MU-NLPC/Calc-aqua_rat huggingface dataset:
Rs. 925 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 925 become in 3 years ?
Choose the correct choice from the following choices
A) Rs. 1020.80	B) Rs. 1025	C) Rs. 1067	D) Data inadequate	E) None of these

Solution: Solution   S.I. = Rs.(956-925 )=Rs.31   Rate = (100x31/925x3) =124/111%   New rate = (124/111 +4)% = 568/111%   New S.I. = Rs.(925 x 568/111 x 3/100) Rs. 142   ∴ New amount = Rs.(925+142)= Rs. 1067.   Answer Rs. 1067
Answer: C
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x?	Choices:	A) 6	B) 7	C) 8	D) 9	E) 10

Solution: x<y<z and="" be="" can="" closest="" could="" each="" even="" find="" for="" if="" is="" least="" minimum="" need="" number="" number,="" odd="" other.="" possible="" some="" that="" the="" then="" to="" value="" values="" we="" what="" x="" y-x="" z="" z-x;="" z.="">5; y>x+5; minimum value for y</y<z>=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]   Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. 9ifference between two odd numbers is 2]   Q=z-x = x+9-x= 9   Ans:9
Answer: D
Find large number from below question The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder	Select the correct option:
A) 1254
B) 1376
C) 1659
D) 1555
E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1385).   x + 1385 = 6x + 15   5x = 1370   x = 274   Large number = 274+1385= 
274+1385 = 1_659
1659   1659
Answer: C
A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, 2^(43112609) - 1, is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product? Choices: A) 2 B) 3 C) 4 D) 6 E) 8

Solution: First of all, think which is the smallest Mersenne prime?   The smallest prime 1 less than a power of 2 is 3.   We need the last digit of 2^{43112609} - 1. What will be the last digit of 2^{43112609}?   Recall cyclicity of last digits. After every 4 powers, the last digit repeats itself. Let's look at the last digits of powers of 2.   2^1 = 2   2^2 = 4   2^3 = 8   2^4 = 6   2^5 = 2   2^6 = 4   and so on...   When 43112609 is divided by 4, you get remainder 1 (divide just the last two digits by 4. Whatever remainder you get will be the remainder when you divide the actual number by 4)   So the last digit of 2^{43112609} is 2   Last digit of 2^{43112609} - 1 is 1   Product of the last digits is 1*3= 
1*3 = 3
3   Answer (3)
Answer: B
Two trains of length 200 m and 300 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other? Choose the correct choice from the following options.
A) 87/7 sec	B) 20 sec	C) 80/9 sec	D) 80/5 sec	E) 20/7 sec

Solution: Relative speed = (36 + 72)* 5/18 = 6 * 5= 
6 * 5 = 30
30 mps.   The time required= d/s = (100 + 200 + 300)/30   = 600/30= 
600/30 = 20
20 sec.   Answer: 20 sec
Answer: B
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?	Options:
A) 0.5919
B) P(E)=0.5904
C) 0.5929
D) 0.5928
E) 0.594

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904   Answer: P(E)=0.5904
Answer: B
There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
Choose the correct choice from the following choices.
A) 1/5	B) 2/3	C) 3/5	D) 3/7	E) 3/8

Solution: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5   1/5
Answer: A
If the average cost of a house was $50,000 in 1960 and was x in 2005, what was the average increase in home prices per year over this period?  Choose the most appropriate option: A) A)(x+50,000)/40 B) E)x/40 C) C)(50,000/40)+x D) D)(50,000-x)/40 E) B)(x-50,000)/45

Solution: Average house price in 2005: x   Average house price in 1965: 50,000   2005-1960= 
2005-1960 = 45
45   Average increase per year: (x-50,000)/45   Answer is B)x/40
Answer: E
The total of the ages of Amar, Akbar and Anthony is 50 years. What was the total of their ages three years ago ?  Choose one:
A) 48 years B) 42 years C) 41 years D) 47 years E) 45 years

Solution: Explanation:   Required sum = (50 - 3 x 3) years = (50 - 9)= 
(50 - 9) = 41
41 years.   Answer: Option 41 years
Answer: C
Vijay bought 160 shirts at the rate of Rs. 200 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options
A) s.225 B) s.288 C) s.485 D) s.255 E) s.282

