MU-NLPC/Calc-aqua_rat huggingface dataset:
In a room filled with 7 people, 3 people have exactly 1 sibling in the room and 4 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings? Select the correct option
A) 5/21	B) 3/7	C) 4/7	D) 5/7	E) 13/21

Solution: There are suppose A B C D 13/21 F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning 13/21FG are 4 people who have exactly 2 siblings....(13/21 has F and G as his/her sibling and so on..)   there are now 3 different set of siblings (A and B)   (C and D);(13/21FG)   Now first selecting 2 people out of 7 is 7C2=21   first sibling pair----(A and B)--selecting 2 people --2C2=1   second sibling pair (C and D)--selecting 2 people--2C2=1   third sibling pair (13/21 F G)--selecting 2 out of 4 --4C2=6   total= 1+1+6= 
1+1+6 = 8
8   but,a/c to formula P(success)-1-p(fail)   here,p(failure)is selecting 2 people who are siblings=8/21(21 is 7C2)   =1-8/21   =13/21   ANS 13/21
Answer: E
If the sum of one-half, one-third and one-fourth of a number exceeds the number itself by 4, what could be the number ?	Answers:
A) 24
B) 36
C) 72
D) None of these
E) Cannot be determined

Solution: Answer   Let the number be N   ∴ (1/2 + 1/3 + 1/4)N = {(6 +4 +3) x N } / 12   = 13N / 12   According to the question,   13N/12 - N = 4   ∴ N = 48   Option: None of these
Answer: D
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is	Pick
A) 6%	B) 5%	C) 12%	D) 10%	E) 8%

Solution: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.   S.I. for 5 years = Rs.	2205/3x 5= Rs. 3675   Principal = Rs. (9800 - 3675) = Rs. 6125.   Hence, rate =(100 x 3675)/(6125 x 5)%	= 12%   answer : 12%
Answer: C
A sum amount to Rs.1344 in two years at simple interest. What will be the compound interest on the same sum at the same rate of interest for the same period?	Choose the correct choice from the following answers
A) 10.28%	B) 10.35%	C) 10.25%	D) 14.25%	E) 11.25%

Solution: 100   5 ---- I   5   0.25 --- II   -----------   10.25%   Answer: 10.25%
Answer: C
A and B complete a job in 6 days. A alone can do the job in 24 days. If B works alone, how many days will it take to complete the job?
Choose the correct choice from the following answers:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: The rate of A and B is 1/6   A's rate is 1/24   B's rate is 1/6 - 1/24 = 1/8   B can complete the job in 8 days.   The answer is 8.
Answer: A
How many odd three-digit integers greater than 800 are there such that all their digits are different?  Choose the correct choice from the following:  A) 40  B) 60  C) 72  D) 81  E) 104

Solution: In the range 800 - 900:   1 choice for the first digit: 8;   5 choices for the third digit: 1, 3, 5, 7, 9;   8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.   1*5*8= 
1*5*8 = 40
40.   In the range 900 - 999:   1 choice for the first digit: 9;   4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);   8 choices for the second digit: 10 digits - first digit - third digit= 8 digits.   1*4*8= 
1*4*8 = 32
32.   Total:  40+32= 
 40+32 = 72
72.   Answer: 72
Answer: C
4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 12 weavers in 12 days?  Pick:
A) 12
B) 18
C) 24
D) 30
E) 36

Solution: 1 weaver can weave 1 mat in 4 days.   12 weavers can weave 12 mats in 4 days.   12 weavers can weave 36 mats in 12 days.   The answer is 36.
Answer: E
For 1rs 1p interest
wat will be for 2000rs?	Choose the correct choice from the following answers:
A) 45Rs
B) 50Rs
C) 20Rs
D) 30Rs
E) 48Rs

