MU-NLPC/Calc-aqua_rat huggingface dataset:
The probability that a girl student gets scholarship is 0.6 and that of a boy is 0.8,then probability that at least one gets the scholarship is: Choose the correct choice from the following options.
A) 0.72  B) 0.82  C) 0.92  D) 1.12  E) 1.22

Solution: Probability that girl gets scholarship = 0.6   Probability that boy gets scholarship = 0.8   Hence, Probability that girl don't get scholarship = 1-0.6= 
1-0.6 = 0.4
0.4   Probability that boy don't get scholarship= 1-0.8= 
1-0.8 = 0.2
0.2   So, Probability that at least one gets scholarship is: (Girl gets and Boy don't get) OR (Boy gets and Girl don't get) OR (Both Gets)=(0.6*0.2)+(0.8*0.4)+(0.6*0.8)   =0.12+0.32+0.48= 
0.12+0.32+0.48 = 0.92
0.92   ANSWER:0.92
Answer: C
1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member	Choose the correct choice from the following
A) A.10%	B) B.20%	C) C.45%	D) D.55%	E) E.50%

Solution: A,B, C.45% is too low so I eliminated those answers, E was too high of a number, so I chose D as my final answer.C.45%
Answer: C
An organisation has 3 committees, only 2 persons are members of all 3 committee but every pair of committee has 3 members in common. what is the least possible number of members on any one committee?	Pick:	A) 6	B) 7	C) 8	D) 9	E) 4

Solution: Total 4 members minimum required to serve only on one committee.   \Answer:4
Answer: E
What percent of a day is 6 hours?
Choose the most appropriate option
A) 6.25%  B) 20%  C) 25%  D) 12.5%  E) 10 %

Solution: Total hours in a day = 24   Required percent =6×100=25%   ---   24   Answer: Option 25%
Answer: C
In how many ways a committee of 5 members can be selected from 6men and 5ladies, consisting of 3 men and 2 ladies?	Pick one:
A) 120	B) 115	C) 250	D) 160	E) 200

Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen   Required number of ways = 6C3 * 5C2 = (6*5*4*5*4)/(3*2*1*2*1)= 
(6*5*4*5*4)/(3*2*1*2*1) = 200
200   Answer is 200
Answer: E
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is?	Choose the correct choice from the following choices:
A) 4320 B) 4325 C) 4330 D) 4884 E) 4336

Solution: 4884ivisor = (5 * 44)= 
(5 * 44) = 220
220= 10 * Quotient = 4884ivisor   => Quotient = 220/10= 
220/10 = 22
22   4884ividend= (4884ivisor * Quotient) + Remainder   4884ividend = (220 * 22) + 44= 
(220 * 22) + 44 = 4_884
4884   4884
Answer: D
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 18 hours and 8 hours respectively. The ratio of their speeds is
Choose the correct option:	A) 4 : 9	B) 4 : 3	C) 4 : 12	D) 4 : 8	E) 4 : 5

Solution: Let us name the trains as A and B. Then, (4 : 9's speed) : (B's speed) = b : a = 8 : 18 = 4 : 9.4 : 9nswer: 4 : 9
Answer: A
Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 25% the new mean is $850.What was original rent of friend whose rent is increased?  Select the correct option
A) 800  B) 900  C) 1000  D) 1100  E) 1200

Solution: 0.25X = 4(850-800)   0.25X = 200   X = 800   answer 800
Answer: A
There are 14 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Pick:
A) 288  B) 267  C) 261  D) 211  E) 240

Solution: The total number of stations = 16   From 16 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 16P₂ ways.   16P₂ = 16* 15= 
16* 15 = 240
240.   Answer: 240
Answer: E
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? Choose the correct choice from the following options:
A) 9:37 B) 9:31 C) 9:38 D) 9:32 E) 9:35

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16   ------   9:31   Answer: 9:31
Answer: B
A sum of money becomes double itself in 8 years at simple interest. How many times will it become 12 years at the same rate?	Choose the correct choice from the following answers:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: P ---- 2P ---- 8 years3P ---- 12 years Answer: 3
Answer: C
18 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Choose the correct choice from the following choices:
A) 32	B) 87	C) 36	D) 99	E) 77