Solution: Total CP per shirt = 200 + 1400/160 + 1.75 + 320/160 = Rs. 212.5   SP = CP[(100 + profit%)/100]   = 212.5 * [(100 + 20)/100] = Rs.255.   Answer:s.255
Answer: D
In an examination, 300 students appeared. Out of these students; 30 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.  Choose the correct choice from the following options:
A) 33
B) 37
C) 54
D) 99
E) 48

Solution: The number of students with first division = 30 % of 300 = 30/100 × 300 = 9000/100= 
9000/100 = 90
90   And, the number of students with second division= 54 % of 300   = 54/100 × 300   =16200/100= 
16200/100 = 162
162   Therefore, the number of students who just passed= 300 – (90 + 162) = 48   Answer:48
Answer: E
A rock is dropped into a well and the distance traveled is 16 t 2 feet, where t is the time. If the water splash is heard 3 seconds after the rock was dropped, and that the speed of sound is 1100 ft / sec, approximate the height of the well	Select the correct option
A) 134.8 feet B) 136.2 feet C) 132.7 feet D) 132.2 feet E) 115.3 feet

Solution: Let T1 be the time it takes the rock to reach the bottom of the well. If H is the height of the well, we can write   H = 16 T1 2   Let T2 be the time it takes sound wave to reach the top of the well. we can write   H = 1100 T2   The relationship between T1 and T2 is   T1 + T2 = 3   Eliminate H and combine the equations H  1 +  2= 
 1 +  2 = 3
3   Eliminate H and combine the equations H= 16 T1 2 and H = 1100 T2 to obtain   16 T1 2 = 1100 T2   We now substitute T2 by 3 - T1 in the above equation   16 T1 2 = 1100 (3 - T1)   The above is a quadratic equation that may be written as   16 T1 2 + 1100 T1 - 3300 = 0   The above equations has two solutions and only one of them is positive and is given by   T1 = 2.88 seconds (2 decimal places)   We now calculate the height H of the well   H = 16 T1 2 = 16 (2.88) 2 = 132.7 feet   Answer 132.7 feet
Answer: C
If (10^4 * 3.456789)^10 is written as a single term, how many digits would be to the right of the decimal place?	Options:
A) 12 B) 16 C) 20 D) 32 E) 48

Solution: 3.456789^10 has   6*10= 
  6*10 = 60
60 decimal places.   10^40 moves the decimal place to the right 40 places.   (10^4 * 3.456789)^10 has   60-40= 
  60-40 = 20
20 digits after the decimal point.   The answer is 20.
Answer: C
If 1 is added to the denominator of fraction, the fraction becomes
1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is	Choose the correct choice from the following choices: A) 4/7 B) 5/9 C) 2/3 D) 10/11 E) None of these

Solution: Explanation:   Let the required fraction be a/b. Then   ⇒a/b+1=1/2⇒2a–b=1 ---- (1)   ⇒a+1/b=1⇒a–b=–1⇒a–b=–1 ------- (2)   Solving (1) & (2) we get a = 2, b=3   Fraction = a/b=2/3   2/3orrect Option: 2/3
Answer: C
5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?  Options:
A) 6:9
B) 6:89
C) 6:0
D) 6:5
E) 6:1

Solution: 5M + 12B ----- 4 days   7M + 6B ------- 5 days   20M + 48B = 35M + 30B   18B = 15M => 5M = 6B   M: B = 6:5   Answer: 6:5
Answer: D
a lady's age is between 50 and 70.each of her sons has many sons as his
brothers. the sum of the sons and grandsons in the lady's age. what is her age?	Choose the correct option:  A) 61  B) 62  C) 63  D) 64  E) 65

Solution: Let assume Lady has 'N' children.   Each child have (N-1) children. (Grandsons for that lady).   S0, total children = N+(N*(N-1))   By, putting N=6, we get   6+(6*(6-1))= 
  6+(6*(6-1)) = 36
36 childrens.   By, Putting N=7, we get   7+(7*(7-1))= 
  7+(7*(7-1)) = 49
49 childrens.   By, putting N=8, we get   8+(8*(8-1))= 
  8+(8*(8-1)) = 64
64 childrens.   By, putting N=9, we get   9+(9*(9-1))= 
  9+(9*(9-1)) = 81
81 childrens.   Here, Lady's age between 50 to 70.   So, answer is 64.   ANSWER:64
Answer: D
If five persons sit in a row, then the probability that three particular persons are always together is?  Pick:
A) 3/5  B) 3/4  C) 1/9  D) 1/6  E) 3/10

