MU-NLPC/Calc-aqua_rat huggingface dataset:
If (x +3 )^2 = 144, which of the following could be the value of 2x?	Choose the correct choice.
A) –26 B) –22 C) –30 D) 12 E) 13

Solution: You can also get to the answer by backsolving using answer choices   Starting with x = -15   (x + 3)^2 = 144   (-15+3)^2 = 144 =====> (-12)^2 = 144 Bingo, –30learly, among the answer choices only -15 will result in 144 in the equation so x must be -11,   Then 2x = 2 * -15 = -30   Answer: –30
Answer: C
Solve:-
333 x 333 x 333 + 555 x 555 x 555 = ?(333 x 333 - 333 x 555 + 555 x 555)  Pick:
A) 888  B) 333  C) 555  D) 988  E) 889

Solution: Given Exp. = (a3 + b3) = (a + b) = (333 + 555)= 
(333 + 555) = 888
888(a2 - ab + b2)   888nswer 888
Answer: A
The average speed of a bus from Koyambedu to Salem is 57 km per hour. The bus is scheduled to leave Koyambedu Bus station at 10 pm and reach Salem at 4.35 am on the next day. The distance between Salem and Koyambedu bus station is 342 km. On the way in between Koyambedu and Salem a halt is scheduled compulsorily. Find out the duration of this halt scheduled? Choices:	A) 45 minutes	B) 35 minutes	C) 60 minutes	D) cannot be determined	E) None of these

Solution: Actual time takes= 342/57= 
342/57 = 6
6 hrs   Duration of journey frm 10pm to 4.35am= 6 hrs 35 min   duration of halt scheduled= 35min   ANSWER:35 minutes
Answer: B
If a and t are positive integers, at + a + t cannot be  Pick:
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Let at + t + a = x   Add 1 on both sides:   at + t + a + 1 = x + 1   t(a + 1) + a + 1 = x + 1   (a + 1)(t + 1) = x + 1   Minimum value of (a + 1) = 2   Minimum value of (t + 1) = 2   Hence x + 1 cannot be prime   Substitute x from the given options:   6 + 1= 
  6 + 1 = 7
7 --> prime -->at + t + a cannot be 6   Answer: 6
Answer: B
A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 350-meter long platform?	Choose the correct choice
A) 43	B) 45	C) 47	D) 49	E) 51

Solution: Let the length of the train be x meters.   When a train crosses an electric pole, the distance covered is its own length x.   speed = 36 km/h = 36000 m / 3600 s = 10 m/s   x = 14 * 10= 
14 * 10 = 140
140 m.   The time taken to pass the platform= (140 +350)/ 10= 
(140 +350)/ 10 = 49
49 seconds   The answer is 49.
Answer: D
The cross-section of a river bank is a trapezium in shape. If the river bank is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 500 sq m, the depth of river bank is?	Choose the correct choice from the following answers.
A) 20 m  B) 60 m  C) 40 m  D) 50 m  E) 90 m

Solution: 1/2 * d (12 + 8) = 500   d = 50   ANSWER:50 m
Answer: D
A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?	Choose the correct choice from the following answers:
A) A)1km B) B)500m C) C)650m D) D)750m E) E)400m

Solution: Relative speed of the policeman = 20-16= 
20-16 = 4
4 km/hr   time taken by policeman to cover 100m= (100/1000)*(1/4) = 1/40 hr   In 1/40 hr the thief covers a distance of 16/40 km = 2/5 km = 400m   Answer is 400m
Answer: E
A, B and C enter into a partnership in the ratio 7/2:4/3:6/5.After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:  Choose the most appropriate option:
A) Rs. 2100 B) Rs. 2400 C) Rs. 3600 D) Rs. 4000 E) Rs. 3800

