MU-NLPC/Calc-aqua_rat huggingface dataset:
Here is a simple arithmetical puzzle in his own flowery, poetical language.
If one-fifth of a hive of bees flew to the badamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbour, and one bee continued to fly about, attracted on each side by the fragrant Ketaki and Malati, what was the total number of bees?  Choose the correct answer.
A) 11 B) 15 C) 18 D) 17 E) 19

Solution: 15   15   The number of bees was 15
Answer: B
Machine A and machine R are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine R. Machine R produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?	Choose one: A) 6 B) 6.6 C) 60 D) 100 E) 110

Solution: [Reveal]Spoiler:   TimeR: 660/x   Time6: [660/x+10]   660/x = [660/x+10] *110/100   660/x =66*11/x+10   660x+10= 66*11*x   660x +6600 = 66*11*x   x= 100   plug in back to time6   660/100+10 => 660/110= 
660/110 = 6
6
Answer: A
How many positive even integers less than 100 contain digits 3 or 9? Choose the most appropriate option:	A) 16	B) 17	C) 18	D) 19	E) 10

Solution: Two digit numbers:   3 at tens place: 30,32,34,36,38   9 at tens place: 90,92,94,96,98   If 3 and 7 is at units place, the number cant be even   Total:5+5= 
5+5 = 10
10   Answer 10
Answer: E
For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 2| + |-b| + |b – a| + |ab| =
Select: A) -ab + 3 B) ab + 2b + 2 C) ab + 2b – 2a – 3 D) -ab + 2b + 3 E) ab + 3

Solution: Observation-1: |a – b| = b – a   which is possible only when signs of a and b are Same   Since Given a > 0   so we figure out that a and b are both positive   Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a   Now you may choose the values of a and b based on above observations   e.g. b = 2 and a=1 and check the value of given functions and options   |a + 2| + |-b| + |b – a| + |ab| = |1 + 2| + |-2| + |2 – 1| + |1*2| = 8   -ab + 3 = -1*2+3= 
-1*2+3 = 1
1   ab + 2b + 2= 1*2+4+2= 
1*2+4+2 = 8
8   ab + 2b – 2a – 3=1*2+2*2-2*1-3= 
1*2+2*2-2*1-3 = 1
1   -ab + 2b + 3=5   ab + 3+ 2  + 3= 
+ 2  + 3 = 5
5   ab + 3=5   Answer : ab + 2b + 2
Answer: B
Rathi took a loan for 6 years at the rate of 5% per annum on Simple Interest, If the total interest paid was Rs. 1230, Find the principal amount?
Select
A) 4000	B) 3500	C) 3100	D) 4100	E) 5000

Solution: P = SI * 100/R*T   P = 1230*100/6*5==>4100   ANSWER 4100
Answer: D
Winson will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
Select the correct option.
A) 5
B) 6
C) 9
D) 24
E) 26

Solution: Winson will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are   0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1= 
  0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5
5 cases...5
Answer: A
Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
Choose the correct choice:
A) 130
B) 140
C) 150
D) 220
E) 280

Solution: Let the amount paid to A per week = x   and the amount paid to B per week = y   Then x + y = 550   But x = 150% of y = 150y/100 = 15y/10   ∴15y/10 + y = 550   ⇒ y[15/10 + 1] = 550   ⇒ 25y/10 = 550   ⇒ 25y = 5500   ⇒ y = 5500/25 =Rs.220   220)
Answer: D
A military garrison in a wild frontier has 600 men who have provisions to last 22 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?	Pick one
A) 13 1/3
B) 12 1/3
C) 10 2/3
D) 12 1/2
E) 12 3/4

Solution: Total provisions=600*22*7= 
600*22*7 = 92_400
92400   Provisions used for in 6 weeks=6*7*600= 
6*7*600 = 25_200
25200   remaining provisions=67200   remaining provisions need to be split between 900(600+300) people.   Number of provisions per person= 67200/900   we need to find the answer in terms of weeks=(67200/900)/7=10 2/3   Answer:10 2/3
Answer: C
I sold a book at a profit of 10%. Had I sold it for $110 more, 15% would have been gained. Find the cost price?	Choose the correct choice:
A) $2000  B) $2200  C) $3000  D) $3120  E) $1540