Solution: For 1rs , 1p interest   for 2000rs, x   x= 2000/1 * 1p ==> 2000 paise   To express in rs, 2000/100 = 20rs   ANSWER:20Rs
Answer: C
If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is:	Pick:	A) 8	B) 9	C) 12	D) 14	E) 13

Solution: Let the numbers be x and y   Then x2-y2=39   8nd x-y=3   We get x+y=13   Solving x-y=3, x+y=13   X=8, y=5   Larger number 8   8NSWER 8 8
Answer: A
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:  Choices:
A) 2:5
B) 3:5
C) 4:5
D) 6:7
E) 7:8

Solution: Explanation:   Let the third number be x.   Then, first number = 120% of x =120X/100=6X/5   Second number = 150% of x =150X/100=3X/2   Ratio of first two numbers =(6X/5-3X/2)= 12x : 15x = 4 : 5.   ANSWER IS 4:5
Answer: C
Ashle and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashle and Vinnie will be chosen?	Select
A) 1/10  B) 3/28  C) 2/9  D) 1/4  E) 1/2

Solution: I did slightly different and hence obviously ended up with the answer 2/9.   I assumed that because Ashle and Winni have to be chosen, the remaining selection is 3 people from 8.   8C3/10C5= 2/9. Option 2/9.
Answer: C
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 35%, then find the population of city atthe end of the year 2007 Choose the correct choice from the following answers:	A) 976374	B) 979923	C) 1009125	D) 2356677	E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 35/100)   = 1009125   1009125
Answer: C
The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
Select:	A) 1:3	B) 2:1	C) 3:1	D) 4:1	E) None of these

Solution: Let the present ages of A and B be 5x and 3x years respectively.   Then, (5x - 4)/(3x + 4) = 1/1   2x = 8 => x = 4   Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1   ANSWER:3:1
Answer: C
Abhijit started a business investing 70000. Anuja joined him after six months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, two years after Abhijit started the business?  Pick
A) 4 : 9 : 4
B) 5 : 9 : 5
C) 8 : 9 : 8
D) 7: 9 : 7
E) 3 : 9 : 4

Solution: Ratio of their investments   = 70 × 24 : 105 × 18: 140 × 12 = 8 : 9 : 8   Answer 8 : 9 : 8
Answer: C
The population of a bacteria colony doubles every day. If it was started 8 days ago with 4 bacteria and each bacteria lives for 12 days, how large is the colony today?  Choose the correct choice from the following answers:	A) 512	B) 768	C) 1024	D) 131072	E) 409600

Solution: 4^8(2) = 131072   The answer is 131072.
Answer: D
4 dice are thrown simultaneously on the board. Find the probability show the same face. Choose the correct answer.
A) 1/113 B) 2/213 C) 1/216 D) 2/215 E) 3/211

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
An article is bought for Rs.675 and sold for Rs.900, find the gain percent? Choose one.
A) 33 1/7% B) 33 0/3% C) 33 1/3% D) 37 1/3% E) 32 1/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer: 33 1/3%
Answer: C
The average age of a group of 10 students is 14 years. If 5 more students join the group, the average age rises by 1 year. The average age of the new students is: Choose the correct answer:
A) 22
B) 38
C) 11
D) 17
E) 91

Solution: Explanation:   Total age of the 10 students = 10 × 14 = 140   Total age of 15 students including the newly joined 5 students = 15 × 15 = 225   Total age of the new students = 225 − 140 = 85   Average age = 85/5= 
85/5 = 17
17 years   Answer: 17
Answer: D
A big container is 30% full with water. If 18 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?  Pick:
A) 36 liters
B) 40 liters
C) 45 liters
D) 54 liters
E) 60 liters

Solution: A big container is 30% full with water and after 18 liters of water is added, the container becomes 75% full. Hence these 18 liters account for 45% of the container, which means that the capacity of it is  18/0.45= 
 18/0.45 = 40
40 liters.   OR: if the capacity of the container is x liters then: 0.3x+18=0.75x --> x=40 liters.   Answer: 40 liters.
Answer: B
The average of first 10 odd numbers is?
Choose one:
A) 44	B) 10	C) 99	D) 77	E) 62