Solution: Explanation:   Ratio of initial investments =(7/2:4/3:6/5)=105 : 40 : 36.   Let the initial investments be 105x, 40x and 36x.   A : B : C =(105 X4+150/100X105X8):(40X X 12):(36x x 12)   = 1680x : 480x : 432x = 35 : 10 : 9.   Hence, B's share = Rs.(21600 X 10/54)=Rs. 4000.   ANSWER IS Rs. 4000
Answer: D
What is the tens digit of 7^957? Options
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: 7^1 = 7   7^2 = 49   7^3 = 343   7^4 = 2401   7^5 = 16807   7^6 = 117649   We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )   0 , 4 , 4 , 0 .   957= 4*239 + 1   The ten's digit will be 0 .   Answer 3
Answer: D
If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost?
Options.
A) 65 paise B) 70 paise C) 52 paise D) 48 paise E) 75 paise

Solution: Explanation:   (Chain Rule)   Let 200 gm potato costs x paise   Cost of 14 Kg potato = 60 Paise   => Cost of 250 gm potato = 60 Paise (∵1/4 kg=1000/4= 
1000/4 = 250
250 gm)   More quantity, More Paise (direct proportion)   Hence we can write as   (Quantity) 200 : 250 :: x : 60   ⇒200×60=250 × x   ⇒4×60=5 × x   ⇒4×12= x   ⇒x=48   Answer: Option 48 paise
Answer: D
A man watched his wife run around the neighborhood block 4 times. He was curious how fast she was running. Each block is 500 meters and she ran the distance in one hour. How fast was his wife running in kilometers per hour?	Answers
A) 3  B) 1  C) 2  D) 4  E) 5

Solution: The distance of each block was 500 meters.   She made the roundtrip 4 times.   Multiply 4 by 500 to get 2000 meters or 2 km.   Because it took her one hour to run the distance the answer is already in kilometers per hour.   2orrect answer is 2km/hour
Answer: C
Having scored 95 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?	Choices
A) 28	B) 27	C) 23	D) 22	E) 24

Solution: Explanation :   Let the average score of the first 18 innings be n   18n + 95 = 19(n+4)=> n = 19   So, Average score after 19th innings = x+4 =23.   Answer : 23
Answer: C
Joan gave harvey 60 out of 500 nuts. He then gave Joan 66 out of the remainder. What will be the percentage increase in the ratio of nust given to nuts owned? Choose one: A) A) 22% B) B) 60% C) C) .8% D) D) 80% E) E) 44%

Solution: Ratio in 1st instance: 6/50   Ratio in the 2nd instance:66/(500-60)= 66/440 =(6/40)   percentage increase is (difference/initial quantity)*100   (6/50)/(6/40 )* 100= 
(6/50)/(6/40 )* 100 = 80
80%   Correct answer is 80%
Answer: D
A and B together can do a work in7 days. If A alone can do it in 14 days. In how many days can B alone do it? Choose one
A) 14
B) 10
C) 21
D) 20
E) 25

Solution: 14   14   1/7 â€“ 1/14 = 1/14 => 14
Answer: A
A trained covered x km at 90 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km. Choose the correct choice:
A) 22
B) 99
C) 27
D) 66
E) 887

Solution: Total time taken = x/90 + 2x/20 hours   = x/9 hours   Average speed = 3x/(x/9) = 27 kmph   Answer: 27
Answer: C
All factors of a positive integer A are multiplied and the product obtained is A^3. If A is greater than 1, how many factors does A have?	Choose the correct choice from the following answers: A) 2 B) 3 C) 5 D) 6 E) 8