Solution: 115% of cost - 110% of cost = $110   5% of cost = $110   cost = 110*100/5= 
110*100/5 = 2_200
$2200   Answer is $2200
Answer: B
eleven books,consisting of 5 engineering books , 4 maths books,2 physics books are arranged in a shelf at random .what is the probability that books of each kind are all together?
Choose the correct choice from the following:
A) 0.001443
B) 0.002443
C) 0.003443
D) 0.004443
E) 0.005443

Solution: 3 lots can be arranged in 5!x3!x4!x2!   total arrangements possible= 11!   hence probability of the same=(5!x3!x4!x2!)/11!=0.001443   0.001443NSWER:0.001443
Answer: A
If the probability of rain on any given day in City X is 50%, what is probability that it rains on exactly 3 days in a 4 day period?  Choose the correct choice from the following choices: A) 1/2 B) 1/4 C) 1/8 D) 1/16 E) 3/16

Solution: One possible way is rain-rain-rain-no rain.   The probability of this is 1/2*1/2*1/2*1/2 = 1/16   The number of possible ways is 4C3 = 4, so we multiply this by 4.   P(rain on exactly 3 days) = 4*1/16 = 4/16 = 1/4   The answer is 1/4.
Answer: B
An escalator moves towards the top level at the rate of 11 ft.sec and its length is 140 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.  Select.
A) 14 sec
B) 10 sec
C) 12 sec
D) 8 sec
E) 9 sec

Solution: Time taken to cover the entire length = tot.dist/resultant speed   = 140/ (11+3)= 
140/ (11+3) = 10
10sec   ANSWER:10 sec
Answer: B
A seller has 1000 kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is? Choose one
A) 350 kg
B) 360 kg
C) 400 kg
D) 600 kg
E) 700 kg

Solution: By rule of alligation,   Profit% by selling 1st part Profit% by selling 2nd part   8 18   Net % profit   14   18-14= 
18-14 = 4
4 14-8=6   => Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3   Total quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit)   =1000×35   = 600 kg   600 kg
Answer: D
A bullet train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform? Choose the correct choice from the following
A) 240 m  B) 180 m  C) 260 m  D) 224 m  E) 239 m

Solution: A   180 M   Speed = 54 x 5/18 = 15 m/s   Length of the bullet train = (15 x 24)m = 360 m.   Let the length of the platform be x metres.   Then, (x + 360)/36 = 15   --> x + 360 = 540   x = 180m. 180 m
Answer: B
A and B tanks are there. 1/8th of the tank B is filled in 22Hrs. What is time to fill the full tank
Choose the correct choice from the following: A) 175 B) 176 C) 177 D) 178 E) 179

Solution: 1/8th = 22 hrs   therefore entire tank is 8 x 22.   176hrs   Full tank ll be filled in 176 hrs   ANSWER:176
Answer: B
Jerry is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 mint , and the remainder an even mixture of salt, pepper and sugar. If Jerry accidentally doubles the mint and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
Pick one
A) 15/29	B) 5/8	C) 5/16	D) 1/2	E) 13/27

Solution: Olive oil = 5/8 = 15/24 --> 15 parts out of 24;   mint = 1/4 = 6/24 --> 6 parts out of 24;   Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;   If mint = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0= 
15+12+1+1+0 = 29
29 parts out of which 15 parts are olive oil --> proportion= 15/29.   15/29nswer: 15/29.
Answer: A
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?	Choices
A) 0.15  B) 0.2  C) 0.25  D) 0.3  E) 0.33

Solution: The total number of pairs possible is 4*5= 
4*5 = 20
20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.   Answer: 0.2.
Answer: B
If CRY is coded as MRYC then how will GET be coded?  Choose the correct choice from the following answers:
A) MTEG B) MGET C) MEGT D) METG E) None of these

