MU-NLPC/Calc-aqua_rat huggingface dataset:
The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.8 kg. The weight of the new student is Pick
A) 22 kg  B) 21.6 kg  C) 22.4 kg  D) 21 kg  E) 23 kg

Solution: The total weight of 29 students = 29* 28   The total weight of 30 students = 30* 27.8   Weight of the new student = ( 30*27.8 – 29*28)   = 834 - 812= 
834 - 812 = 22
22   22 kgNSWER:22 kg
Answer: A
What is the lowest positive integer that is divisible by 4 through 6, inclusive? Choose the correct choice from the following answers:
A) 120 B) 48 C) 82 D) 76 E) 160

Solution: The integer should be divisible by: 4, 5, and 6. The least common multiple of these integers is LCM=4*5*6=7920   120nswer: 120
Answer: A
The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 150. What is the rate of interest per annum?  Pick.
A) 8
B) 2
C) 10
D) 4
E) 6

Solution: Explanation:   [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 150   15000[(1 + R/100)2 - 1 - 2R/100] = 150   15000[(100 + R)2 - 10000 - 200R]/10000 = 150   R2 = (159 * 2)/3 = 100 => R = 10   Rate = 10%   Answer: Option 10
Answer: C
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
Choose the correct choice: A) 2300 B) 600 C) 250 D) 300 E) none of these

Solution: 1st line - 0 points   2nd line - new 1 point   3td line - new 2 points + old 1 point   4th line - new 3 points + old 2+1 points   5th line - new 4 points + old 3+2+1 points   n-th line - (n-1) points + (n-2) .... 3+2+1   therefore, S=1+2+3...(n-1)   S=(n-1)n/2=24*25/2= 
24*25/2 = 300
300   ANS;300
Answer: D
john bakes 6 cakes for 6 friends. 3 of the friend arrive early and eat 3 cakes each. How many cakes are left over if the other friends all have the same number of cakes?	Select the correct option
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: john made 6*6= 
6*6 = 36
36 cakes. 3 friends eat 3 cakes, leaving 27 remaining for 3 friends.   2+7= 
2+7 = 9
9, divisible by 3.   27 is divisible by 3. The 3 friends ate a cumulative number of cakes that must be divisible by 3, because the number is the same.   27-27= 
27-27 = 0
0   0 is the correct answer
Answer: A
Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony? Choices:  A) 20%  B) 30%  C) 40%  D) 50%  E) 60%

Solution: 4C1/(6C3/2)   6C3 = 6!/3!3! = 20 sub committees   Michael will be included in 1/2 or 10 of these   If Michael and Anthony are in a 3 person committee together there is only one spot left and 4 people left to fill it.   4C1 = 4!/3! = 4   4/10 = 40%   Ans:30%
Answer: B
The length of the bridge, which a train 170 metres long and travelling at 45 km/hr can cross in 30 seconds, is?  Choose the correct choice from the following.
A) 876 m	B) 157 m	C) 205 m	D) 156 m	E) 167 m

Solution: Speed = [45 X 5/18] m/sec   = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (170 + x)/30 = 25/2   => 2(170 + x) = 750 => x   = 205 m.   Answer: 205 m
Answer: C
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?	Choose the correct choice from the following answers.
A) 69.5 km/hr	B) 70 km/hr	C) 79 km/hr	D) 79.2 km/hr	E) 89.2 km/hr

Solution: Let the length of the train is x   x/8=x+264/20   on solving this we get x=176 m   Speed of the train=176/8= 
176/8 = 22
22m/sec   22*18/5=396/5= 
396/5 = 396/5 = around 79.2
79.2 Kmph   ANSWER:79.2 km/hr
Answer: D
The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?	Choose the correct choice from the following options: A) 2:5 B) 2:7 C) 2:1 D) 1:7 E) 2:3

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2   => h1/h2 = 2/5   i.e. h1 : h2 = 2:5   2:5nswer:2:5
Answer: A
What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 7), (x, 7)?  Answers.
A) 64 B) 121 C) 169 D) 225 E) 441

Solution: To find the area of a square, knowing the length of one side is sufficient.   From the coordinates given, we can see that one side equals 13.   The area is 13*13= 
13*13 = 169
169.   The answer is 169.
Answer: C
If a is 50% greater than b, then a is what % less than b?  Select the correct option.
A) 33.33%  B) 50%  C) 66.78%  D) 70.6%  E) 10%

Solution: if b=150 a=100   150-100= 
150-100 = 50
50   75 is 50% of b.   50 is little less than 75 so answer is 33.33%   33.33%nswer is 33.33%
Answer: A
A batsman in his 12th innings makes a score of 55 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been ‘not out’?	Choose the correct choice from the following options
A) 42  B) 43  C) 44  D) 45  E) 46

Solution: Let ‘x’ be the average score after 12 th innings   ⇒ 12x = 11 × (x – 1) + 55   ∴ x = 44   Answer 44
Answer: C
A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?	Answers
A) 480 B) 266 C) 287 D) 1661 E) 211

Solution: 1/x - 1/20 = -1/24   x = 120   120 * 4= 
120 * 4 = 480
480   480nswer: 480
Answer: A
The smallest number which when diminished by 4, is divisible by 12, 16, 18, 21 and 28 is
Options
A) 1008 B) 1012 C) 1022 D) 1032 E) 1043