Solution: Answer = D = 6   Number ................ Factors ........................ Product   2 ............................. 1, 2 ................................. 2   3 ............................... 1, 3 ............................... 3   4 ................................ 1, 2, 4 ............................... 8   5 ............................... 1, 5 .................................. 5   6 ............................... 1, 2, 3, 6 ......................... 36   7 ................................ 1, 7 ................................. 7   8 ................................. 1, 2, 4, 8 ........................... 64   9 ............................... 1, 3, 9 ............................ 27   10 ................................ 1, 2, 5 ............................ 10   11.................................... 1, 11 ........................... 11   12 ................................... 1, 2, 3, 4, 6, 12 ................. 12 * 12 * 12   Number which we are looking for = 12   Answer = 6
Answer: D
Three-twentieths of the members of a social club are retirees who are also bridge players, nine-twentieths of the members are retirees, and one-half of the members are bridge players. If 120 of the members are neither retirees nor bridge players, what is the total number of members in the social club? Choices.
A) 150 B) 300 C) 360 D) 400 E) 480

Solution: {Total} = {Retirees} + {Bridge players} - {Both} + {Neither}   x = 9/20*x + x/2 - 3/20*x + 120   20x = 9x + 10x - 3x + 120*20 (multiply by 20)   16x = 120*20   x = 150   150nswer: 150
Answer: A
In the following sequence: [x, y, z, 6, 8, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+y? Choose the correct choice from the following.
A) 2  B) 3  C) 4  D) 5  E) -2

Solution: lets start from z, as per the question stem   z + 6 + 8 = 16   -->> z= 2   similarly, y +2 + 6= 
+2 + 6 = 8
8   --> y= 0   similarly,, x + 0 + 2 = 6   --> x = 4   hence , x+y = 4-0= 
4-0 = 4
4 --> x+y=4   ANSWER:4
Answer: C
A certain sum becomes three times itself at simple interest in five years. the sum become 1200 after 9 year.calculate the principal amount.
Options
A) 250  B) 260.86  C) 288.6  D) 265.66  E) 280

Solution: Let the sum be Rs. x, then it becomes Rs. 3x in five years Rs. 2x is the interest on x for five years.   R = (100 * 2x)/(x * 5) = 40 %   s.i=p*r*t/100=x*40*9/100=3.6x   x+3.6x=1200=4.6x=1200,x=1200/4.6=260.86   ANSWER:260.86
Answer: B
How many ways are there to award a gold, silver and bronze medal to 6 contending teams? Choose the correct choice from the following answers
A) 10 × 9 × 8 B) 10!/(3!7!) C) 6!/3! D) 564 E) 6 * 5 * 4

Solution: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways   if gold medal is given to 1 of the teams then only possible 5 teams can be considered for silver medal. we can do selection in 5 ways   similarly if gold and silver medals are awarded then only remaining 4 teams can be considered for a bronze medal. we can do the selection in 4 ways   Total number of ways to select the 3 possible medal winners = 6 * 5 * 4   Correct answer - 6 * 5 * 4
Answer: E
A is 25% bigger than B B is 20% less than C then the relation between A, B, C ?
Select:
A) 5:4:5
B) 5:4:6
C) 5:4:7
D) 5:4:8
E) 6:4:5

Solution: 5:4:5ssume C = 100 Then   B is 20%less than C   Therefore, 20*100/100 = 20 ;   B= 100-20= 
100-20 = 80
80   B=80   5:4:5 = 25% more than B :   So,   5:4:5 = B + 25% of B   = 80 + 20= 
80 + 20 = 100
100   So, the proportion are 100:80:100= 5:4:5   5:4:5NSWER:5:4:5
Answer: A
The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side. Choose the correct choice:
A) Rs. 850 B) Rs. 860 C) 876 RUPEES D) Rs. 886 E) None of these

Solution: Explanation:   We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.   Here we go,   Surface area =6a2=6∗8(2)=384sq feet   Quantity required =38416=24kg   876 RUPEESost of painting =36.50∗24= Rs.876   Option 876 RUPEES
Answer: C
A boy has Rs. 560 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?  Answers:  A) 90  B) 105  C) 140  D) 130  E) 120

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 560   16x = 560   x = 35.   Hence, total number of notes = 3x = 105.   105
Answer: B
A group of men decided to do a work in 17 days, but 8 of them became absent. If the rest of the group did the work in 21days, Find the original number of men?	Choose the correct choice from the following options:
A) 15 B) 20 C) 42 D) 25 E) 18