Solution: The letters of word (1)(2)(3) is written by prefixing M and ordering letters   (2)(3)(1)   So GET= METG   ANSWER:METG
Answer: D
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?  Choices: A) 77 cm2 B) 66 cm2 C) 54 cm2 D) 44 cm2 E) 35 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 28/2= 
2.5 * 28/2 = 35
35 cm2   Answer: 35 cm2
Answer: E
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?	Choose the correct answer:  A) 22  B) 17  C) 25  D) 27  E) 12

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (100 - 75)= 
(100 - 75) = 25
25 points to 25.Answer: 25
Answer: C
A motorist knows five different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
Choices.
A) 4	B) 8	C) 12	D) 24	E) 30

Solution: Explanation:   Total number of routes from Bristol to Carlisle = (5 x 3 x 2) = 30.   Answer: 30
Answer: E
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? Choose the correct choice
A) 65 liters	B) 88 liters	C) 10 liters	D) 45 liters	E) 8 liters

Solution: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P = 10 liters. Answer: 10 liters
Answer: C
A number whose one-fourth part is increased by 5 is equal to the third part diminished by 5.
Pick one:
A) 100
B) 80
C) 120
D) 60
E) 50

Solution: Explanation:   Let the number be x. Then,   x/4 + 5 = x/3 - 5 => x/4 - x/3 = -10   => 3x - 4x = -120   => x = 120   Answer: Option 120
Answer: C
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 5. If 1 < m < 300, what is the greatest possible value of m?  Choose the correct choice:	A) 160	B) 180	C) 200	D) 220	E) 240

Solution: 13*9= 
13*9 = 117
117   Let's start with 5, and keep adding 13 until we find a number with the form 9k+2.   5, 18, 31, 44, 57, 70, 83= 9*9+2   The next possible number is  83 + 117= 
 83 + 117 = 200
200   The next possible number would be greater than 300.   The answer is 200.
Answer: C
If a is an odd integer and b is an even integer which of the following must be an integer : Options: A) a/b B) ab C) 2a+b D) 2(a+b) E) option B C and D

Solution: a= odd = e.g 3   b=even = e.g 6   A. odd/even for example   3/6= 
  3/6 = 1/2 = around 0.5
0.5 no even no odd   B. odd * even= 3 * 6= 
3 * 6 = 18
18 even   C. 2*odd + even= even + even even   D. 2(even + odd) = 2(odd) even   Hence option B C and D it is.
Answer: E
In Jessica's opinion, her weight is greater than 65 kg but less than 72 kg. Her brother doest not agree with Jessica and he thinks that Jessica's weight is greater than 60 kg but less than 70 kg. Her mother's view is that her weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Jessica?	Choose the correct choice from the following
A) 67 kg. B) 68 kg. C) 69 kg. D) Data inadequate E) None of these

Solution: Explanation: Let Jessica's weight by X kg.   According to Jessica, 65 < X < 72   According to Jessica's brother, 60 < X < 70.   According to Jessica's mohter, X <= 68   The values satisfying all the above conditions are 66, 67 and 68.   Required average= (66+67+68 /3) = (201 /3)= 
(201 /3) = 67
67kg   67 kg.nswer: Option 67 kg.
Answer: A
List D consists of 12 consecutive integers. If -4 is the least integer in list D, what is the range of positive integers in list D? Choose the correct option
A) 5  B) 6  C) 7  D) 11  E) 12

Solution: Since -4 is the least integer in list D, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is   7-1= 
  7-1 = 6
6.   Answer: 6.
Answer: B
If n and k are integers whose product is 4900, which of the following statements must be true?  Answers.
A) n+k>0
B) n does not equal k
C) Either n or k is a multiple of 10
D) If n is even, then k is odd
E) If n is odd, then k is even

Solution: If n is odd and k is odd, then the product is odd.   The answer is If n is odd, then k is even.
Answer: E
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.	Pick one:
A) 140 B) 130 C) 120 D) 150 E) 145

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.   Answer is 145.
Answer: E
Find the best average of the first 10 multiples of 7....	Choose the correct choice from the following:	A) 30.5	B) 38.5	C) 40	D) 43.5	E) 55.5