Solution: Sum of 10 odd no. = 100   Average = 100/10= 
100/10 = 10
10   Answer: 10
Answer: B
There are 24 students in Chadâ€™s class. He brought 26 cookies to pass out
for his birthday. How many cookies will each student get? Will there be
any cookies left over?
Choose the correct choice from the following answers:
A) 1-9
B) 1-7
C) 2-8
D) 1-2
E) 3-10

Solution: 26/24 = 1 R 2 Chad will give each student 1 cookie and there will be 2   cookies left over   correct answer 1-2
Answer: D
if a@b = a * b^(1/2) then 4@9 = ?
self made Choose the correct option:  A) 12  B) 6  C) 3  D) 8  E) 4

Solution: a@b = a * b^(1/2)   4@9 = 4*9^(1/2) = 4*3= 
4*3 = 12
12   Correct Option: 12
Answer: A
If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n?	Select.
A) 10	B) 12	C) 15	D) 18	E) 20

Solution: There are 10 numbers divisible by 2   There are 5 numbers divisible by 4   There are 2 numbers divisible by 8   There is 1 number divisible by 16.   Hence the total number of 2’s in 20! are 10+5+2+1= 
10+5+2+1 = 18
18   ANSWER:18
Answer: D
A batch of widgets costs p + 15 dollars for a company to produce and each batch sells for p(11 – p) dollars. For which of the following values of p does the company make a profit?	Select:
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: to make profit, selling price should be greater than cost price   p(11-p) - p-15 >0   => p^2-10*p+15<0   hence p=8   8
Answer: A
A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 3/4 of the current inventory is Speedsters, of which 3/5 are convertibles. If there are 30 vehicles that are not Speedsters, how many Speedster convertibles are there?  Pick one
A) 30 B) 54 C) 60 D) 70 E) 90

Solution: Total Vehicle = 3/4 of speedster + 1/4 of others.   Speedster convertibles = 3/4 total vehicle * 3/5   Given : 1/4 constitutes 30 Vehicles. hence 3/4 constitutes 90   Speedster convertibls = 90 * 3/5= 
90 * 3/5 = 54
54   54
Answer: B
A train passes a man standing on the platform. If the train is 150 meters long and its speed is 72 kmph, how much time it took in doing so?  Choices
A) 6 Â½ sec	B) 6 Â½ sec	C) 9 Â½ sec	D) 8 Â½ sec	E) 7 Â½ sec

Solution: 7 Â½ sec   7 Â½ sec   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 150/20 = 7 Â½ sec
Answer: E
A and B started a business by investing Rs.6000 and Rs. 8000, respectively. After 6 months, B withdrew half of his investment. If after one year they get a profit of Rs.4000 then what is B's share?	Choose the correct choice from the following: A) Rs.2000 B) Rs.1000 C) Rs.3000 D) Rs.5000 E) None of the above

Solution: B's share=2000   6000*12 :8000*6+4000*6=1:1   2 parts=4000   then 1 part=2000   Rs.2000NSWER:Rs.2000
Answer: A
The average score of a cricketer in 2 matches is 30 and in other 3 matches is 40. Then find the average score in all the 5 matches?	Choose the correct choice:	A) 25	B) 27	C) 30	D) 35	E) 36

Solution: Average in 5 matches = (2*30 + 3*40)/2+3 = 60+120 / 5 = 180/5= 
180/5 = 36
36   Answer is 36
Answer: E
find missing number
-5 1 -11 23 29 17 -20 -14,?	Options:
A) -26
B) -27
C) -28
D) -29
E) -30

Solution: (-5)+6= 
(-5)+6 = 1
1 23+6=29 (-20)+6=(-14)   1-12= -11 29-12=17 (-14)-12=(-26)   ans is -26   -26NSWER:-26
Answer: A
A vantakes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Choose one.
A) 60 Kmph  B) 61 Kmph  C) 62 Kmph  D) 64 Kmph  E) 66 Kmph