Solution: Original number of men = 8*21 / (21-17)= 
8*21 / (21-17) = 42
42   Answer is 42
Answer: C
A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 50% are drinking beer, 20% are drinking mixed drinks, and 30% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks? Options
A) 1 B) 4/7 C) 10/19 D) 7/24 E) 7/10

Solution: Suppose there are 100 students   Group A : 40% = 40 students   50% drink beer = 20   30% mixed = 12   20% both = 8   Group B 60% = 60   30% beer= 18   30% mixed = 18   20% both= 12   now we need both ( beer + mixed = both)   probability = total beer drinker = 20+18= 
20+18 = 38
38 and both= 20   thus 20/38 = 10/19   Hence 10/19
Answer: C
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?	Choose the correct choice:
A) 4082.89 B) 4082.49 C) 4082.477 D) 4082.4 E) 4082.41

Solution: Length of the first carpet = (1.44)(6) = 8.64 cm   Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)   = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m   Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6   = Rs.4082.40   Answer: 4082.4
Answer: D
A train covers a distance of 20 km in 30 min. If it takes 18 sec to pass a telegraph post, then the length of the train is?
Choose the most appropriate option
A) 298 m
B) 125m
C) 120 m
D) 217 m
E) 200 m

Solution: Speed = (20/30 * 60) km/hr   = (40 * 5/18) m/sec   = 100/9 m/sec.   Length of the train   = 100/9 * 18= 
100/9 * 18 = 200
200 m.   Answer: 200 m
Answer: E
A man swims downstream 100 km and upstream 30 km taking 10 hours each time; what is the speed of the current? Choose the correct choice from the following answers:
A) 2.5  B) 3.5  C) 4.5  D) 5.3  E) 3.4

Solution: 100 --- 10 DS = 10   ? ---- 1   30 ---- 10 US = 3   ? ---- 1 S = ?   S = (10 - 3)/2= 
(10 - 3)/2 = 7/2 = around 3.5
3.5   Answer: 3.5
Answer: B
In what ratio must rice of Rs.54per kg be mixed with rice of Rs.35 per kg so that cost of mixture is Rs.42 per kg? Choose the correct choice: A) 9:7 B) 7:12 C) 12:7 D) 5:6 E) 7:9

Solution: (42-35)/(54-42)=7/12=7:12   ANSWER:7:12
Answer: B
Find the area of circle whose radius is 3m?
Choices:
A) 18.57 B) 15.84 C) 17.27 D) 28.28 E) 29.88

Solution: 22/7 * 3 * 3   = 28.28   Answer:28.28
Answer: D
Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?  Choose the correct answer:
A) 20  B) 16  C) 24  D) 28  E) 21

Solution: Let the pipe B be closed after x minutes.   30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16   => x = 14/16 * 24= 
14/16 * 24 = 21
21.   Answer:21
Answer: E
total dinning bill of 9 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
Choose the correct choice from the following
A) 21.84
B) 12.84
C) 16.98
D) 24.84
E) 15.84

Solution: dinner bill of 9 person = 139 + 10% tip   so,   10% of 139 = (139*10)/100= 
(139*10)/100 = 139/10 = around 13.9
13.9   So, the actual total amount= 139+13.9= 
139+13.9 = 152.9
$ 152.9   so per head bill= 152.9/9 = $ 16.98   ANSWER:16.98
Answer: C
A train 350 m long, running with a speed of 63 km/hr will pass a tree in?	Choose the correct choice from the following:
A) 18 sec
B) 20 sec
C) 76 sec
D) 15 sec
E) 17 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 350 * 2/35= 
350 * 2/35 = 20
20 sec   Answer:20 sec
Answer: B
Can X and can В are both right circular cylinders. The radius of can X is twice the radius of can B, while the height of can X is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can X with the same brand of gasoline? Answers:	A) $1	B) $2	C) $4	D) $8	E) $16