Solution: 3W = 2M   18M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   18 * 21 * 8 = 14 * x * 6   x = 36   Answer: 36
Answer: C
A utensil contain the amount of milk which is as much lesser than 80 is more than 42. The amount of milk is?  Select the correct option:  A) 45  B) 49  C) 71  D) 61  E) 56

Solution: Answer   Let the amount be x.   Then, x - 42= 80- x   ’ 2x = 80+ 42= 
80+ 42 = 122
122   2x= 122   ´ x = 61   Correct Option: 61
Answer: D
If 16 men working 7 hours day can plough a fieid in 4l days, inhow many days will 14 men working 12 hours a clay plough the samefield ?
Select
A) 22  B) 32  C) 36  D) 39  E) 40

Solution: Explanation :   (Men 14 : 16) : (Hrs/Day 12 : 7) :: 48 : x14 * 12 * x = 16 * 7 * 48 or x = 32   Answer : 32
Answer: B
The product of two positive integers is 783 and their difference is 2. What is the bigger number?
Select:
A) 23	B) 25	C) 27	D) 29	E) 31

Solution: Let's use trial and error to find the two numbers.   30*28= 
30*28 = 840
840 (too high)   29*27= 
29*27 = 783
783   The answer is 29.
Answer: D
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 30 days more. What is the reinforcement?  Choose the most appropriate option.
A) 1800 men	B) 3900 men	C) 600 men	D) 3800 men	E) 900 men

Solution: 2000 ---- 54   2000 ---- 39   x ----- 20   x*30 = 2000*39   x = 2600   2000   -------   600   ANSWER:600 men
Answer: C
A girl has nine jeans and 12 shirts. In how many different ways can she select a jeans and a shirts? Choose the correct choice from the following choices:
A) 100
B) 102
C) 108
D) 110
E) 112

Solution: The girl can select one jeans in nine ways.   The girl can select one shirt in 12 ways.   The number of ways in which he can select one jeans and one shirt is 9 * 12= 
9 * 12 = 108
108 ways.   108
Answer: C
The L.C.M. of two numbers is 36. The numbers are in the ratio 2 : 3. Then sum of the number is: Choose the correct choice from the following:  A) 28  B) 30  C) 40  D) 53  E) 54

Solution: Let the numbers be 2x and 3x.   Then, their L.C.M. = 6x.   So, 6x = 36 or x = 6.   The numbers are 12 and 18.   Hence, required sum = (12 + 18)= 
(12 + 18) = 30
30.   Answer: Option 30
Answer: B
Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
Choose the correct choice:
A) 9  B) 10  C) 11  D) 14  E) 2

Solution: B   10   This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
Answer: B
The minimum number of tiles of size 16 by 24 required to form a square by placing them adjacent to one another is
Choose the correct choice from the following choices.
A) 4 tiles B) 5 tiles C) 6 tiles D) 7 tiles E) 8 tiles

Solution: L6 tilesM of 16,24 = 48   48*48 is the minimum size of square made with 16 by 24 tiles   Number of tiles required = area of square/area of one tile   =48*48/(16*24)= 
48*48/(16*24) = 6
6 tiles   ANSWER:6 tiles
Answer: C
If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of an orange fruit ?  Choose the correct option.
A) Green  B) BLUE  C) PINK  D) ORANCE  E) BLACK

Solution: Explanation:   Pink → Orange   Orange → Blue   Blue → Red   Red → Green   Green → Black   Black → White   The color of an orange fruit is 'Orange' but in coding language, 'Orange' is called 'Blue'.   ANSWER: BLUE
Answer: B
A bag contains 2 yellow balls, 3 white balls and 5 red balls. In how many ways can two balls be drawn from the bag? Choose the correct option:
A) 2C2  B) 10C2  C) 8C2  D) 5C2  E) 6C2

Solution: Total number of balls= 2+3+5= 
2+3+5 = 10
10   2 balls can be drawn from 10 balls in 10C2   ANSWER:10C2
Answer: B
If a train, travelling at a speed of 160 kmph, crosses a pole in 18 sec, then the length of train is?  Choose the most appropriate option:
A) 800
B) 125
C) 288
D) 266
E) 121

