MU-NLPC/Calc-aqua_rat huggingface dataset:
Consider a right triangle EBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle EBC	Choose the correct choice.
A) [A] x+y+z/3	B) [B] x-y+z/3	C) [C] x-y+z/2	D) [D] (x^2 + y^2 + z^2)/3	E) [E] cannot be determined

Solution: Radius of a circle inscribed in the right triangle EBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.   Answer: [C] x-y+z/2
Answer: C
A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 6m/h. what is the speedof the person while he was going to his office? Choose the correct choice from the following
A) 4km/h	B) 9km/h	C) 10km/h	D) 11km/h	E) 13km/h

Solution: u = k , v= 3k   {2uv}{u+v}/2uv   \frac{2\times k\times 3k}{(k+3k)}=6   1.5k = 6   k=4km/h   4km/h
Answer: A
Two trains, A and B, started simultaneously from opposite ends of a 75-mile route and traveled toward each other on parallel tracks. Train A, traveling at a constant rate, completed the 75-mile trip in 3 hours; Train B, traveling at a constant rate, completed the 75-mile trip in 2 hours. How many miles had train A traveled when it met train B? Choose one
A) 20
B) 22.5
C) 30
D) 37.5
E) 45

Solution: As the ratio of the rates of A and B is 2 to 3 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 2/(2+3)=2/5 of 75 miles:   75*2/5= 
  75*2/5 = 30
30 miles.   Answer: 30.
Answer: C
A certain auto manufacturer sold 5% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007? Choose the correct option.
A) 63,000  B) 2,000,000  C) 2,030,000  D) 2,040,000  E) 2,300,000

Solution: Let's assume in 2006 the manufacturer sold X.   In 2007 he sold X-5/100(X)   If sales in 2006,X= 2.1 million find X-5/100(X)   (2.1 x 10^6)-5/100(2.1 x 10^6)   2100000-105000=1,995,000-----> 2,000,000(approx)   ANSWER:2,000,000
Answer: B
The ratio of the present ages of Giri and Hari is 5:8. 12 years hence, the ratio of their ages will be 11:14. Find the difference in their present ages?
Choose the correct choice from the following choices
A) 7
B) 6
C) 9
D) 2
E) 5

Solution: Let the present ages of Giri and Hari be 5x and 8x years respectively.   (5x + 12)/(8x + 12) = 11/14   70x + 168 = 88x + 132 => x = 2   Difference in their ages will be the same at all times.   This difference = Difference of their present ages   => 8x - 5x = 3x 8  - 5= 
8  - 5 = 3
3x=> 6 years   Answer: 6
Answer: B
How many times are the hands of a clock at right angle in a day?	Pick one:  A) 22  B) 44  C) 48  D) 50  E) 52

Solution: IN 12 HR RIGHT ANGLES = 22   IN 24 HRS RIGHT ANGLES = 44 times   ANSWER 44
Answer: B
Gold is 10 times as heavy as water and copper is 6 times as heavy as water. In what ratio should these be mixed to get an alloy 8 times as heavy as water?
Choose the correct option:
A) 3:2  B) 1:1  C) 3:1  D) 5:2  E) 4:3

Solution: G = 10W   C = 6W   Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy   1gm gold + x gm copper = x+1 gm of alloy   10W+6Wx = x+1 * 8W   10+6x = 8(x+1)   x = 1/1= 
1/1 = 1
1:1= 1:1   Answer is 1:1
Answer: B
Which of the following data sets has the smallest standard deviation?	Select the correct option
A) {1, 2, 3, 4, 5}	B) {2, 3, 3, 3, 4}	C) {2, 2, 2, 4, 5}	D) {0, 2, 3, 4, 6}	E) {-1, 1, 3, 5, 7}

Solution: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..   The SIMILARITY is - the SUM of all sets is equal =15..   and hence average = 15/5 = 3...   Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..   clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..   Next is D, which has a range of 6-0 or 6..   and {2, 3, 3, 3, 4} has smallest standard of deviation.   ans {2, 3, 3, 3, 4}
Answer: B
A store owner estimates that the average price of type A products will increase by 20% next year and that the price of type B products will increase by 11% next year. This year, the total amount paid for type A products was $3500 and the total price paid for type B products was $8600. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
Choose the correct answer:
A) $13,746  B) $15,325  C) $16,000  D) $16,225  E) $17,155