Solution: Let x be the radius of b and 2h be the height of B. Therefore, radius of X = 2x and height = h   Vol of b = 3.14*x^2*2h   Vol of a = 3.14*4x^2*h   cost to fill half of B = $4 --> cost to fill full B = $8   --> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16   Ans $16
Answer: E
The ages of two persons differ by 16 years. 3 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person Choose the correct choice from the following choices.
A) 15	B) 20	C) 25	D) 27	E) 35

Solution: Explanation:   Let's take the present age of the elder person = x   and the present age of the younger person = x � 16   (x � 3) = 3 (x-16-3)   => x � 3 = 3x � 57   => 2x = 54   => x = 54/2= 
54/2 = 27
27   Answer: Option 27
Answer: D
A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in
Choose the correct option
A) 18 sec B) 12 sec C) 15 sec D) 20 sec E) 13.5 sec

Solution: Length of train = 12 Ã— 15 = 180 m.   Then, speed of train = 180â„18 = 10 m/s   Now, length of train = 9 Ã— 15 = 135m   âˆ´ Required time = 135â„10 = 13.5 sec.   Answer 13.5 sec
Answer: E
What is the volume of a cube?
I. The area of each face of the cube is 64 square metres.
II. The length of one side of the cube is 8 metres.
Choose the correct choice from the following choices.
A) I alone sufficient while II alone not sufficient to answer  B) II alone sufficient while I alone not sufficient to answer  C) Either I or II alone sufficient to answer  D) Both I and II are not sufficient to answer  E) Both I and II are necessary to answer

Solution: EXPLANATION   Let each edge be a metres. Then,   I. a2 = 64 a = 8 m Volume = (8 x 8 x 8) m3 = 512 m3.   Thus, I alone gives the answer.   II. a = 8 m Volume = (8 x 8 x 8) m3 = 512 m3.   Thus, II alone gives the answer.   Either I or II alone sufficient to answerorrect answer is (Either I or II alone sufficient to answer).
Answer: C
Ajit opened a shop investing Rs. 30000. Sujeet joined him 2 months later, investing Rs. 45000. They earned a profit of Rs. 54000 after completion of one year. What will be Sujeet's share of profit ?
Options:
A) 27000 B) 24000 C) 30000 D) 36000 E) None of these

Solution: Explanation :   Ajit : Sujeet = 30000*12 : 45000*10 = 4 : 5.   Sujeet's share = Rs. 54000 * (5/9) = Rs. 30000.   Answer : 30000
Answer: C
Insert the missing number.
2, 6, 12, 20, 30, 42, 56, 72, 90 (....)  Choose the most appropriate option:
A) 110
B) 38
C) 72
D) 66
E) 19

Solution: Explanation:   The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8,8 x 9, 9 x 10.   So, the next number is 10 x 11 = 110.   110nswer: 110) 110
Answer: A
A train 700 meters long is running with a speed of 50 kmph. The time taken by it to cross a tunnel 160 meters long is?	Choose the correct choice from the following answers:
A) 29
B) 18
C) 48
D) 62
E) 11

Solution: 62 = 700 + 160= 
700 + 160 = 860
860   S= 50 * 5/18 = 13.89 mps   T = 860/13.89 = 62 sec   Answer: 62
Answer: D
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? Choose the correct option:  A) 16 seconds  B) 15 seconds  C) 14 seconds  D) 12 seconds  E) 13 seconds

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 60/5= 
60/5 = 12
12 seconds.   Answer:12 seconds
Answer: D
If the average (arithmetic mean) of seven consecutive integers is 20, then the product of the greatest and least integer is
Choose one
A) 343 B) 393 C) 363 D) 391 E) 409

