Solution: Explanation:   Formula: (Divisor*Quotient) + Remainder = Dividend.   Soln:   (56*Q)+29 = D -------(1)   D%8 = R -------------(2)   From equation(2),   ((56*Q)+29)%8 = R.   => Assume Q = 1.   => (56+29)%8 = R.   => 85%8 = R   => 5 = R.   Answer 5
Answer: B
Total dinning bill for 5 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
Choose the correct choice from the following choices:
A) $30.14 B) 48.53 C) 34.66 D) 32.29 E) 33.16

Solution: 211*15= 
211*15 = 3_165
3165/100= 
3165/100 = 633/20 = around 31.65
31.65   211+31.65= 
211+31.65 = 242.65
242.65   242.65/5= 
242.65/5 = 48.53
48.53   ANSWER:48.53
Answer: B
he probability that a number selected at random from the first 50 natural numbers is a composite number is ?  Choose the correct option:  A) 17/25  B) 4/25  C) 21/25  D) 8/25  E) 9/25

Solution: Explanation:   The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50 = 17/25.   17/25)
Answer: A
If the positive integer x is a multiple of 7 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8
II. 12
III 18
Choose the correct choice from the following:
A) II only	B) I and II only	C) I and III only	D) II and III only	E) I, II and III

Solution: Ans A   From question x/4 is an integer.   x/4 = 2*2*q/4 ---> where q is the integer   II onlylso y/6 = p => y/6 = 2*3*p/6   So, xy =  2*2*2= 
 2*2*2 = 8
8 and   2*3*2= 
  2*3*2 = 12
12 satisfy
Answer: A
A grocer stacked oranges in a pile. The bottom layer was rectangular with 4 rows of 8 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer? Choices
A) 14	B) 12	C) 10	D) 7	E) 4

Solution: 12ottom Layer = 8 x 4 = 32   IInd Layer = (8-1) x (4-1) = 21   IIIrd Layer = (7-1) x (3-1) = 12   Answer = 12 = 12
Answer: B
A trumpet section includes four musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?  Answers
A) 240 B) 125 C) 120 D) 100 E) 24

Solution: We have a word problem using permutations. We must identify the number of total items in the group. There are four possible musicians who could be placed in the first chair, three possible musicians for the second, two for the third, one for the fourth. To determine the number of possible orderings, we multiply these numbers, which we can express as 4!. Now 4! = (4)(3)(2)(1) = 24=24
Answer: E
A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room. Choose one
A) 017
B) 117
C) 127
D) 137
E) 147

Solution: Let us calculate both the length and width of the room in centimeters.   Length = 6 meters and 24 centimeters = 624 cm   width = 4 meters and 32 centimeters = 432 cm   As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.   Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48   Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117 Answer: 117
Answer: B