MU-NLPC/Calc-aqua_rat huggingface dataset:
RADIO X sells cheap radios for commercial use by buying surplus supplies. A surplus bag of 100 diodes costs $2.00. A surplus bag of diodes, on average, has 10% faulty diodes (the faulty diodes are thrown away, and the remaining diodes are used in production). It takes 5 diodes to make 1 circuit board. If it takes 3 circuit boards to make a radio, how much money is needed to buy diodes to make x number of radios, in dollars?
Select the correct option:
A) x/3
B) 3x
C) 2x/3
D) x
E) 3x/4

Solution: Initial cost for 1 bag of diodes = $2, but ONLY 100(1 - 0.1) = 90 are used. So the cost for 90 diodes = $2. The number of diodes for making a radio is (3 circuit boards)(5 diodes) = 15 diodes. So, the cost for diodes to make a radio is $2(15/90) = $1/3.   $x/3 =cost of diodes to make x number of radios.   x/3nswer is x/3
Answer: A
A Positive number which when added to 999 given a sum which is greater than when it is multiplied by 999. Which of the following could be the value of the positive integer?	Choose the correct choice.
A) 5  B) 3  C) 1  D) 2  E) 4

Solution: Explanation:   Let the positive integer = x   Then, 999 + x > 999x   By trial and error, when x = 1,   1000 > 999   So, the required positive integer is 1,   1000 > 999   So, the required positive integer is 1.   Answer: Option 1
Answer: C
X starts a business with Rs.77000. Y joins in the business after 5 months with Rs.42000. What will be the ratio in which they should share the profit at the end of the year? Pick
A) 21:23  B) 23:45  C) 22:7  D) 25:29  E) None of these

Solution: Explanation :   Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   = 77000 * 12: 42000 * 7   = 77 * 12: 42 * 7   = 11*2: 7   = 22:7.   Answer : Option 22:7
Answer: C
A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds in passing him. The speed of the train was Choose the correct option:
A) 25.2 km/hr B) 32.4 km/hr C) 50.4 km/hr D) 75.6 km/hr. E) None of these

Solution: Explanation:   Let the train’s length be L m.   L/9=(L+84)/21   21 L = 9L +756   12L= 756   L=63 m   Speed = 63 /9= 
63 /9 = 7
7 m/s= 7 x 18/5 = 25.2 Km/hr.   25.2 km/hrnswer 25.2 km/hr
Answer: A
By travelling at 40 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? Pick:  A) 20 kmph  B) 30 kmph  C) 87 kmph  D) 99 kmph  E) 77 kmph

Solution: Let the time taken to reach the destination be 3x hours. Total distance   = 40 * 3= 
40 * 3 = 120
120x km   He covered 2/3 * 120= 
2/3 * 120 = 80
80x km in 1/3 * 3x= x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed   = 40x/2x = 20 kmph.   20 kmphnswer:20 kmph40 /2= 
40 /2 = 20
20 kmph.   20 kmphnswer:20 kmph
Answer: A
When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?  Answers.
A) 9
B) 10
C) 11
D) 13
E) 15

Solution: The given number =7y86038   Sum of the odd places =8+0+8+7= 
8+0+8+7 = 23
23   Sum of the even places= 3+6+y   (Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)   23-(9+y) = divisible by 11   14 � y = divisible by 11.   Y must be 3, to make given number divisible by 11.   11
Answer: C
A certain city with a population of 108,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
Choose the correct choice from the following options
A) a) 10,700  B) b) 10,800  C) c) 9,000  D) d) 11,000  E) e) 11,100

Solution: Let x = number of people in smallest district   x*1.1 = number of people in largest district   x will be minimised when the number of people in largest district is maximised   10*x*1.1 = 11x = total number of people in other districts   So we have 11x + x = 108k   x = 9,000   Answer : c) 9,000
Answer: C
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is seven times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution? Select
A) 1:1
B) 2:3
C) 3:2
D) 9:4
E) 63:8

Solution: Water:soap = 3:2   Soap:Salt=21:2   => For 21 soap, salt = 2   => For 2 Soap, salt = (2/21)*2 = 4/21   So, water:soap:salt = 3:2:4/21 = 63:42:4   After open container, water:soap:salt = 31.5:42:4   So, water:salt = 31.5:4 = 63:8   63:8
Answer: E
A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
Choices:  A) 6  B) 7  C) 9  D) 5  E) 3