Solution: n = smallest number   n+6 = largest number   (n + n + 6)/2 = 20   => (2n+6)/2 = 20   => n + 3 = 20   => n = 17   So Product of n and n+6 = (17) (23)   = 391   Answer - 391
Answer: D
How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 9?	Choose the correct choice from the following answers.
A) a. 220
B) b. 249
C) c. 432
D) d. 216
E) e. 288

Solution: Taking Question with it's same language as given   To make number divisible by 5, the unit digit should be either 0 or 5 only   Case 1: If unit digit is fixed as zero   With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15   With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120   Total Such cases = 120+15= 
120+15 = 135
135   Case 2: If unit digit is fixed as Five   With two6s and one0The choice to fill the remaining three digits= 2 [6605 or 6065]   With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12   With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40   With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60   Total Such cases = 2+12+40+60= 
2+12+40+60 = 114
114   Total numbers= 135+114 = 432   ANSWe. 288R OPTION e. 288
Answer: E
A sum fetched a total simple interest of 4034.25 at the rate of 9 %.p.a. in 5 years. What is the sum?  Pick:
A) 5768	B) 8925	C) 8965	D) 6474	E) 8723

Solution: Principal = (100 x 4034.25)/(9 x 5)   = 403425/45= 
403425/45 = 8_965
8965.   ANSWER 8965
Answer: C
The average of six numbers is 3.95. The average of two of them is 3.6, while the average of the other two is 3.85. What is the average of the remaining two numbers?	Choose the most appropriate option
A) 4.4
B) 4.6
C) 4.7
D) 4.8
E) 4.9

Solution: Sum of the remaining two numbers   = (3.95 × 6) – [(3.6 × 2) + (3.85 × 2)]   = 23.70 – (7.2 + 7.7)   = 23.70 – 14.9 = 8.80   ∴ Required average = (8.8⁄2) = 4.4   4.4nswer 4.4
Answer: A
In how many different ways can the letters of the word "CORPORATION" be arranged in such a way that no two vowels are together?
Options:
A) 6!/2!∗C57∗5!3!	B) 4!/2!∗C57∗5!3!	C) 6!/2!∗C57∗6!3!	D) 3!/2!∗C57∗5!3!	E) 12!/2!∗C57∗5!3!

Solution: Step 1: Separate consonants with 7 empty slots *C*R*P*R*T*N*.   Step 2: 6 consonants CRPRTN can be arranged in 6!/2! ways (6 letters with two R's);   Step 3: we have 5 vowels OOAIO. Choose 5 slots out of 7 for them (this way no two vowels will be together): C57   Step 4: 5 vowels in their slots can be arranged in 5!/3! ways (5 letters with three O's).   Total = 6!/2!∗C57∗5!3!   6!/2!∗C57∗5!3!nswer: 6!/2!∗C57∗5!3!
Answer: A
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:00 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?	Choose the correct choice from the following:
A) 10.18 p.m
B) 10.29 p.m
C) 10.00 p.m
D) 10.38 p.m
E) 10.32 p.m

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.00 + 7= 
  3.00 + 7 = 10
10.00 p.m.   Answer:10.00 p.m
Answer: C
Kingfisher company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?  Choose the correct answer.
A) 3,024  B) 4,536  C) 5,040  D) 9,000  E) 10,000

Solution: Kingfisher company plans to assign identification numbers to its employees.The first digit can take 9 values from 1 to 9 inclusive;   The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);   The third digit can take 8 values;   The fourth digit can take 7 values.   Total = 9*9*8*7 = something with the units digit if 6.   Answer: 4,536.
Answer: B
Length of a rectangular plot is 16 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?	Choose the correct choice from the following choices
A) 58 m  B) 60 m  C) 80 m  D) 82 m  E) 84 m

Solution: Let breadth = x metres.   Then, length = (x + 16) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 16) + x] = 200   2x + 16 = 100   2x = 84   x = 42.   Hence, length = x + 16 = 58 m   58 m
Answer: A