Solution: D = 160 * 5/18 * 18= 
160 * 5/18 * 18 = 800
800 m   800nswer: 800
Answer: A
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 6hrs if the speed of the bike is twice speed of the tractor?	Pick:  A) 400 km  B) 500 km  C) 360 km  D) 540 km  E) 600 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 6 h is   90 × 6= 540 km   Ans.(540 km)
Answer: D
Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 50 milliliters of solution X to create a solution that is 25 percent alcohol by volume? Choices:
A) 150	B) 500/3	C) 400	D) 480	E) 600

Solution: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?   W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.   If X = 50 then Y = 150   150NSWER:150
Answer: A
What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?	Answers.
A) 227
B) 814
C) 168
D) 686
E) 218

Solution: In this type of questions, first we need to calculate the area of tiles. With we can get by obtaining the length of largest tile.   Length of largest tile can be obtained from HCF of length and breadth.   So lets solve this,   Length of largest tile = HCF of (1517 cm and 902 cm)   = 41 cm   Required number of tiles =   Area of floorArea of tile=(1517×90241×41)=814   Answer:814
Answer: B
How much does a watch lose per day, if its hands coincide ever 64 minutes? Choose the correct choice
A) 32 8/11
B) 32 8/19
C) 32 8/12
D) 32 8/13
E) 32 8/17

Solution: 55min spaces are covered in 60min   60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.   loss in 64min=(65+5/11)- 64 =16/11   Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.   32 8/11nswer: 32 8/11) 32 8/11
Answer: A
Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Pick.
A) 22  B) 77  C) 26  D) 20  E) 99

Solution: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20   Answer: 20
Answer: D
Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second vessel. In what ratio should the contents be mixed such that the resultant mixture has milk and water in the ratio of 2:5.  Choose the correct choice from the following options:	A) 1:5	B) 2:5	C) 3:5	D) 4:5	E) 5:5

Solution: Let 1st vessel contains X liters of mixture of milk and water.   Milk in 1st vessel = 4/13x   Water in 1st vessel=9/13x   Let 2nd vessel contains Y liters of mixture of milk and water   Milk in 2nd vessel = 2/9y   Water in 2nd vessel =7/9y   Let the two mixture combine such that the milk to water ratio is 2:5   4x/13 + 2y/9 / 9x/13 +7/9y =2/5   36x+26y/81x+91y=2/5   180x+130y=162x+182y   18x=52y   x/y=26/9   Hence mixture from vessel 1 and vessel 2 should be mixed in the ratio 26/9 for milk and water to be in ratio 2:5   ANSWER:2:5
Answer: B
In six successive games, a baseball team scored 2 runs once, 5 runs twice, and 6 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period? Choices: A) 8 B) 7 C) 6 D) 5 E) 4

Solution: 2 runs once (one game)   5 runs twice (two game)   6 runs three times (three games)   SO we have (2*1 + 5*2 + 6*3)/6 = 30/6= 
30/6 = 5
5.   ANS: 5.
Answer: D
If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true?
I. (x + z)^2 > y
II. yz > x
III. x+y>z  Answers:
A) III only
B) II only
C) II,III only
D) I only
E) I,III only

Solution: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.   III) x+y>z   Not necessarily true as 1+5<7   II) yz>x   Not necessarily true as 5.7<1   I) We don't need to check option as all the options except D can be discarded.   Thus Answer I only
Answer: D
A and B started a business with initial investments in the ratio 6 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?	Choose the correct choice from the following options
A) 6 months	B) 8 months	C) 21 months	D) 5 months	E) 7 months

Solution: Let Sumit in the business for ‘a’ months.   Investment Ratio Amit to Sumith = 6 : 3.   Profit sharing ratio = 8 : 7.   Amit is in the business for 12 months.   Then Sumit in the business for   (6× 12) / (3 × a) = 8 / 7 => 24a = 504 or   a = 504 / 24= 
504 / 24 = 21
21 or 21 months   Option 21 months
Answer: C
a little girl went to the farm to buy fruits. she bought 10 apples, 10 oranges and 30 strawberries. what is the ratio of the apples to all the fruits bought? Choose the correct choice from the following choices:  A) 1/2  B) 1/5  C) 1/10  D) 10/30  E) 3/5