Solution: 4/10 + 9/x = 1 => x = 15   1/10 + 1/15 = 1/6 => 6 days   6nswer: 6
Answer: A
Set A: 3, r, 8, 10
Set B: 4, g, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of g – r?
Choose the correct answer.
A) -2 B) -1 C) 0 D) 1 E) 2

Solution: So we have even no. of elements in the Set   So median is the average of Middle two numbers   (r+8)/2= (g+9)/2   g - r= -1   Answer -1
Answer: B
A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?  Choose the correct choice from the following answers:  A) 3 : 9  B) 3 : 7  C) 3 : 8  D) 3 : 4  E) 3 : 1

Solution: Since S # 1/t   S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4   Answer:3 : 4
Answer: D
John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?	Options:
A) 6
B) 9
C) 12
D) 18
E) 19

Solution: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)   and Rupesh + 6 = | (Ravi + 6) ...(ii)   Solving both the equations we get,   Ravi = 12 years.   12
Answer: C
What is the sum of all consecutive integers from 10 to 100, inclusive?	Choose the most appropriate option
A) 4550  B) 4950  C) 5005  D) 5500  E) 5555

Solution: SUM= n/2(Starting number+ Ending number)   n: total numbers between the starting no. and ending no.   n= 100-10+1= 
100-10+1 = 91
91   SUM= (91/2)*(10+100)   = 91*55= 
91*55 = 5_005
5005   Hence, answer 5005
Answer: C
How many three digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 11?  Select
A) 14 B) 16 C) 18 D) 20 E) 22

Solution: A number is divisible by 11 when Difference of Sums of even place digits and odd place digits is either zero or a multiple of 11.   i.e. a 3-Digit Number abc will be divisible by 11 if (a+c) - b = 0 or multiple of 11   @b=1, a+c should be 1 or 12 i.e. (a,c) can be (5, 7), (7, 5) --- 2 cases   @b=2, a+c should be 2 or 13 i.e. (a,c) can be (6, 7), (7, 6) ---- 2 cases   @b=3, a+c should be 3 or 14 i.e. (a,c) can be (1, 2), (2, 1) ---- 2 cases   @b=4, a+c should be 4 or 15 i.e. (a,c) can be (1, 3), (3, 1) ---- 2 cases   @b=5, a+c should be 5 or 16 i.e. (a,c) can be (1, 4), (2, 3), (3, 2), (4, 1) ---- 4 cases   @b=6, a+c should be 6 or 17 i.e. (a,c) can be (1, 5), (2, 4), (4, 2), (5, 1) ---- 4 cases   @b=7, a+c should be 7 or 18 i.e. (a,c) can be (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) ---- 6 cases   Total Cases = 2+2+2+2+4+4+6= 
2+2+2+2+4+4+6 = 22
22 cases   Answer: option 22
Answer: E
A boat having a length 5 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is Choose the correct choice:
A) 12 kg
B) 60 kg
C) 72 kg
D) 96 kg
E) None

Solution: Solution   Volume of water displaced	= (5 x 3 x 0.01)m3   = 0.15m3.   Mass of man	=Volume of water displaced ×Density of water   = (0.15×1000) kg   = 150 kg.   Answer None
Answer: E
An article is bought for Rs.800 and sold for Rs.1200, find the loss percent? Choices:
A) 55%  B) 25.25%  C) 33.33%  D) 45%  E) 50%

Solution: 800 ---- 400   400 ---- ? => 50%   Answer: 50%
Answer: E
Average age of 7 members of a family is 29 years. If present age of the youngest member is 5 year, find average age of the remaining members at the time of birth of the youngest member.  Choose one: A) 28 B) 37 C) 29 D) 237 E) 212

Solution: Average age (present) of 7 members = 29 years   5 years ago, average age of 7 members was  29 - 5= 
 29 - 5 = 24
24 years.   Since, the youngest member was not born 5 years ago.   Therefore, Average age of remaining 6 members is increased by 246246= 4 years.   Therefore, 5 years ago, average age of 6 members was  24 + 4= 
 24 + 4 = 28
28 years.   28nswer:28
Answer: A
What is the probability of finding exactly 33 multiples of 3 when 100 consecutive
natural nos are selected?
Choose the correct choice from the following answers:	A) 1/3	B) 2/3	C) 1	D) 2	E) none of these

Solution: out of 3x,3x+1,3x+2 as starting numbers,   Only case when starting no. is 3x we'll get 34 multiples of 3.   ANSWER:2/3
Answer: B
What is the probability that a three digit number is divisible by 7?
Choose the correct choice from the following choices
A) 1/7  B) 127/900  C) 32/225  D) 129/900  E) 1/8