Solution: Five persons can be arranged in a row in 5! ways.   Treat the three persons to sit together as one unit then there three persons and they can be arranged in 3! ways.   Again three persons can be arranged among them selves in 3! ways.   Favourable outcomes = 3!3!   Required probability = 3!3!/5! = 3/10   Answer:3/10
Answer: E
If a,b,c,d,e are five consecutive odd numbers, their average is :
Choose the correct choice from the following:	A) 22	B) 77	C) 288	D) 22	E) 20

Solution: Correct Option: D   Explanation:   If the first number is a, then the remaining numbers a a +2, a+4, a + 6, a + 8   22verage : = (a+(a+2)+(a+4)+(a+6)+(a+8)5)=(a+4)   22nswer:22
Answer: A
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in? Choose one:  A) 7 hrs  B) 8 hrs  C) 10 hrs  D) 12 hrs  E) 14 hrs

Solution: Work done by the leak in 1 hour = 1	-	3 =	1	.   2	7	14   Leak will empty the tank in 14 hrs.   14 hrs)
Answer: E
A password of a computer used five digits where they are from 0 and 9. What is the probability that the first digit of the password is a 0 and the second digit is even ?
Select
A) 1/10
B) 1/15
C) 1/20
D) 1/100
E) 1/200

Solution: There is one possibility out of ten that the first digit is zero, and five possibilities out of ten that the second digit is even. We don't care about the remaining digits, so the overall probability is 1/10 * 5/10 or 1/20 or answer 1/20.
Answer: C
Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 56 people bought tickets to the concert, what was the total revenue from ticket sales?  Choose the correct choice from the following choices
A) $600
B) $740
C) $850
D) $980
E) $1,140

Solution: Price of 1 ticket = 20$   Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )   = 10 * 12= 
10 * 12 = 120
120   Revenue generated from sales of next 20 tickets= 20 *(85/100 * 20 )   =20*17= 
20*17 = 340
340   Revenue generated from sales of last 26 tickets= 20 * 26= 
20 * 26 = 520
520   Revenue generated from sales of 56 tickets= 120 + 340 + 520= 
120 + 340 + 520 = 980
980 $   Answer $980
Answer: D
There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 5 days more?	Pick.
A) 2280	B) 2240	C) 2299	D) 2288	E) 2266

Solution: 760 ---- 22   760 ---- 20   x ----- 5   x*5 = 760*20   x = 3040   760   -------   2280   2280nswer: 2280
Answer: A
If xyz represents a positive three-digit number, where x, y and z are one-digit integers, which of the following CANNOT be true? Choose the correct option
A) y – x - z = 9 B) x – y - z = 9 C) x + y + z = 9 D) xyz = 9 E) x/y/z = 9

Solution: The (hundreds place digit, x) cannot be zero, but (tens and ones place digits; y and z) can be zero.   y – x - z = 9 is NOT possible   B is possible   C is possible   D is possible   E is possible   y – x - z = 9nswer: y – x - z = 9
Answer: A
The denominator of a fraction is 7 greater than the numerator. If the numerator and the denominator are increased by 4, the resulting fraction is equal to 5â„6. What is the value of the original fraction?
Select the correct option:
A) 23/30 B) 25/32 C) 31/38 D) 37/44 E) 47/54

Solution: Let the numerator be x.   Then the denominator is x+7.   x+4 / x+11 = 5/6.   6x+24=5x+55.   x=31.   The original fraction is 31/38.   The answer is 31/38.
Answer: C
A single discount equivalent to the discount series of 20%, 10% and 5% is?
Options:
A) 31.0 B) 31.2 C) 31.6 D) 31.3 E) 31.1

Solution: 100*(80/100)*(90/100)*(95/100)= 
100*(80/100)*(90/100)*(95/100) = 342/5 = around 68.4
68.4   100 - 68.4= 
100 - 68.4 = 31.6
31.6   Answer: 31.6
Answer: C
The original price of a car was $22,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 10%. After a week, the car had not sold, so the owner discounted the new price by 10%, and the car was finally sold. What price was the car sold for?	Choose the correct choice from the following answers:
A) $21,660	B) $21,700	C) $21,740	D) $21,780	E) $21,820

