MU-NLPC/Calc-aqua_rat huggingface dataset:
a box contains 12 marbels of 3 different colours green,yellow and blue 4each,if you were to close your eyes and pick them at random how many marbels must you take out to be sure that there are at least two of each colour among the marbels you picked out?	Choose the correct option.
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: you have 12 marbles:   g g g g y y y y b b b b   In order to definitely 2 of one color --   So you take out g y b. Then the next one you take will be the 2nd for one of these marbles. So you need to take out 4.   4NSWER:4
Answer: A
A batsman scored 90 runs which included 2 boundaries and 7 sixes. What percent of his total score did he make by running between the wickets. Choices:
A) 30%
B) 40%
C) 44.44%
D) 60%
E) 80%

Solution: Explanation:   Number of runs made by running = 90 - (2 x 4 + 7 x 6)   = 90- (50)= 
90- (50) = 40
40   Now, we need to calculate 40 is what percent of 90.=> 40/90 * 100 = 44.44 %   Option 44.44%
Answer: C
In a simultaneous throw of 2 dice what is the probability of getting a total of 8?  Choose the correct choice from the following.
A) 2/13
B) 3/45
C) 5/36
D) 6/73
E) 4/15

Solution: n(S) = 6*6= 
6*6 = 36
36   E= {(2,6),(3,5),(4,4),(5,3),(6,2)}   Probability = 5/36   Answer is 5/36
Answer: C
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 26000, then the share of A is?
Options:  A) s.14028  B) s.14000  C) s.14003  D) s.14029  E) s.24029

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 26000   Share of s.14000 = 7/13 (26000) = Rs.14000   Answer: s.14000
Answer: B
city A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?  Choose the correct choice from the following answers
A) 45	B) 57.5	C) 58	D) 59.5	E) 61

Solution: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,   Average Speed=(Total DistanceTotal Time)=2304=57.5   57.5
Answer: B
A man’s current age is (2/5) of the age of his father. After 8 years, he will be (1/2) of the age of his father. What is the age of father at now?	Select:
A) 40
B) 45
C) 38
D) 50
E) 39

Solution: A   40   Let, father’s current age is A years.   Then, Man’s current age =[ (2/5)A ]years.   Therefore, [ (2/5)40 + 8 ]= (1/2)(40 + 8)   2(240 + 40) = 5(40 + 8)   40 = 40
Answer: A
A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Choose the correct answer
A) 7500  B) 7509  C) 7507  D) 7505  E) 7502

Solution: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3   B's share = 25000 * 3/10 = Rs. 7500.   7500nswer: 7500
Answer: A
When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of E?  Choose the correct choice from the following choices
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: A simple and elegant solution.   As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1   39-15= 
39-15 = 24
24   24 divide by 3 is 8.   Meaning mean of the n terms is 15+8= 39-16= 
39-16 = 23
23   Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.   E*23 +39= 25*(E+1)   E = 7   Ans. (7)
Answer: A
The average age of 4 boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is? Choose the correct choice from the following options: A) 10years B) 15years C) 20years D) 25years E) 18years

Solution: Total age of 4 boys = 25*4= 
25*4 = 100
100   ratio of their ages= 3:5:7   Age of the youngest = 100*3/15= 
100*3/15 = 20
20 years   Answer is 20years
Answer: C
A garden center sells a certain grass seed in 5-pound bags at $13.82 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25	per bag. If a customer is to buy at least	65 pounds of the grass seed,	but no more than 80 pounds,	what is the least possible cost of the grass seed that the customer will buy?
Choose one.
A) $94.03  B) $96.75  C) $98.75  D) $102.07  E) $105.3

Solution: there can be 2 cases   1)25+25+10+5=$98.75 or   2)25+25+25=$96.75   $98.75
Answer: C
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
Choose the correct choice from the following answers:
A) 15 cm
B) 25 cm
C) 35 cm
D) 40 cm
E) 42 cm

Solution: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm   Answer: Option 35 cm
Answer: C
If x>y>0, which of the following must be true:
I. x^2<y^2
II. x^3 > y^3
III. |x|<y Choose the correct choice from the following answers:
A) I only	B) II only	C) III only	D) II and III	E) I, II and III