Solution: Total 3 digit integers which are divisible by 7 :     (994-105)/7+1= 
  (994-105)/7+1 = 128
128   The total number of 3 digit integers= (999-100)+1= 
(999-100)+1 = 900
900   The required probability : 128/900= 32/225   answer:32/225.
Answer: C
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:	Choose the correct choice from the following options.
A) 5324  B) 5334  C) 5336  D) 5356  E) 5400

Solution: Divisor = (5 * 46)= 
(5 * 46) = 230
230= 10 * Quotient = Divisor   => Quotient = 230/10= 
230/10 = 23
23   Dividend= (Divisor * Quotient) + Remainder   Dividend = (230 * 23) + 46= 
(230 * 23) + 46 = 5_336
5336.   5336
Answer: C
How much space, in cubic units, is left vacant when maximum number of 5x5x5 cubes are fitted in a rectangular box measuring 10x15x18 ?  Choose the correct answer:
A) 50
B) 150
C) 250
D) 350
E) 450

Solution: No of cubes that can be accommodated in box = (10*15*18)/(5*5*5)   15*10 in numerator can be perfectly divided by 5*5 in denominator.   side with length 18 can't be perfectly divided by 5 and hence is the limiting factor. Closet multiple of 5 less that 18 is 15. so vacant area in cube =   =15*10*(18-15)   =15*10*3= 
15*10*3 = 450
450   Ans - 450
Answer: E
If the wheel is 8 cm then the number of revolutions to cover a distance of 948 cm is?
Choose the correct choice from the following choices.
A) 11	B) 14	C) 14	D) 12	E) 19

Solution: 2 * 22/7 * 8 * x = 948 => x = 18.9   Answer: 19
Answer: E
When toys are grouped into 12 and 18, always 3 toys remain ungrouped. What is the minimum number of toys to be added so that when they are grouped into 7, no toys will remain ungrouped ?  Answers
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: T= 12a+3 = 18b + 3   2a=3b --> min (a,b) = (3,2)   So minimum number of toys --> 12*3+3 = 39   When toys are grouped into 7, 4 will remain ungrouped so in order to make another group of 7 toys -->   7-4   --  12*3+3= 
  --  12*3+3 = 39
39   When toys are grouped into 7, 4 will remain ungrouped so in order to make another group of 7 toys -->    7-4= 
 7-4 = 3
3 toys at least to be added.   ANSWER: 3
Answer: D
The expenditure of a businessman increase consistently by 10% per year. If his present expenditure is Rs. 20000 then what will his expenditure be after 2 years ?  Options.
A) 24500
B) 24400
C) 24300
D) 24200
E) 24100

Solution: Explanation :   Expenditure = 20000 x 1.1 x 1.1 = 24200   Answer : Option 24200
Answer: D
In a 500 m race,the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m.Then,A wins by  Choose the correct choice from the following answers:
A) 60 m B) 40 m C) 20 m D) 10 m E) 50 m

Solution: Solution   To reach the winning post A will have to cover a distance of ( 500 -140)m, i.e,360m.   While A covers 3 m, B covers 4 m.   While A covers 360 m, B covers (4/3 x 360)m =480m   Thus,when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.   ∴ A wins by 20 m.   Answer 20 m
Answer: C
Two pipes A and B can separately fill a cistern in 45 minutes and 60 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 40 minutes. In how much time, the third pipe alone can empty the cistern?
Choose the correct choice from the following:  A) 90 min  B) 100 min  C) 72 min  D) 75 min  E) 130 min

Solution: 1/40-(1/45+1/60)=-1/72   third pipe can empty in 72 minutes   ANSWER:72 min
Answer: C
Which of the following CANNOT be the median W of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?
Choose the correct choice from the following options:	A) (w+x)/2 - 1	B) (w+z)/2	C) (x+y)/2	D) (y+z)/2 -1	E) (w+x+y+z)/4

Solution: Using the properties of consecutive positive integers we could right away eliminate B,C and E.   (B) - The average of first and last terms is the median   (C) - For even number of integers, the median is the average of middle terms   (E) - The average is equal to median if the integers are consecutive   Remaining answer choices are A and D.   For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median W.   (w+x)/2 - 1nswer ((w+x)/2 - 1)
Answer: A
The time it took car P to travel 600 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
Pick one:
A) 40  B) 50  C) 60  D) 70  E) 80