Solution: the exp is - 7(1+2+3+4+5+6+7+8+9+10)/10 =>   7(10(10+1)/10*2 =>   7(110)/10*2 = 38.5   ANSWER 38.5
Answer: B
What is 35% of 4/13 of 845?
Options
A) 58
B) 69
C) 80
D) 91
E) 102

Solution: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 845, or 1/9 of 845. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.   The number 845 is a bit more than 810, so (1/9)*845 will be a bit more than 90.   Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.   The closest answer is 91, so this is the answer to choose.   The answer is 80.
Answer: C
Which of these expressions has the greatest value? Answers:
A) 1856721/1856725  B) 1288542/1288743  C) 1354321/1314325  D) 1608521/1608526  E) 1532156/1532159

Solution: Using elimination method on options   1354321/1314325 = 1.03043082951...   ANSWER:1354321/1314325
Answer: C
For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 2/7, what are the odds of it burning out during the period from 6months to 1 year following its purchase?  Choose the most appropriate option: A) 5/27 B) 2/9 C) 1/2 D) 4/9 E) 2/3

Solution: P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period)   P(of burning out in 1st 6 mnth)= 2/7   --->P( of not burning out in 1st 6 mnth)=1-2/7=5/7   ---->P(of not burning out in a six mnth period)=1/2 *5/7=1/3   --->P(of burning out in a six mnth period)=1-1/3=2/3   now   P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth)   =5/7 * 2/3=1/2   Ans 1/2
Answer: C
What day of the week does May 28 2006 fall on Choose the correct choice from the following answers:
A) Saturday  B) Monday  C) Sunday  D) Thursday  E) Tuesday

Solution: Explanation :   28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)   Number of odd days in the period 2001-2005   = 4 normal years + 1 leap year   = 4 x 1 + 1 x 2 = 6   Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)   = 148   148 days = 21 weeks  + 1= 
 + 1 = 1
1 odd day   Total number of odd days= (0 + 6 + 1)= 
(0 + 6 + 1) = 7
7 odd days= 0 odd day   0 odd day = Sunday   Hence May 28 2006 is Sunday   Answer : Option Sunday
Answer: C
If $2000 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years? Choose one
A) 2000 (1.056)(3)	B) 2000 (1.056)^3	C) 2000 (1+3(0.056))	D) 2000 (1+(0.056)^3)	E) 2000 (3+1.056)

Solution: the formula is CI=P(1+r/100)^t   in this case i think 2000 (1.056)^3 is the ans
Answer: B
The heights of three individuals are in the ratio 4 : 5 : 6. If the sum of the heights of the heaviest and the lightest boy is 150cm more than the height of the third boy, what is the weight of the lightest boy?  Select:	A) 120cm	B) 150cm	C) 160cm	D) 190cm	E) of these

Solution: Let the heights of the three boys be 4k, 5k and 6k respectively.   4k + 6k = 5k + 150   => 5k = 150=> k = 30   Therefore the height of the lightest boy   = 4k = 4(30) = 120 cm.   120cmNSWER:120cm
Answer: A
The sum of number of boys and girls in a school is 400. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
Choose the most appropriate option:	A) 50	B) 40	C) 60	D) 80	E) 70

Solution: We have x+x% of 400 = 400   x + x/100 * 400 = 400   5 * x = 400   x = 80   Answer is 80
Answer: D
Given the two equations 5r + s = 26 and r + 5s = 10, by how much does r exceed s?
Choose the correct choice from the following answers:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Solve by Simultaneous Equations.   My Answer is B.   r=5   s=1
Answer: B
The sum of first six prime numbers is? Choices
A) 12	B) 23	C) 24	D) 28	E) 41

Solution: Required sum = (2 + 3 + 5 + 7 + 11+13)= 
(2 + 3 + 5 + 7 + 11+13) = 41
41.   Note: 1 is not a prime number.   Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.   41
Answer: E
The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?	Choose the correct choice from the following answers: A) 300 km B) 320 km C) 360 km D) 430 km E) 670 km