Solution: Assuming x and y to be integers   X=3,Y=2   X^2=3^2=9   Y^2=2^2=4   So I is true   Now lets look at option III because if option 3 is true E is the answer or else A   As per question X>Y>0 Hence |X| >Y   So OA=II only
Answer: B
2.505/10.02 =  Answers.
A) 0.35	B) 0.3505	C) 0.25	D) 0.351	E) 0.3527

Solution: 2.505 / 10.02   2505 / 1002= 
2505 / 1002 = 5/2 = around 2.5
2.5   move the comma two places to the left as we have 2 decimal places from the divisor: 0.25. Answer: 0.25
Answer: C
45 men can complete a work in 15 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?  Pick:
A) 5.4  B) 10  C) 1.5  D) 7  E) 8

Solution: 45*15 men can complete the work in 1 day   1 man's 1 day work = 1/675   45 men 6 days work = 6*1/15 = 2/5   remaining work = 1-2/5 = 3/5   75 men's 1 day's work = 75/675 = 1/9   3/5 work is done by them in  9 *3/5= 
 9 *3/5 = 27/5 = around 5.4
5.4 days   5.4nswer is 5.4
Answer: A
Rajeev's age after 15years will be 5 times his age 5years back. What is the present age of Rajeev? Select:
A) 10years B) 15years C) 18years D) 20years E) 19years

Solution: Let Rajeev's present age be x   Rajeev's age after 15 years = x+15   Rajeev's age 5 years back = x-5   x+15 = 5(x-5)   x = 10   Rajeev's present age = 10 years   10yearsnswer is 10years
Answer: A
In the fifth grade at Parkway elementary school there are 420 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Choose the most appropriate option:
A) 69.
B) 73.
C) 81
D) 65
E) 108

Solution: Total students = 420   Boys = 320, Girls = 100   Total playing soccer = 250   86%of 250 = 215 are boys who play soccer.   Girls who play soccer = 35.   Total girls who do not play soccer = 100 - 35= 
100 - 35 = 65
65.   Correct option: 65
Answer: D
The ratio, by weight, of coffee to sugar to water in a pot of coffee is 5:2:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration?	Choose the correct choice from the following answers
A) 22.5	B) 20	C) 17.5	D) 15	E) 12.5

Solution: The new ratio of coffee to sugar is 2.5:2 = 5:4   The new ratio of coffee to water is 10:15.   The new ratio of coffee to sugar to water is 10:8:15.   If there are 12 grams of sugar, then there are  (15/8)*12= 
 (15/8)*12 = 45/2 = around 22.5
22.5 grams of water.   The answer is 22.5.
Answer: A
Find the unit digit in 264^102+264^103? Select the correct option.
A) 0  B) 2  C) 3  D) 4  E) 6

Solution: Required unit's digit = unit's digit in 4102+4103.4102+4103.   Now, 4242 gives unit digit 6.   ⇒ 41024102 gives unit digit 6.   ⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.   Hence, unit's digit in 264102+264103264102+264103   = unit's digit in (6+4)=0   0
Answer: A
10 women are equal to as many men as are equal to 7 boys. All of them earn Rs.30 only. Women’s wages are?
Choose the correct choice from the following answers.
A) 1  B) 5  C) 2  D) 7  E) 2

Solution: 10w = xm = 7b   10w+xm+7b ----- 30 Rs.   10w+10w+10w ----- 30 Rs.   30w ------ 30 Rs. => 1Mw= 1Rs.   1nswer: 1
Answer: A
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is -.	Select:
A) 1/3
B) 1/2
C) 7/8
D) 3/4
E) 7/3

Solution: Answer: Option B   The number of exhaustive outcomes is 36.   Let e be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(e) = 1 - 1/2 = 1/2.
Answer: B
Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 08:00 and starts climbing at a constant pace. Ken starts climbing only at 10:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?  Select the correct option
A) 13:00 B) 13:30 C) 14:00 D) 15:00 E) 15:30

Solution: Both Sari and Ken climb in the same direction.   Speed of Sari = 700/2= 
700/2 = 350
350 meters/hr (since she covers 700 meters in 2 hrs)   Speed of Ken= 500 meters/hr   At 8:00, distance between Ken and Sari is 700 meters. Ken needs to cover this and another 50 meters.   Time he will take = Total distance to be covered/Relative Speed = (700 + 50)/(500 - 350)= 
(700 + 50)/(500 - 350) = 5
5 hrs   Starting from 10:00, in 5 hrs, the time will be 15:00   Answer (15:00)
Answer: D
The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?  Choose one.
A) 432 sq m
B) 356 sq m
C) 452 sq m
D) 428 sq m
E) 528 sq m