Solution: Time = 6   Distence = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   60 Kmph)
Answer: A
If a/b = 5/4, Then (4a + 3b) / (4a - 3b) = ?
Select the correct option
A) 7  B) 6  C) 3  D) 5  E) 4

Solution: Answer   Dividing numerator as well as denominator by b, we get   Given Exp. = (4a + 3b) / (4a - 3b) = (4a/b + 3) / (4a/b - 3)   Since a/b = 5/4   this implies that   =[(4*5)/4 +3]/[(4*5)/4 -3)]   = (5+ 3) / (5 - 3)= 
(5+ 3) / (5 - 3) = 4
4   Option: 4
Answer: E
(0.756 x 3/4) terms of rate percent is equivalent to ?  Pick one:
A) 18.9%
B) 37.8%
C) 56.7%
D) 75%
E) None

Solution: Answer   (0.756 x 3/4) = (756/1000) x (3/4) x 100 % = 56.7%   56.7%orrect Option: 56.7%
Answer: C
The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Choose one
A) 23.53 cm B) 23.52 cm C) 23.51 cm D) 23.37 cm E) 23.57 cm

Solution: Explanation:   Let the side of the square be a cm.   Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm   i.e. 4a = 60   A = 15   Diameter of the semicircle = 15 cm   Circimference of the semicircle   = 1/2(∏)(15)   = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places   Answer: Option 23.57 cm
Answer: E
On dividing 15698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?  Choose the correct choice from the following options:
A) 743
B) 154
C) 852
D) 176
E) 785

Solution: 176ivisor *quotient+remainder=dividend   divisor=(dividend)-(remainder)/quotient   (15698-14)/89=176   Answer(176)
Answer: D
How many days are there in x weeks x days?
Pick.
A) 8x	B) 14x	C) 7	D) 7x	E) 8

Solution: x weeks x days = (7x + x) days = 8x days.   8xnswer is 8x.
Answer: A
If b = 4p, where p is a prime number greater than 2, how many different positive even divisors does b have, including b ?  Choose the correct answer.
A) Two  B) Three  C) Four  D) Six  E) Eight

Solution: b=4p   since b = 4p thenevendivisors are:   4p/4p= 1   4p/2p  4 /4= 
  4 /4 = 1
1   4p/2p= 2   4p/44 /2= 
4 /2 = 2
2   4p/4= p   4p/2= 2p   so the answer is (Four)4 /2= 
4 /2 = 2
2p   so the answer is (Four)
Answer: C
In a class there are 10 boys and 15 girls. In how many ways can a boy and a girl be selected?
Choose the correct option
A) 150	B) 500	C) 600	D) 530	E) 630

Solution: Explanation:   We can select one boy from 10 boys in 10 ways.   We select one girl from 15 girls in 15 ways   We select a boy and girl in 10 * 15 ways i.e., = 150 ways.   150nswer: Option 150
Answer: A
Average of 10 numbers is zero. At most how many numbers may be greater than zero Choose the correct answer:
A) 0	B) 1	C) 5	D) 9	E) 10

Solution: Option 9
Answer: D
The area of a square is equal to five times the area of a rectangle of dimensions 32 cm *10 cm. What is the perimeter of the square?
Choose one.
A) 289 cm  B) 160 cm  C) 829 cm  D) 288 cm  E) 289 cm

Solution: Area of the square = s * s   = 5(32 * 10)= 1600   => s =40   = 40 cm   Perimeter of the square   = 4 * 40= 
4 * 40 = 160
160 cm.   Answer: 160 cm
Answer: B
A cycle is bought for Rs.900 and sold for Rs.1160, find the gain percent?	Pick
A) 11	B) 29	C) 99	D) 77	E) 18