Solution: cost of type $13,746 products next year = 1.20 * 3500= 
1.20 * 3500 = 4_200
4200   cost of type B products next year= 1.11 * 8300 = 9546   total 4200 +9546= 
4200 +9546 = 13_746
13746   $13,746NSWER:$13,746
Answer: A
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?	Select the correct option.
A) 15 B) 10 C) 12 D) 17 E) 14

Solution: 4/12 + x/15 = 1   x = 10   Answer:10
Answer: B
How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336,528,1320,660  Choose the correct choice:
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Explanation:   A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.   Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.   Also, 5184 is not divisible by 11.   Each one of remaining 7 is divisible by each one of 11, 3 and 4 and therefore, by 132.   Answer: 7
Answer: D
Two trains of equal are running on parallel lines in the same direction at 44 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? Choose the correct choice from the following answers.
A) 40 B) 88 C) 66 D) 55 E) 22

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 44 - 36= 
44 - 36 = 8
8 km/hr.= 8 * 5/18 = 20/9 m/sec.   2x/36 = 20/9 => x = 40.   40nswer:40
Answer: A
What is the unit digit in (4137)754? Pick
A) 6
B) 5
C) 9
D) 13
E) 15

Solution: Explanation:   Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}   =Unit digit in { 292915317923361 x 17114769 }   = (1 x 9) = 9   9
Answer: C
A husband wants to share of x% of his savings of total $10,0000 to his wife. After home expenses, the husband reduce this amount by (x − 9)%. In terms of x, how much $ amount will the wife get?  Options.
A) x*x – 9x B) (x)(1009 – x) C) (1000)(1009 – x) D) (1000)(91– x) E) (x-9)/1000

Solution: Based on the answer choices and the question, this question begs the use of x=9 as a sample number.   Initial = 9%*100000 = 9000   Reduction = 9-9= 
9-9 = 0
0%, so no math required here to calculate the reduction; just make sure that you can calculate 9000 in your answer.   A. x*x – 9x= 0; No   B. (x)(1009 – x) = 9000; Winner!   C. (1000)(1009 – x) > 9000; No   D. (1000)(91 – x) > 9000; No   E. (x-9)/1000 = 0; No   (x)(1009 – x)
Answer: B
Find the missing figures :
?% of 70 = 2.125 Choose the correct choice from the following choices.
A) 3.04
B) 6.05
C) 8.7
D) 7.7
E) 4.05

Solution: (i)	Let x% of 70= 2.125. Then , (x/100)*70 = 2.125   X = (2.125 * 100/70) = 3.04   3.04nswer is 3.04.
Answer: A
What is the sum of natural numbers between 90 and 100
Pick:  A) 1045  B) 4860  C) 5000  D) 5500  E) 5550

Solution: a = first number   l = last number   Sn = n/2[a + l]   between 90 and 100 numbers = 11 => 100 - 90= 
100 - 90 = 10
10 + 1= 
10 + 1 = 11
11   Sn= 11/2 Ã— 190 = 11 Ã— 95 = 1045   1045nswer : 1045
Answer: A
The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum.	Choose the correct choice from the following options:  A) 33498  B) 17000  C) 2665  D) 28876  E) 313

Solution: The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year   So rate of the interest = (100 * 1530)/ (5100 * 1)= 
(100 * 1530)/ (5100 * 1) = 30
30% p.a.   So P= (100 * 10200)/ (30 * 2) = Rs.17000   Answer:17000
Answer: B
Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? Pick one:
A) 2998
B) 2799
C) 2890
D) 1485
E) 2780

Solution: 22/7 * 14 * 3/2 * 3/2= 
22/7 * 14 * 3/2 * 3/2 = 99
99 m2   99 * 15= 
99 * 15 = 1_485
1485   Answer:1485
Answer: D
The banker's discount on Rs.1800 at 12% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?
Choose the correct choice from the following:
A) 3 months
B) 4 months
C) 5 months
D) 6 months
E) 7 months

Solution: Solution   S.I on Rs.1800 = T.D on Rs.1872.   P.W on Rs.1872 is Rs.1800.   Rs.72 is S.I on Rs. 1800 at 12%.   Time	=(100x72 / 12x1800)   = 1/3 year   = 4 months.   Answer 4 months
Answer: B
Which of the following is a prime number?	Select the correct option:	A) 2	B) 4	C) 25	D) 9	E) 27

Solution: Clearly, 2 is a prime number. 2ns : 2
Answer: A
How many multiples of 5 are there between 50 and 500 ? Choose the correct option.
A) 128 B) 91 C) 89 D) 61 E) 60