Solution: total # of fruits is 10+10+30= 
10+10+30 = 50
50; ratio of her apples to all the fruits bought is 10/50= 1/5   ANSWER:1/5
Answer: B
The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x?  Choices:	A) 26	B) 27	C) 28	D) 29	E) 30

Solution: The average of 24, 35, and 58 is 39.   The average of 19, 51 and x is 33.   Then 19 + 51 + x = 99.   x = 29.   The answer is 29.
Answer: D
A train traveling at 40 kms / hr while inside the tunnel meets another train of half its length traveling at 60 kms / hr and passes it completely in 4.5 seconds. Find the length of the tunnel if the first train passes completely through it in 4 minutes 37.5 seconds.  Pick one
A) 2000 meters B) 3000 meters C) 4000 meters D) 5000 meters E) 6000 meters

Solution: 3000meters   ANSWER:3000 meters
Answer: B
A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is Choose one:
A) 240
B) 250
C) 260
D) 230
E) 220

Solution: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s   Length of the train = speed × time taken to cross the man = 15×20 = 300 m   Let the length of the platform = L   Time taken to cross the platform = (300+L)/15   => (300+L)/15 = 36   => 300+L = 15×36 = 540   => L = 540-300= 
540-300 = 240
240 meter   240nswer is 240.
Answer: A
How many times the keys of a writterhave to bepressed in order to write first 400 counting no.'s?	Answers
A) 980  B) 990  C) 1092  D) 1100  E) 1230

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 400= 301 * 3= 
301 * 3 = 903
903   -----------   1092   1092
Answer: C
If j and k are integers, and 2j + k = 15, which of the following must be true?	Choose the correct choice from the following answers
A) j + k is odd.	B) j + k is even.	C) j is odd.	D) k is odd.	E) k > j

Solution: 2j+k=15   even+odd=odd   So k is odd. k is odd. is the answer.
Answer: D
Sheik Abdullah decides to buy 4 new cars for his collection. If he has to choose between eight different cars, what is the number of purchasing possibilities he has?	Choose the correct choice from the following answers
A) A)7  B) B)11  C) C)14  D) D)18  E) E)21

Solution: Sheik Abdullah decides to buy 4 new cars for his collection. He has to choose between eight different cars   8143= 8*7*6/(4*3*2*1)= 
8*7*6/(4*3*2*1) = 14
14 ANS:14
Answer: C
A man took a loan from a bank at the rate of 11% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was : Select the correct option.
A) Rs. 16363.64
B) Rs. 10,000.64
C) Rs. 15,000,64
D) Rs. 21,353.64
E) None

Solution: Solution   Principal = Rs.(100x5400/11x3)= Rs. 16363.64.   Rs. 16363.64nswer Rs. 16363.64
Answer: A
A certain league has three divisions. The respective divisions had 10, 12 and 15 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion? Choose the correct answer:
A) 70	B) 72	C) 73	D) 78	E) 80

Solution: Overall, there can be 73 minuses. Tus, it is 73.
Answer: C
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?  Select the correct option.
A) 277 B) 299 C) 245 D) 888 E) 291

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer:245
Answer: C
Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?  Choose the correct answer:  A) 39  B) 23  C) 20  D) 27  E) 26

Solution: 1/x + 1/(x + 10)   = 1/12   x = 20   Answer:20
Answer: C
A charity collected $3,199 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?	Choose the correct option:  A) 145  B) 150  C) 155  D) 159  E) 165

Solution: Min fund = 20   Total = 3199   The closest multiple of 20 to 3199 is : 159   Which implies 158 people gave 20 and 1 person gave 39   Ans. 159
Answer: D
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 17, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:	Choose the correct choice: A) 6 B) 7 C) 9 D) 10 E) 11

Solution: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 17   5x = 15   x = 3.   Hence, B's age = 2x = 6 years.   6nswer: Option 6
Answer: A
A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?	Answers.
A) 21000
B) 22882
C) 12112
D) 27788
E) 27712

Solution: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.   Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)   => 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)   x = 28000   35000 - x = 7000   Difference in the cost prices of televisions = Rs. 21000   21000nswer: 21000
Answer: A
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Choose the correct option: A) 76 B) 87 C) 72 D) 11 E) 26

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   Answer: 72
Answer: C
What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?
Choose the correct option.
A) 0  B) 1  C) 5  D) 7  E) 8