Solution: Let speed of car R be=x   Then speed of car P= x+10   A/Q,   (600/x)-(600/(x+10))=2   Solving for x=50 miles\hr   ANSWER:50
Answer: B
Carrie likes to buy t-shirts at the local clothing store. They cost $8.75 each. One day, she bought 18 t-shirts. How much money did she spend?
Choose the correct choice from the following options:
A) $150
B) $70
C) $200
D) $171.6
E) $190

Solution: $8.75*18=$70. Answer is $70.
Answer: B
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
Choose the correct option
A) Rs.122  B) Rs.129  C) Rs.125  D) Rs.120  E) Rs.121

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 1/2 = Rs.125   Answer:Rs.125
Answer: C
The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. Choose the correct answer.
A) Rs.17277 B) Rs.17000 C) Rs.17287 D) Rs.172827 E) Rs.172711

Solution: Explanation:   The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year   So rate of the interest = (100 * 1530)/ (5100 * 1)= 
(100 * 1530)/ (5100 * 1) = 30
30% p.a.   So P= (100 * 10200)/ (30 * 2) = Rs.17000   Answer: Rs.17000
Answer: B
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B? Choose the correct choice from the following:
A) 1 years B) 20 years C) 10 years D) 15 years E) 25 years

Solution: Explanation:   Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25   x = 5.   Hence, B's age = 2x = 10 years.   Answer: 10 years
Answer: C
There are 40 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
Pick one:
A) 6  B) 12  C) 20  D) 24  E) 27

Solution: 40*2/3 *3/4= 
40*2/3 *3/4 = 20
20   Answer: 20
Answer: C
A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent? Choose the correct answer: A) 28% B) 25% C) 11.11% D) 28% E) 55%

Solution: 900 --- 100   100 --- ? => 11.11%   Answer: 11.11%
Answer: C
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 6 inches, then what is the maximum number of soap boxes that can be placed in each carton?
Choose the correct choice from the following options
A) 210  B) 252  C) 250  D) 300  E) 420

Solution: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers   Dimensions of the box =25*42*60   Dimensions of the soap = 6*6*7   placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60   we get = 5x5x10 = 250   so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number   the answer is (250)
Answer: C
If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 4y) is odd
II. xy^2 is an even negative integer
III. (y^2 - x) is an odd negative integer  Options.
A) (3X-4Y) IS ODD TRUE  B) II only  C) I and II  D) I and III  E) II and III

Solution: If x is an odd negative integer and y is an even integer, which of the following statements must be true?   I. (3x - 4y) is odd   3x - is always negative and odd   2y - can be 0, when y=0, or always even integer (positivie or negative)   odd integer +/- even integer = always odd   I statement is always true   II. xy^2 is an even negative integer   y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true   III. (y^2 - x) is an odd negative integer   y can be 0 => -x will be positive => III statement is not true   basing on above, only I statement will always be true   answer is (3X-4Y) IS ODD TRUE
Answer: A
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Choose the correct choice from the following choices.
A) 100 B) 150 C) 140 D) 130 E) 123

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x = 150 m.   Answer: Option 150
Answer: B
Two trains are moving at 50 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? Pick
A) 7 1/2 sec  B) 2 sec  C) 3 sec  D) 5 sec  E) 7 sec

Solution: 70 + 50= 
70 + 50 = 120
120 * 5/18= 100/3 mps   D = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 3/100 = 15/2 = 7 Â½ sec   7 1/2 secNSWER 7 1/2 sec
Answer: A
The jogging track in a sports complex is 900 m in circumference. Sunil and Sachin start from the same point and walk in opposite directions at 5.4 km/hr and 3.6km/hr respectively. They will meet for the first time in?  Choose the correct choice from the following answers
A) 2.98 min B) 5.7 min C) 6.0 min D) 6.3 min E) 7.2 min

Solution: Clearly, the two will meet when they are 900m apart.   To be (5.4+ 3.6)= 
(5.4+ 3.6) = 9
9.0 km apart, they take 1 hour.   To be 900 m apart, they take= (900/9000 * 60)= 
(900/9000 * 60) = 6
6.00 min.   Answer: 6.0 min
Answer: C
Which of the following is an integer?
I. 11! / 6!
II. 11! / 8!
III. 11! / 7!5!
Pick one.
A) I only B) II only C) III only D) I and II only E) I, II and III