Solution: Sol. Average speed of a tractor = 25 km / h   The speed of a bus in an hour = 25 × 2 = 50 km   The speed of a car in an hour = 9/5 * 50= 
9/5 * 50 = 90
90 km   So, the distance covered by car in 4 h is   90 × 4= 360 km   Ans.(360 km)
Answer: C
15% of a certain number is subtracted from 299, the result is the same number. What is the number? Pick one.
A) 199  B) 260  C) 365  D) 175  E) 238

Solution: 299 - (15/100) * X = X   299 - .15*X = X   299 = 1.15 * X   X = 260   Answer: 260
Answer: B
Set S consists of integers {1,2,3,4}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 6?
Choices:  A) 1/3  B) P(E)=1/6  C) 2/3  D) 2/5  E) 3/7

Solution: Number of ways you can choose 2 from 4 = 4C2 = 6   E = event of getting the 2 numbers is more than 6 = (3,4) = 1   probability = 1/6   Answer is P(E)=1/6
Answer: B
Three hoses work to fill a tub at at different rate. Hose P and B, working together, can fill the tub in 6/5 of an hour. Hoses P and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution  Pick:
A) 3/10  B) 2/5  C) 1/2  D) 1  E) 6/5

Solution: Convert the given time to rate and you will be able to add it up.   Total Rate of P and B = Rate of P + Rate of B = 1/(6/5) = 5/6   Total Rate of P and C = Rate of P + Rate of C = 1/(3/2) = 2/3   Total Rate of B and C = Rate of B + Rate of C = 1/2   Adding all three,   2(Rate of P + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2= 
5/6 + 2/3 + 1/2 = 2
2   Rate of P + Rate of B + Rate of C= 1 tub/hour   Time taken by all three together to fill up the tub is 1 hour=1
Answer: D
In a rectangular coordinate system, points O (2,0), P (2,8), and Q (8,0) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?  Select the correct option
A) (3,5)	B) (4,3)	C) (5,4)	D) (4,4)	E) (5,3)

Solution: All points equidistant from O and Q lie on the line x = 5, so the fire station should lie on this line.   All points equidistant from O and P lie on the line y = 4, so the fire station should lie on this line.   These two intersect at (5,4) and that will be the point equidistant from all 3 points.   The answer is (5,4).
Answer: C
The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? Choose the correct answer:
A) 12300
B) 12350
C) 12100
D) 12500
E) 12600

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 Ã— 110/100 Ã— 110/100 = 12100   12100
Answer: C
The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to Choose the correct choice from the following choices
A) 1/35  B) 3/35  C) 5/37  D) 2/35  E) None

Solution: Answer   We have, m x n = 6 x 210 = 1260   ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35   Correct Option: 2/35
Answer: D
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
Select:
A) 3	B) 6	C) 4	D) 9	E) 1

Solution: S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3   3nswer:3
Answer: A
When a random experiment is conducted, the probability that event A occurs is 1/4. If the random experiment is conducted 4 independent times, what is the probability that event A occurs exactly twice?	Choose the most appropriate option.
A) 14/65
B) 27/128
C) 33/140
D) 37/165
E) 41/187

Solution: One case is: 1/4*1/4*3/4*3/4=9/256   The total number of possible cases is 4C2 = 6   P(event A occurs exactly twice) = 6*(9/256) = 27/128   The answer is 27/128.
Answer: B
A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?  Pick one
A) 7 B) 5.1 C) 6 D) 9 E) 3

Solution: M = 5.5   S = 1.5   DS = 7   US = 4   AS = (2 * 7 * 4) /11 = 5.1   Answer:5.1
Answer: B
A coin is tossed 6 times. What is the probability of getting exactly 5 heads?
Choose the correct choice from the following:
A) 3/8
B) 3/16
C) 5/16
D) 3/32
E) 7/64

Solution: The number of possible outcomes is 2^6 = 64   There are 6 ways to get exactly 5 heads.   P(exactly 5 heads) = 6/64 = 3/32   The answer is 3/32.
Answer: D