Solution: The car was sold for (0.9)(1.1)($22,000)=$21,780.   The answer is $21,780.
Answer: D
Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?  Choose the correct answer:
A) s.16000 B) s.20000 C) s.24000 D) s.Rs 28000 E) s.29000

Solution: 3:1   2:1   ------   6:1   1 ----- 4000   7 ----- ? => Rs.28,000   ANSWER: s.Rs 28000
Answer: D
A train 640 m in length crosses a telegraph post in 16 seconds. The speed of the train is?	Choose the correct answer:
A) 22 kmph	B) 77 kmph	C) 144 kmph	D) 71 kmph	E) 88 kmph

Solution: S = 640/16 * 18/5= 
640/16 * 18/5 = 144
144 kmph   Answer:144 kmph
Answer: C
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?  Choose one:  A) 291  B) 178  C) 150  D) 287  E) 182

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: 150
Answer: C
Find the next number in the series ?
2 3/4 5/7 7/10 11/13 13/16 ? Pick one
A) 14/19  B) 15/19  C) 17/19  D) 16/19  E) 18/19

Solution: Solution:   17/19   series is 2/1 3/4 5/7 7/10 11/13 13/16   Numerator is prime number series 2-3-5-7-11-13-17   and Denominator is +3 series 1-4-7-10-13-16-19   Answer 17/19
Answer: C
A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 4 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?	Pick
A) 44/5  B) 13  C) 17  D) 21  E) 23

Solution: Let Bucket 44/5 be 44/5 and Bucket B be B   Scenario 1   44/5-4 = 1/3 (B+4) ----> 344/5-12 =B+4   Scenario 2   B-4 = 1/2 (44/5+4) -----> 2B-8 = 44/5+4   From Scenario 1, B = 344/5-16   Substitute B with this information in Stmt 2   2 (344/5-16) -8 = 44/5+4 ------> 644/5 -32-8 = 44/5+4 ------> 644/5- 44/5 = 40+4 ---> 544/5= 44   44/5= 44/5, 44/5nswer choice 44/5
Answer: A
70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 24.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?  Answers.
A) one  B) two  C) three  D) four  E) five

Solution: The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.   it is easier to group numbers:  130*3= 
 130*3 = 390
390; 105*2=210; 75+85=160; 70+80=150; 90;   Next stage combine results, again using more convenient ways to calculate: 390+210= 
390+210 = 600
600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-24,4=75,6. There are only two numbers below 75,6. The answer is two
Answer: B
If p^2 – 13p + 40 = l, and p is a positive integer between 1 and 10, inclusive, what is the probability that l < 0?  Select:
A) 1/10	B) 1/5	C) 2/5	D) 3/5	E) 3/10

Solution: p2 – 13p + 40 = l   so (p – 8)(p – 5) = l   For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.   The correct answer is 1/5.
Answer: B
The number that does not have a reciprocal is ____________.	Select.
A) 0 B) 1 C) 2 D) 3 E) -1

Solution: O does not have any reciprocal   as 1/0 is not defined 0NSWER:0
Answer: A
One packet of flower seeds was enough to just fill the area of the smaller garden in #3. How
many packets of seed are needed for the larger garden? Round each answer to the nearest square
foot before continuing. Pick one.
A) 1 seed packet	B) 2 seed packets	C) 3 seed packets	D) 4 seed packets	E) 5 seed packets

Solution: 3.14 x 32 = 28.26 sq. ft. area of small garden   28 sq. ft. rounded   3.14 x 62 = 113.04 sq. ft. area of large garden   113 sq. ft. rounded   113 ÷ 28 = 4.04 or 4 seed packets (rounded)   correct answer 4 seed packets
Answer: D
Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?	Pick one.
A) 6.24	B) 8	C) 10	D) 15	E) 24

Solution: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9   New time in minutes to cross 10 miles stretch = 10*60/35 = 10*12/7 = 17.14   Time difference = 6.24   6.24ns:6.24
Answer: A
How many seconds does a train 125 meters long, traveling at 72 km/h, take to completely cross a bridge of 205 meters in length?	Options:
A) 12.5  B) 14.5  C) 16.5  D) 18.5  E) 20.5