Solution: 900 ---- 260   100 ---- ? => 29%   Answer: 29
Answer: B
The ratio of male to female in a class is 2:7. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
Choices
A) a)160 degree
B) b) 168 degree
C) c)191 degree
D) d)192 degree
E) e)213 degree

Solution: here is my approach => males => 2x and females =7x => total =9x   now 9x=> 360   therefore 16x/3 => 213 degree .   P.S => 16x/3 is nothing but total number of students with the given preference   Answer e)213 degree
Answer: E
Two trains 100 meters and 120 meters long are running in the same direction with speeds of 72 km/hr, 54 km/hr In how much time will the first train cross the second	Choose the correct choice
A) 36 sec
B) 40 sec
C) 44 sec
D) 46 sec
E) 48 sec

Solution: Explanation:   Relative speed of the trains = (72 - 54) km/hr = 18 km/hr   = (18 × 5/18) m/sec = 5 m/sec.   Time taken by the trains to cross each other   = Time taken to cover (100 + 120) m at 5 m /sec = (220/5)= 
(220/5) = 44
44 sec.   Answer: Option 44 sec
Answer: C
What is the remainder when 135^77 is divided by 7 ?
Select the correct option:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: (15^77 * 9^77)/7;   (15^77)/7 * (9^77)/7;   1 * 2^77/7;   ((2^3)^25 * 2^2)/7;    1 * 4= 
 1 * 4 = 4
4   ANSW4R:4
Answer: E
Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
Choose the correct choice from the following answers:
A) 1 hour 10 minutes B) 1 hour 82 minutes C) 2 hour 12 minutes D) 1 hour 12 minutes E) 1 hour 62 minutes

Solution: New speed = 6/7 of usual speed   Speed and time are inversely proportional.   Hence new time = 7/6 of usual time   Hence, 7/6 of usual time - usual time = 12 minutes   => 1/6 of usual time = 12 minutes   => usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes   Answer :1 hour 12 minutes
Answer: D
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the correct choice from the following answers:
A) 76 kmph B) 10 kmph C) 29 kmph D) 25 kmph E) 16 kmph

Solution: Speed of the boat in still water   = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph.   Answer:10 kmph
Answer: B
A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.  Options.
A) 1/7  B) 1/6  C) 2/3  D) 2/5  E) 3/5

Solution: The sample space has 216 outcomes.   Now X =   (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)   (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)   (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)   Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}   and X n Y = {(6,5,4)}.   Now P(Y) = 6/216   and P (X n Y) = 1/216   Then P(X|Y) = (1/216)/(6/216) = 1/6.   1/6)
Answer: B
A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?  Choose one:
A) 1 B) 4.2 C) 5.3 D) 1.5 E) 5.2

Solution: M = 3   S = x   DS = 3 + x   US = 3 - x   3 + x = (3 - x)2   3 + x = 6 -2x   3x = 3   x = 1   1nswer:1
Answer: A
How many positive integers less than 130 are there such that they are multiples of 13 or multiples of 12 but not both?  Select the correct option.
A) 16 B) 18 C) 20 D) 24 E) 28

Solution: for 13: 13...130=13*10   for 12: 12...130 =12*10   but there is one integer 13*12. so   N=(10)+(10)= 
(10)+(10) = 20
20   20
Answer: C
Find the lowest common multiple of 24, 30 and 40. Options:
A) 360 B) 420 C) 120 D) 320 E) 280

Solution: LCM=2*2*2*3*5= 
2*2*2*3*5 = 120
120.   Answer is 120
Answer: C
If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is	Select the correct option:
A) 54.48 B) 54.68 C) 54.6 D) 54.58 E) 54.9

Solution: Explanation:   (55×50)+(60×55)+(45×60)/55+60+45   8750/160=54.68   Answer: Option 54.68
Answer: B
Find the LCM of 23,46,827 Pick one:  A) 227  B) 83  C) 23  D) 827  E) None of these