Solution: It should be mentioned whether 50 and 500 are inclusive.   If 50 and 500 are inclusive, then the answer is   (500-50)/5+1= 
  (500-50)/5+1 = 91
91.   If 50 and 500 are NOT inclusive, then the answer is   (495-55)/5+1= 
  (495-55)/5+1 = 89
89.   Since OA is 89, then we have NOT inclusive case.
Answer: C
What is the remainder when 14,451 × 15,651 × 16,788 is divided by 5?
Pick one.
A) 1 B) 2 C) 4 D) 3 E) 5

Solution: Only the unit's digit of the product will decide the remainder when divided by 5.   Hence, 1*1*8= will give units digit as 8   So, whatever be the number, if it ends in 8, the remainder after dividing with 5 will be 3.   Option3
Answer: D
If P represents the product of the first 14 positive integers, then P is NOT a multiple of Answers:
A) 99  B) 84  C) 72  D) 65  E) 85

Solution: Answer is E.   Since prime factor of 85 is 5x17. 17 is a prime number and not part of the first 14 positive integers.   A) 9 x 11   B) 12 x 7   C) 12 x 6   D) 13 x 5   85) 5 x 17
Answer: E
Six persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with them. Hence the current average age has become 45. Find the age of the 7th person. Choose one:
A) 69
B) 70
C) 71
D) 72
E) 73

Solution: Let ‘x’ be the average of 6 persons   Since there are 6 after 2 years the age will be increased by 2 for each. So  6*2= 
 6*2 = 12
12   69fter two years age will be=x+12   69verage age is 43   That is (x+12)/6=43   =>x=246   Let ‘y’ be the 7th person age   (x+y)/7 =45   (246+y)/7=45   y=(45*7)-246= 
(45*7)-246 = 69
69   69nswer 69
Answer: A
15 men and 12 boys finish a job in 11 days, 13 men and 13 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?  Choose the correct choice from the following answers.
A) 18
B) 17
C) 12
D) 11
E) 12

Solution: 13 M + 4 B ----- 11 days   9 M + 9 B ------- 10 days   12 M +12 B -------?   117 M + 36 B = 108 M +108 B   72 B =9 M => 1 M = 8 B   104 B + 4 B = 108 B ---- 11 days   96 B + 12 B = 108 B -----? => 11 days   Answer: 11
Answer: D
A grocer is storing soap boxes in cartons that measure 30 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton? Select: A) 360 B) 252 C) 280 D) 300 E) 420

Solution: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers   Dimensions of the box =30*42*60   Dimensions of the soap = 5*6*7   we get = 6x6x10 = 360   so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number   the answer is (360)
Answer: A
A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 210, then how much amount should C pay as his share of rent?
Choose the correct choice from the following choices
A) 54  B) 45  C) 25  D) 15  E) 55

Solution: 54 : B : C   =10×7:12×5:15×3   =2×7:12×1:3×3   =14:12:9   54mount that C should pay   =210×9/35=6×9=54   54nswer is 54
Answer: A
In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 65π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?  Choose the correct choice from the following answers:
A) 105π B) 130π C) 200π D) 260π E) 320π

Solution: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.   4(65π) = 260π   The answer is 260π.
Answer: D
A basketball is dropped from a height of 20 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 2 full bounces.	Choose the correct choice from the following answers:
A) 50  B) 55  C) 60  D) 75  E) 100

Solution: Initial distance = 40 feet   first bounce = 20 feet up + 20 feet down = 40 feet   second bouche = 10 feet up + 10 feet down = 20 feet   total distance covered = 40+40+20= 
40+40+20 = 100
100   ANSW100R IS 100
Answer: E
At a certain zoo, the ratio of sea horse to penguins is 5 to 11. If there are 85 more penguins than sea horses at the zoo, how many sea horses are there? Choose the correct choice from the following
A) 24	B) 36	C) 48	D) 70	E) 132

Solution: 5/11 = x / x+85   5*85 = 6x   x=70   D. 70
Answer: D
How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 10-percent solution?	Choose the correct choice from the following options.
A) 35  B) 33 1/3  C) 27  D) 16 2/3  E) 15

Solution: 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 10% of the solution. Set up an inequality and solve for x:   1.5/x = 1/10   x = 15   Since you need a 15L solution, you must evaporate 35 of the original 50L solution to get a 10% solution.   35nswer is 35.
Answer: A
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 50 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?	Pick one:	A) 20	B) 34	C) 38	D) 40	E) 46