Solution: 2(3x + x) = 96   l = 36 b = 12   lb = 36 * 12= 
36 * 12 = 432
432   432 sq mNSWER:432 sq m
Answer: A
A five digit number divisible by 7 becomes divisible by 3 when 13 is added to it. The largest such number is :  Options.
A) 54375  B) 54354  C) 54336  D) 54341  E) 54012

Solution: Out of all the 5 options, only 54341 is NOT divisible by 3. All others are divisible   So Answer = 54341 (No further calculation required)   Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3   13 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3   Applying the above rule,It means that the number which we are going to add should be non-divisible by 3   So comes the answer = 54341   Answer : 54341
Answer: D
A batsman in his 17th innings makes a score of 80, and thereby increases his average by 2. What is his average after the 17th innings? He had never been ’not out’. Choose the correct choice from the following options.
A) 48  B) 37  C) 39  D) 43  E) 42

Solution: 48verage score before 17th innings   = 80 - 2 × 17= 46   48verage score after 17th innings   => 46 + 2= 
46 + 2 = 48
48   48NSWER:48
Answer: A
The average monthly salary of 8 workers and one supervisor in a factory was $$430. When the supervisor, whose salary was $$870 per month, retired, a new person was appointed and then the average salary of 9 people was $$400 per month. The salary of the new supervisor is:	Choose the correct answer.
A) 233 B) 600 C) 287 D) 771 E) 191

Solution: Explanation:   Total salary of 8 workers and supervisor together = 9 × 430 = 3870   Now total salary of 8 workers = 3870 − 870 = 3000   Total salary of 9 workers including the new supervisor = 9 × 400 = 3600   Salary of the new supervisor = 3600 − 3000 = 600   Answer: 600
Answer: B
Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?
Choose the correct answer:
A) 40 minutes B) 28 minutes C) 30 minutes D) 36 minutes E) 34 minutes

Solution: DETAILED SOLUTION   Let us assume that the tank has a capacity of 120 litres. So, the pipes discharge the following amounts of water:   (A) 4 litres per minute   (B) 2 litres per minute   (C) 1 litre per minute.   Part 1: B and C (3 litres/min) are kept open for 10 minutes, filling 3 × 10 = 30 litres. 90 litres remain to be filled in the tank.   Part 2: Now, B is shut and A is opened. Effectively, this means that A and C are filling the tank together (5 litres / minute). We don’t yet know how long A and C are open together.   Part 3: C is closed 10 minutes before the tank overflows. This means that only A works for the last 10 minutes, filling 40 litres (working@4 litres/min)   Since 30 litres are filled in Part 1 and 40 litres in Part 3, the balance (50 litres) should have been filled in Part 2.   Working together, A and C fill 5 litres per minute in Part 2. This means that they would have taken 10 minutes to fill 50 litres.   So, the entire time it took to fill the tank is:   10 + 10 + 10= 
10 + 10 + 10 = 30
30 mins.   Answer choice (c)   Alternate Solution   In one minute, A fills (1/30)th of the tank, B fills (1/60)th of the tank, and C fills (1/120)th of the tank.   (B + C) work for 10 minutes, followed by (A + C), which works for “t” minutes, followed by A, which work for 10 minutes. This ensures that the tank gets filled. This can be written in an equation form:   10 x (1/60 + 1/120) + t x (1/30 + 1/120) + 10 x (1/30)= 1   10 x (1/40) + t x (1/24) + 10 x (1/30) = 1.   Or, 1/4 + t/24 + 1/3 = 1. Or t = 10.   So, the entire tank was filled in 30 mins.   Answer choice (30 minutes).
Answer: C
Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
Choose the most appropriate option:
A) 11 1/6% B) 11 7/9% C) 11 1/9% D) 11 1/8% E) 11 2/9%

Solution: 900 --- 100   100 --- ? => 11 1/9%   Answer:11 1/9%
Answer: C
The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?	Select: A) 1/56 B) 1/42 C) 1/40 D) 1/41 E) 1/47