Solution: 1/3 + 1/9 + 1/27 = 13/27.= 
13/27. = 0.481481
.481481…   1/37=.027027…   13/27 + 1/27 = .508508..   Hence 101st digit is 0.(3*33 +2=> hence the second digit of the recurring decimal which is 0)   0nswer:0
Answer: A
Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 50% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?	Choose the correct choice from the following choices.
A) 1 to 4	B) 1 to 3	C) 3 to 6	D) 3 to 4	E) 3 to 2

Solution: Correct Answer: C   Solution: C. We know that when Pam and Stanley were both working, the ratio was 3 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 3 to 6. Answer 3 to 6 is correct.
Answer: C
The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 15 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
Choose the correct answer:  A) 40.2  B) 40.4  C) 40.5  D) 40.8  E) None of the above

Solution: Sum of 10 numbers = 402   40.5orrected sum of 10 numbers   = 402 – 13 + 31 – 15 = 405   Hence, new average = 405⁄10 = 40.5   Answer 40.5
Answer: C
Solve the equation :
A) 7(3x – 6) + 5(x - 3) - 2(x - 7) = 5 ,
B) (x -3)(x + 4) - 2(3x - 2) = (x - 4)2,
C) (x + 1)3 – (x - 1)3 = 6(x2 + x + 1) Choose the most appropriate option:
A) 3, 8, -2/3	B) 2, 8, -2/3	C) 4, 8, -2/3	D) 5, 8, -2/3	E) None

Solution: Solution:   A) 21x - 42 + 5x - 15 - 2x + 14 = 5<=>   21x + 5x - 2x = 5 + 42 + 15 - 14<=>   24x = 48 <=> x = 2   2, 8, -2/3) x2 + 4x - 3x - 12 - 6x + 4 = x2 - 8x + 16 <=>   x2 - 5x – x2 + 8x = 16 + 12 – 4 <=>   3x = 24 <=> x = 8   C) x3 + 3x2 + 3x + 1 – (x3 - 3x2 + 3x - 1) = 6x2 + 6x + 6 <=>   x3 + 3x2 + 3x + 1 – x3 + 3x2 + 1 = 6x2 + 6x + 6 <=>   2 = 6x + 6 <=> 6x = -4 <=> x = -2/3   Answer 2, 8, -2/3
Answer: B
A single discount equivalent to the discount series of 20%, 10% and 5% is?
Choose the correct choice.
A) 31.9 B) 31.2 C) 31.6 D) 71.2 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
In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
Choose the correct choice:
A) Rs. 50000 B) Rs. 52000 C) Rs. 57000 D) Rs. 60000 E) Rs. 62000

Solution: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m   Total area of the hall to be covered with mat = 2(lb + bh + hl)   = 2(20 * 15 + 15 * 5 + 5 * 20)   =2(300 + 75 + 100)   = 2 * 475= 
2 * 475 = 950
950 sq. m   Total expenditure= 60 * 950   = Rs. 57000   Rs. 57000
Answer: C
Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 288. What is their H.C.F.? Choose the correct choice from the following choices
A) 18  B) 24  C) 36  D) 42  E) 48

Solution: Let the numbers be 2x, 3x, and 4x.   LCM of 2x, 3x and 4x is 12x.   12x = 288   x = 24   HCF of 2x, 3x and 4x = x = 24   The answer is 24.
Answer: B
The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?	Choose the correct choice from the following choices:
A) 1/64  B) 1/9  C) 1/16  D) 1/25  E) 1/2

Solution: There are two cases. All boys and all girls   case 1. all boys.   1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128   case 2 .all girls.   1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128   We will add the cases to get 1/64
Answer: A
A rectangular block 10cm by 20cm by 30cm is cut into an exact number of equal cubes. Find the least possible number of cubes?  Answers
A) 6  B) 10  C) 15  D) 40  E) 22

Solution: Volume of the block = 10*20*30= 
10*20*30 = 6_000
6000 cm^3   Side of the largest cube= H.C.F of 10,20,30 = 10cm   Volume of the cube = 10*10*10= 
10*10*10 = 1_000
1000 cm^3   Number of cubes= 6000/1000= 
6000/1000 = 6
6   6nswer is 6
Answer: A