Solution: Nice question +1   We have that X/24 - (60-X)/2R = 40   Also X/R - (60-X)/2R = 120   So we get that 2x - 60 = 80R   3x - 60 = 240R   Get rid of R   120 = 3x   x = 46   Hence answer is 46
Answer: E
A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . How many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference?  Pick:
A) 10 feet  B) 12 feet  C) 27 feet  D) 15 feet  E) 18 feet

Solution: total circuit=27/3= 
27/3 = 9
9   total feet squirrel travels=9*3= 
9*3 = 27
27 feet   ANSWER:27 feet
Answer: C
7 people average age is 30. youngest person age is 8. find average of the people when youngest was born. Choose the correct choice:
A) 23  B) 24  C) 25  D) 22  E) 27

Solution: average age of people =30   so have total age =210   before 7 years we have to deduct each person age by seven years   210-56= 
  210-56 = 154
154   so average age would be 154/7= 
154/7 = 22
22   ANSWER:22
Answer: D
The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is? Choose the correct choice from the following choices:  A) 12  B) 14  C) 16  D) 17  E) 19

Solution: 3:4   Total parts = 7   = 7 parts --> 28 (7 × 4 = 28)   = 1 part ---->4 (1 × 4 = 4)   = The greater of the two number is = 4   = 4 parts ----> 16 (4 × 4 = 16)   16)
Answer: C
At the time of marriage, a man was 10 years elder to his wife. 16 years after their marriage, his age is 6/5 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.	Choose the correct option.
A) 36 years B) 16 years C) 14 years D) 24 years E) 10 years

Solution: let wifes age= x   husband age = x+10   now after 16 years of mrg x+16 wifes age   x+10+12 husbands age   6/5(x+16)=x+10+12   after solving x=14   ANSWER:14 years
Answer: C
A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: Choose the correct choice from the following options:
A) 14 years	B) 18 years	C) 20 years	D) 22 years	E) 16 years

Solution: Let the son's present age be x years. Then, man's present age = (x + 24) years.   (x + 22) + 2 = 2(x + 2)   x + 24 = 2x + 4   x = 20.   answer :20 years
Answer: C
Two pipes P and Q can fill a cistern in 12 and 14 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?  Choose the correct choice from the following answers.
A) 11 1/2 min
B) 11 1/4 min
C) 11 2/4 min
D) 11 1/5 min
E) 10 1/2 min

Solution: 3/12 + x/14 = 1   x= 10 1/2   Answer: 10 1/2 min
Answer: E
For a race a distance of 224 meters can be covered by P in 16 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?	Choose the most appropriate option:  A) 232m  B) 238m  C) 224m  D) 331m  E) 236m

Solution: Explanation:   This is a simple speed time problem. Given conditions:   =>Speed of P= 224/16= 
224/16 = 14
14m/s=>Speed of Q=224/32= 
224/32 = 7
7m/s=>Difference in time taken = 16 seconds   Therefore, Distance covered by P in that time= 14m/s x 16 seconds = 224 metres   ANSWER: 224m
Answer: C
If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 12?	Pick.
A) 5/6
B) 7/36
C) 5/36
D) 1/36
E) 12/36

Solution: The sum of numbers appeared is 12.   Therefore, the required probability = n(E)/n(S) = 1/36.   ANSWER:1/36
Answer: D
On a certain planet where people usually tend to live for more than a century, the ratio of present ages of father and son is 7:4. 10 years later, the ratio of their ages will be 5:3. What is the sum of their present ages?	Answers: A) 220 B) 200 C) 140 D) 80 E) 60

Solution: The ratio of present ages of father and son is 7:4, so suppose the present ages are 7x and 4x, respectively.   10 years later, the ages of father and son, respectively, shall be 7x + 10 and 4x + 10.   The ratio of ages 10 years later is given to be 5:3.   This means   (7x + 10)/(4x + 10) = 5/3   Solving we get x = 20.   So present age of father is 7x = 140 and present age of son is 4x = 80.   The sum of present ages is thus 220.   220ns 220
Answer: A
Venkat purchased twenty dozens of toys at the rate of 375 per dozen. He sold each one of them at the rate of 33. What was his percentage profit? Choose the correct choice from the following choices
A) 6.5 B) 5.6 C) 3.5 D) 4.5 E) None of these