Solution: 11!/6! = 11*10*9*8*7 which is an integer.   11!/8! = 11*10*9 which is an integer.   11!/7!5! = 11*10*9*8 / 5*4*3*2 = 11*3*2 which is an integer.   The answer is I, II and III.
Answer: E
A trainer is standing in one corner of a square ground of side 25m. His voice can be heard upto 140m. Find the area of the ground in which his voice can be heard?	Pick one
A) 12300
B) 14500
C) 15400
D) 16700
E) 18200

Solution: Area covered by goat = Pi*r^2/4 ( here we divide by 4 because the trainer is standing in a corner of the ground and only in 1/4 part , the voice can be heard)   where r= 14 m = length reaching the voice   So area = (22/7)*140*140/4= 
(22/7)*140*140/4 = 15_400
15400 sq m   answer :15400
Answer: C
Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?	Choose the correct choice from the following answers.
A) 17  B) 16  C) 18  D) 77  E) 11

Solution: Explanation:   Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9   => 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18   => x = 18.   Answer: 18
Answer: C
What is the difference between the compound interests on Rs. 5000 for 11â„2 years at 4% per annum compounded yearly and half-yearly?	Pick.
A) 2.04  B) 4.8  C) 3.06  D) 8.3  E) 3.5

Solution: compunded yearly   = 5000*(1+4/100)*(1+1/2*4/100)= 
5000*(1+4/100)*(1+1/2*4/100) = 5_304
5304   compound interest for 1 1/2 years when interest=>(5304-5000)   =>P(1+(R/2)/100)^2T = 5000(1+(4/2)/100)2*3/2 = 5000(1+2/100)^3   =5000(102/100)^3 = 5306.04   1 1/2 Years half yearly = (5306.04 - 5000)=> 2.04   2.04NSWER 2.04
Answer: A
A water tank is four-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely? Choose the most appropriate option.
A) 12 min.to empty  B) 9 min.to empty  C) 5 min.to empty  D) 4 min.to empty  E) 7 min.to empty

Solution: Explanation:   Clearly,pipe B is faster than pipe A and so,the tank will be emptied.   part to be emptied = 4/5   part emptied by (12 min.to empty+B) in 1 minute=(1/6-1/10)=1/15   so, the tank will be emptied in 12 min   12 min.to emptynswer: 12 min.to empty
Answer: A
Which of these lines in the xy-plane does not contain any point with two negative coordinates?	Answers.
A) y = 5x
B) y = x + 6
C) y = x^2 - 7
D) y = x^3 + 2x
E) y = 3x^6

Solution: 3x^6 is 0 when x is 0 and positive for all other values of x.   The answer is y = 3x^6.
Answer: E
A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
Options
A) 1977
B) 1893
C) 1979
D) 1900
E) 1278

Solution: 2000 ---- 54   2000 ---- 39   x ----- 20   x*20 = 2000*39   x = 3900   2000   -------   1900   Answer: 1900
Answer: D
There are 4 books on a shelf, of which 3 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?	Select.
A) a) 40	B) b) 45	C) c) 50	D) d) 55	E) e) 111

Solution: approach 1   at-least 1 paper back = total - no paper back   9c4-6c4 = 111   approach 2   at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back   = 3c1*6c3+3c2*6c2 + 3c3*6c1 = 111   Answer is e) 111
Answer: E
For one toss of a certain coin, the probability that the outcome is heads is 0.8. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times? Choose the correct choice from the following:
A) (0.8)^5  B) 2(0.8)^4  C) 3(0.8)^4  D) 4(0.8)^4(0.2) + (0.8)^5  E) 5(0.8)^4(0.2) + (0.8)^5

Solution: P(5 heads) = (0.8)^5   There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH   P(4 heads) = 5*(0.8)^4(0.2)   The answer is 5(0.8)^4(0.2) + (0.8)^5.
Answer: E
The true discount on Rs.2562 due 4 months hence is Rs.122.The rate % is?	Choose the correct option.
A) 12%
B) 13 (1/3)%
C) 15%
D) 14%
E) 13%

Solution: Explanation:   P.W = Rs.( 2562 - 122) = Rs.2440   S.I on Rs.2440 for 4 months is Rs.122   Rate = [100X 122/2440X1/3 ] % = 15%   12%nswer: 12%
Answer: A
Find the compound interest on $1200 for 5 years at 20% p.a. if CI is component yearly?  Choices:
A) $120	B) $150	C) $1786	D) $250	E) $300

Solution: A = P(1 + R/100)^T   = 1200(1 + 20/100)^5   =$2986   $1786I = $1786   Answer is $1786
Answer: C