Solution: 2/3 * 6/7 * 1/3 * 1/8 = 1/42   Answer:1/42
Answer: B
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 120 metres?
Answers:
A) 16 seconds	B) 34 seconds	C) 14 seconds	D) 12 seconds	E) 24 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 120 m= 120/5= 
120/5 = 24
24 seconds.   Answer: 24 seconds
Answer: E
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 8 sec. What is the length of the fast train?  Select.
A) 27 7/6 B) 277/5 C) 27 7/2 D) 400/9 E) 27 7/1

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 8 = 400/9   = 27 7/9 m.   Answer:400/9
Answer: D
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
Choose the correct choice from the following.
A) 187 min	B) 289 min	C) 144 min	D) 278 min	E) 287 min

Solution: Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/36   4/x = 1/36 => x = 144 min.   Answer:144 min
Answer: C
A wheel that has 6 cogs is meshed with a larger wheel of 18 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: Options
A) 49
B) 4
C) 12
D) 7
E) 27

Solution: Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   18 : 6 :: 21 : x 18 * x = 6 x 21   x =	(6 x 21)/18   x = 7.   Answer is 7.
Answer: D
A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 40km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is Select
A) 8.95km/hr B) 26.7km/hr C) 27.8km/hr D) 37.9km/hr E) 8.45km/hr

Solution: average speed = (2*40*20)/40+20 km/hr   =(1600/60)km/hr =26.7 km/hr   Answer (26.7km/hr)
Answer: B
The ratio of the volumes of two cubes is 1331 : 2197. What is the ratio of their total surface areas?
Choices:
A) 121 : 169 B) 169 : 122 C) 81 : 124 D) 81 : 126 E) 81 : 129

Solution: Ratio of the sides = 3√1331 : 3√2197 = 11 : 13   Ratio of surface areas = 11^2 : 13^2 = 121 : 169   121 : 169nswer: Option 121 : 169
Answer: A
A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/5 of th area of the garden. What is the radius of the circular garden?	Select
A) 1  B) 2  C) 10  D) 8  E) 16

Solution: as per the question-- width is negligible   now,   let L be the length of the fence =2pir   L=1/5(pir^2)   pir^2=10pir   r=10   Answer : 10
Answer: C
38, 69, 22,73, 31,47, 90, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?
Options.
A) a- 56  B) b- 68  C) c- 69  D) d- 71  E) e- 77.5

Solution: Important:- Arrange the numbers in ascending order first.   22, 31, 38, 47, 69, 73, 82, 90   3/4th of the number list represents- 73 (6th number)   remaining 1/4th list represents 82 (7 th number)   77.5 fits in between above 2   Answer:- e- 77.5
Answer: E
Of the 3,600 employees of Company X, 3/4 are clerical. If the clerical staff were to be reduced by 4/5, what percent of the total number of the remaining employees would then be clerical?	Choose the correct choice:  A) 37%  B) 22.2%  C) 20%  D) 12.5%  E) 11.1%

Solution: Let's see, the way I did it was   3/4 are clerical out of 3600 so 2700 are clerical   2700 reduced by 4/5 is 2700*4/5   so it reduced 2160 people , so there is 540 clerical people left   but since 2160 people left, it also reduced from the total of 3600 so there are 1440 people total   since 540 clerical left / 1440 people total   you get (37%) 37%
Answer: A
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.  Answers
A) 1/5	B) 1/6	C) 2/7	D) 3/7	E) 3/11

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
There have 12 basket,7 red balls and 5 white balls,find the probability of getting at least 1 red ball and 1 blue ball, if 8 balls are to be drawn ?
Choose the correct choice.
A) 505  B) 495  C) 425  D) 548  E) 525

Solution: (7c3*5c5)+(7c4*5c4)+(7c5*5c3)+(7c6)5c2)+(7c1*5c1)=495   ANSWER:495
Answer: B
The sum of two numbers is 40 and their product is 375. What will be the sum of their reciprocals?	Choose the correct answer.
A) 1/40	B) 8/75	C) 75/4	D) 75/8	E) 75/6

Solution: (1/a)+(1/b)=(a+b)/ab=40/375=8/75   ANSWER:8/75
Answer: B
According to a recent student poll, 3/4 out of 20 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?	Select:
A) 1/14	B) 4/49	C) 18/19	D) 45/49	E) 13/14