Solution: Cost price of 20 dozen toys = 20 × 375 = 7,500   Selling price of 20 dozen toys = 20 × 33 × 12 = 7,920   Profit percentage = 7920−7500/7500×100=5.6%   Answer 5.6
Answer: B
For one toss of a certain coin, the probability that the outcome is heads is 0.7. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?	Choose the correct choice from the following.
A) (0.7)^5 B) 2(0.7)^4 C) 3(0.7)^4 D) 4(0.7)^4(0.3) + (0.7)^5 E) 5(0.7)^4(0.3) + (0.7)^5

Solution: P(5 heads) = (0.7)^5   There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH   P(4 heads) = 5*(0.7)^4(0.3)   The answer is 5(0.7)^4(0.3) + (0.7)^5.
Answer: E
1/3 of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the avg speed for the whole journey.	Options:
A) 25.56 kmph
B) 28.675 kmph
C) 33.333 kmph
D) 40.134 kmph
E) 50.254 kmph

Solution: Average speed = total distance / total time   L33.333 kmphM = 3, 4 = 12   Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)   = 12/ (4/25 + 3/30+ 5/30   = 150*12/54 = 33.333 kmph   33.333 kmph
Answer: C
In a basketball game, Dhoni scored 10 points more than Dravid, but only half as many points as Shewag. If the three players scored a combined total of 130 points, how many points did Dhoni score?	Choices:
A) 45
B) 55
C) 35
D) 65
E) 70

Solution: Let Dravid scored point = x   Then Dhoni Scored = x+10   Shewag Scored = 2*(x+10) = 2x+20   As given, x+x+10+2x+20 = 130 points   4x+30 = 130   x = 130-30/4 = 25   So Dhoni Scored = x +15 i.e) 25+10 = 35   Answer : 35
Answer: C
If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2.
Answers
A) Cannot be determined	B) 1	C) 2	D) 3	E) 4

Solution: take square of any prime number   remainder will be 1   Ans 1
Answer: B
In the coordinate plane, a circle centered on point (-3, -3) passes through point (1, 1). What is the area of the circle? Choose the correct choice from the following answers:
A) 9π
B) 32π
C) 25π
D) 37π
E) 41π

Solution: r^2=(-3-1)^2+(-3-1)^2=16+16= 
16+16 = 32
32   Area of circle=πr^2=32π   Answer : 32π
Answer: B
Rahul can done a work in 5 days and meena can done a work in 10 days.In how many days that both are work together?	Select the correct option
A) 3/10 B) 10/3 C) 1/3 D) 5 E) 6/3

Solution: A's one day work=1/5   10/3's one day work=1/10   A+10/3=1/5+1/10=10+5/50=10/3 days   Ans:option 10/3
Answer: B
P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?	Choices:
A) 1:5
B) 1:3
C) 1:1
D) 1:2
E) 1:9

Solution: Ratio of investments of P and Q is 2 : 5   Total salary claimed by P = 12 * 5000 = Rs. 60000   Total profit = Rs. 2 lakhs.   Profit is to be shared = Rs. 140000   Share of P = (2/7) * 140000 = Rs. 400000   Share of Q = Rs. 100000   Total earnings of P = (60000 + 40000) = Rs. 100000   Ratio of their earnings = 1 : 1   Answer: 1:2
Answer: D
At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 40% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
Choose the most appropriate option.
A) 4/25 B) 8/23 C) 2/5 D) 8/15 E) 2/5

Solution: let there be 100 books in all   Historic fiction books = 40% of total = 40   Other books = 60   New historic fiction = 40% of 40 = 16   Other new books = 40% of 60 = 24   total new books = 24+16= 
24+16 = 40
40   fraction= 16/40 = 2/5   Ans: 2/5
Answer: E
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is? Choose the correct answer:
A) Rs.7500  B) Rs.7200  C) Rs.6000  D) Rs.5750  E) Rs.6750

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 18000= 
1/3 * 18000 = 6_000
6000   ANSWER:Rs.6000
Answer: C
In how much time will a train of length 140 m, moving at 36 kmph cross an electric pole? Choose the correct answer.
A) sec B) sec C) sec D) sec E) sec

Solution: Convert kmph to mps. 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 140/10= 
140/10 = 14
14 sec.   Answer:sec
Answer: D
There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n41?  Choose the correct answer:
A) 100~1,000	B) 1,000~10,000	C) 10,000~100,000	D) 100,000~1,000,000	E) 1,000,000,000,000~

Solution: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n41=2^40=(2^10)^4>(10^3)^4=10^12   Thus, the answer is 1,000,000,000,000~.
Answer: E