Solution: Explanation:   Whenever we have to solve this sort of question, remember the formula.   LCM = \\begin{aligned} \\frac{HCF of Denominators}{LCM of Numerators} \\end{aligned}   So answers will be option 2,   Please also give attention to the difference in formula of HCF and LCM   Answer: Option 83
Answer: B
A man can row 3 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?  Choose one.
A) 2.9 B) 2.8 C) 2.4 D) 2.8 E) 2.2

Solution: M = 3   S = 1.2   DS = 3.6   US = 1.8   x/3.6 + x/1.8 = 1   x = 1.2   D = 1.2 * 2= 
1.2 * 2 = 2.4
2.4   Answer:2.4
Answer: C
Solution X is 20% chemical A and 80% chemical B by volume; Solution Y is 30% chemical A and 70% chemical B. If a mixture of X and Y is 22% chemical A, what percent of the mixture is Solution X?	Options:  A) 20%  B) 44%  C) 50%  D) 80 percent  E) 90%

Solution: 22% of chemical A in X+Y grams of solution comes from 20% chemical A in solution X and 30% chemical A in solution Y, thus:   0.22(X + Y) = 0.2X + 0.3Y --> X = 4Y --> X/(X+Y)=4/5=0.8.   Answer: 80 percent.
Answer: D
Pipe A and pipe B fill water into a tank of capacity 2000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank? Choices
A) 14 min
B) 18 min
C) 25 min
D) 32 min
E) 40 min

Solution: tank capacity: 2000 L,   1st- 200 l/min for 1 min, volume filled: 200 L   2nd- 100 l/min for 2 min, volume filled: 100 L   3rd (water draining) : 25 l/min*2 : 50 L   total :  (200+100)-50= 
 (200+100)-50 = 250
250 L filled for 1 cycle   number of 250 in 2000 L tank :2000/250= 
2000/250 = 8
8   time taken to fill: 8* total time= 8*5= 
8*5 = 40
40 (option 40 min)
Answer: E
2 pipes P1 and P2 together can fill a tank in 6 hrs and P3 alone can fill the tank in 10 hrs if they work together what is the time taken to fill the tank?  Choose the correct choice from the following choices
A) 7/4 hrs  B) 9/4 hrs  C) 13/4 hrs  D) 15/4 hrs  E) 16/4 hrs

Solution: Explanation:   (P1 +P2) can fill 1/6 tank in 1 hr   P3 can fill 1/10 tank in 1 hr   (P1+P2+P3) can fill tank (1/6+1/10)= 4/15   =>3 pipes can fill the tank in 15/4 hrs   Answer: Option 15/4 hrs
Answer: D
Three candidates contested an election and received 561, 716 and 1111votes respectively. What percentage of the total votes did the winning candidate got?  Choose the correct choice from the following answers
A) 46%
B) 35%
C) 50%
D) 25%
E) 62%

Solution: Total number of votes polled = (561 + 716 + 1111)= 
(561 + 716 + 1111) = 2_388
2388   Required percentage= 1111/2388 * 100 = 46% (approximately)   46%nswer: Option 46%
Answer: A
The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Jayant?	Choices: A) 20 years B) 32 years C) 34 years D) 38 years E) None

Solution: Solution   Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,   (2x + 10)+(3x + 10)+(4x + 10)	= 75.   ‹=›9x = 45   x = 5.   ∴ Jayant's present age = 2x + 10 = 20 years.   20 yearsnswer 20 years
Answer: A
Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?  Choose one:
A) 7 1/7 sec
B) 7 7/2 sec
C) 7 1/8 sec
D) 7 1/2 sec
E) 7 3/2 sec

Solution: 70 + 50= 
70 + 50 = 120
120 * 5/18= 100/3 mps   7 1/2 sec = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 3/100 = 15/2 = 7 1/2 sec   Answer: 7 1/2 sec
Answer: D