Solution: 15 students are interested, 5 are not interested   Prob = 1 - 518/192/2018/192 = 1 - (5*4/(20*19))=1 - 1/19 = 18/19   Answer :18/19
Answer: C
If the ratio of a to b is 4 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?  Choose the correct choice from the following choices.
A) 4/15 B) 1/3 C) 2/5 D) 4/5 E) 7/6

Solution: a:b = 4:3 -- 1   b:c = 1:5   =>b:c = 3 :15 --2   From 1 and 2 , we get   a:c = 4:15   4/15nswer 4/15
Answer: A
In a 100 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
Choose the correct choice from the following:	A) 21	B) 47	C) 45	D) 43	E) 41

Solution: Solution simple   Out of 100 20% are male i.e 20 and 25% are female i.e 25 , so total homeowner is 45.   Now min number homeowner is 20 and max is 45 so question ask us to find least and 21 has least value among all option.   So ans is 21.   21nswer : 21
Answer: A
A letter lock consists of three rings each marked with twelve different letters. The number of distinct unsuccessful attempts to open the lock is at the most?  Choose the correct choice from the following answers: A) 1762 B) 1783 C) 1727 D) 1728 E) 1298

Solution: Since each ring consists of twelve different letters, the total number of attempts possible with the three rings is   = 12 * 12 * 12= 
12 * 12 * 12 = 1_728
1728. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 1728 - 1= 
1728 - 1 = 1_727
1727.   Answer: 1727
Answer: C
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
Choose the correct choice from the following answers.
A) 3665  B) 1015  C) 2676  D) 287  E) 2667

Solution: Required number = (L.C.M. of 12,16, 18, 21, 28) + 7 = 1008 + 7= 
1008 + 7 = 1_015
1015   Answer: 1015
Answer: B
The length of minute hand of a clock is 5.4 cm. What is the area covered by this in 5 minutes
Answers
A) 15.27
B) 16.27
C) 17.27
D) 7.27
E) 7.63

Solution: area of circle is pi*r^2   but in 5 minutes area covered is  (5/60)*360= 
 (5/60)*360 = 30
30 degree   so formula is pi*r^2*(angle/360)=3.14*(5.4^2)*(30/360)=7.63 cm^2   ANSW7.63R:7.63
Answer: E
Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 130 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from Choose the correct choice from the following answers:
A) 30 to 70	B) 70 to 100	C) 110 to 130	D) 130 to 150	E) 150 to 170

Solution: lower point = Sum in each - total possible = 150+130- (200-30) = 280-170 =110...   higher point = entire 130 majoring in electrical major in mechanical too , so = 130..   range = 110 to 130   ANSWER:110 to 130
Answer: C
A lady goes to a bank near her newly possessed home. The bank's policies are weird, but she decides to open the account anyhow with a certain amount. The policy is that at the end of each year, the total amount gets doubled and Rs. 65 is deducted from that amount. After 6 years, when the lady checks her account, the total amount is 0.
Can you find out what was the original amount that she had deposited in the bank?
Answers.
A) 70.853813	B) 33.659045	C) 70.361982	D) 65.443567	E) 63.984375

Solution: E   Explanation:   This question is hypothetical because you cannot transact in fractions in bank account. The following is the solution:   Year	Amount	Interest and Deduction   Start	63.984375   Y1 63.984375nd	62.968750	63.984375 * 2 - 65   Y2 63.984375nd	60.937500	62.96875* 2 - 65   Y3 63.984375nd	56.875000	60.9375 * 2 - 65   Y4 63.984375nd	48.750000	56.875 * 2 - 65   Y5 63.984375nd	32.500000	48.75 * 2 - 65   Y6 63.984375nd	0.000000	32.5 * 2 - 65 = 0
Answer: E
The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years? Choose the correct answer:
A) 3:6	B) 3:2	C) 3:5	D) 3:1	E) 3:2

Solution: Let the present ages of the two brothers be x and 2x years respectively.   Then, (x - 5)/(2x - 5) = 1/3   3(x - 5) = (2x - 5) => x = 10   Required ratio = (x + 5) : (2x + 5) = 15 : 25   = 3:5   Answer:3:5
Answer: C