Solution: 72 km/h = 72000/3600= 
72000/3600 = 20
20 m/s   Time= 330 / 20= 
330 / 20 = 33/2 = around 16.5
16.5 seconds   The answer is 16.5.
Answer: C
If f(x) = k(x - k) and k is a constant, what is the value of f(5) - f(2), in terms of k?	Choose the correct choice from the following options.
A) 3k  B) k  C) 7k - 1  D) k^2 + k  E) k^2 - k

Solution: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(5) and f(2):   f(5) = k(5) - k^2 = 5k - k^2   f(2) = 2k - k^2   f(5)-f(2)= 3k... 3knswer 3k (5)- (2)= 
 (5)- (2) = 3
3k... 3knswer 3k
Answer: A
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 70 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct choice from the following choices
A) 12 sec	B) 24 sec	C) 36 sec	D) 60 sec	E) 62 sec

Solution: Relative speed = 70 + 30= 
70 + 30 = 100
100 km/hr.   100 * 5/18= 250/9 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 9/250= 
1000 * 9/250 = 36
36 sec.   ANSWER:36 sec
Answer: C
I. a2 - 9a + 20 = 0,
II. 2b2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?	Choose the correct choice from the following answers
A) If a < b
B) If a ≤ b
C) If the relationship between a and b cannot be established
D) If a > b
E) If a ≥ b

Solution: I. (a - 5)(a - 4) = 0   => a = 5, 4   II. (2b + 3)(b - 4) = 0   => b = 4, -3/2 => a ≥ b   ANSWIf a ≥ bR:If a ≥ b
Answer: E
If a number p is prime, and 2p+3 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
Choices
A) 1	B) 3	C) 5	D) 7	E) 9

Solution: 1/5 = 0.2.. (a repeating pattern one digit long)   1
Answer: A
Find the odd man out. 15, 25, 30, 51, 85, 90, 115  Choose the correct answer:
A) 15  B) 25  C) 51  D) 90  E) 115

Solution: Explanation :   All except 51 are multiples of 5   Answer : Option 51
Answer: C
Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Choose the correct choice from the following answers:
A) 1235 B) 1456 C) 1567 D) 1678 E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
Plane leaves from Chelsea every 40 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m.
At what time air hostess convey this information to Frank Lampard?	Pick:
A) 5:35 p.m
B) 6:45 p.m
C) 7:35 p.m
D) 8:35 p.m
E) 9:35 p.m

Solution: Solution:   Explanation:   Time of Frank Lampard last missed plane = 7:00 p.m - 40 min = 6:20 p.m   As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:20 p.m + 25 min = 6:45 p.m   Answer 6:45 p.m
Answer: B
100 identical coins each with probability 'pp' showing up heads & tossed. If 0<p<10<p<1 and the probabilityof heads showing on 50coins is equal tothat of heads on 51 coins, then the value of pp is?  Pick:
A) 50/107  B) 53/103  C) 51/101  D) 65/101  E) 89/101

Solution: Let aa be the number of coins showing heads   Then, P(A=50)=P(A=51)P(A=50)=P(A=51)   ⇒10051/10150×P50×(1−P)50⇒10051/10151×P51×(1−P)49⇒10051/10150×P51×(1−P)50=10051/10151×P⇒51(1âˆ′P)=50P⇒P=51/101   51/101
Answer: C
All of the stocks on the over-the-counter market are designated by either a 7-letter or a 6-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Choose the most appropriate option
A) a. 2(26^5) B) b. 26(26^4) C) c. 27(26^4) D) d. 27(26^6) E) e. 27(26^5)

Solution: no of different stocks for 7-letter code = 26^7   no of different stocks for 6-letter code = 26^6   total = 26^7 + 26^6 = 26^6(26+1) = 27(26^6)   [Reveal]Spoiler:   Option d. 27(26^6)
Answer: D
A certain junior class has 1,000 students and a certain senior class has 400 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?	Pick one:	A) 3/20,000	B) 1/3,600	C) 9/2,000	D) 1/60	E) 1/15

Solution: Total number of ways of choosing one student from each group is = 400 * 1000   Number of cases in which a sibling pair will be got is = 60   Thus the probability that the 2 students selected will be a sibling pair is   = 60 /(400 * 1000)   = 3/20,000   3/20,000
Answer: A
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?  Choices:
A) Rs.24098
B) Rs.24090
C) Rs.24000
D) Rs.24006
E) Rs.24202

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 52000   Share of B = 6/13 (52000)   = Rs.24000   Answer: Rs.24000
Answer: C