Solution: Required Number = (L.C.M of 12, 16, 18,21,28)+4   = 1008 + 4= 
1008 + 4 = 1_012
1012   Answer: 1012
Answer: B
A stockiest wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit?
i.	Sell sugar at 10% profit.
ii.	Use 900 g of weight instead of 1 kg.
iii.	Mix 10% impurities in sugar and selling sugar at cost price.
iv.	Increase the price by 5% and reduced weights by 5%.	Choose the correct choice from the following.
A) i or ii  B) ii  C) ii, ii and iv  D) Profits are same  E) None of these

Solution: Solution: Let the CP of 1 kg of sugar be Rs. 100.   Then, CP of 900g sugar = (100*900)/1000 = Rs. 90   Hence, profit % = [(100-90)/90]*100 = 11.11%.   If he add 10% impurity then his CP for 1 kg = (100*1000)/1100 = Rs. 90.9;   And % profit = [(100-90.9)/90.9]*100 = 10.01%   If he reduces weight by 5 % Then, cost price of 950 g = (100*950)/1000= 
(100*950)/1000 = 95
Rs 95 and SP= 105;   % profit = [(105-95)/95]*100 = 10.25 %.   Answer: Option ii
Answer: B
IF IN A AP SERIES 18TH TERM IS 29 & 29TH TERM IS 18. THEN FIND THE 49TH TERM??	Pick
A) 0 B) -1 C) -2 D) 1 E) 2

Solution: 18th term = a + 17d..........(i)   29th term = a + 28d..........(ii)   Solving equation i and ii, we got   d = -1   put d = -1 in any of the above equations and we will get, a = 46   Now, we know 49th term can be written as, a + 48d   now putting the value of a and d in the above equation,   a + 48d = 46 + 48(-1)   = 46 - 48   = -2   ANSWER:-2
Answer: C
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 11th and the 20th terms?  Select the correct option:
A) 324 B) 335 C) 346 D) 357 E) 368

Solution: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.   Thus, 11n – 3 describes the values in the sequence where n is the number of the term.   The 11th term is 11 × 11 – 3 = 118   The 20th term is 20 × 11 – 3 = 220 – 3 = 217.   The sum of these two values is 335.   The correct answer is choice (335).
Answer: B
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money? Select the correct option
A) 11	B) 10	C) 18	D) 16	E) 12

Solution: 7*5: 5*x = 7:10   x = 10   Answer:10
Answer: B
If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? Choose the correct choice from the following.
A) 7	B) 6	C) 5	D) 4	E) 3

Solution: Let the required number days be x.   Less spiders, More days (Indirect Proportion)   Less webs, Less days (Direct Proportion)   spiders 1:7   Webs 7:1   1 x 7 x x = 7 x 1 x 7   => x= 7   7nswer is 7
Answer: A
ratio of girl and boys in class is 5:6.if 20 girl leave the class and ratio become 2:3.calculate the no. of boys?
Choose the most appropriate option:
A) 100 B) 120 C) 80 D) 90 E) none of the above

Solution: girl 5x and boys 6x   5x-20/6x=2/3,15x-60=12x,3x=60,x=20   boys=6x=120   answer 120
Answer: B
1704 x 1704 = ?  Choose the most appropriate option:
A) A)3623216
B) B)2903616
C) C)3624316
D) D)3625116
E) E)3625216

Solution: 1704 x 1704 = (1704)2   = (1700 + 4)2   = (1700)2 + (4)2 + (2 x 1700 x 4)   = 2890000 + 16 + 13600.= 
2890000 + 16 + 13600. = 2_903_616
2903616.   2903616)
Answer: B
Consider the set N = {2, 3, 4, ..., 2n + 1}, where n is a positive integer larger than 10005. If O is the average of the odd integers in N and E is the average of the even integers in N then what is the value of O –E?	Choose the correct choice from the following choices:
A) 2 B) 1 C) 8 D) 9 E) 0

Solution: No need to solve this question. Simply take n = 5. So N = {2, 3, 4, 5, ......11}   Now average of add integers = (3 + 5 + ........11)/5 = 7.   Average of Even integers = (2 + 4 + .....10) / 5 = 6   O - E = 1   Answer:8
Answer: C
A boat can move upstream at 28 kmph and downstream at 50 kmph, then the speed of the current is?  Select the correct option.
A) 5 B) 6 C) 7 D) 54 E) 11

Solution: US = 28   DS = 50   M = (50 - 28)/2= 
(50 - 28)/2 = 11
11.Answer:11
Answer: E
A dealer buys dry fruits at the rate of ` 100, ` 80 and ` 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain or no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity? Select.
A) 30% B) 40% C) 20% D) 50% E) None of these

Solution: Total quantity rate =   (12 * 100 + 15 * 80 + 20 * 60)= 
(12 * 100 + 15 * 80 + 20 * 60) = 3_600
3600   For first 2 qtys, (12 * 100) + (15 * 80)= 2400   40%ut he gets 20% profit = 2400 * 1.2= 
2400 * 1.2 = 2_880
2880   So the third quantity= 3600 – 2880 = 720   Actual third quantity rate = 20  60 = 1200   Loss suffered = (1200 - 720) / 1200   = 480/1200 = 40 %   Answer: 40%
Answer: B
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 2,450. What was Simran share in the profit?
Choose one
A) s 9500
B) s 1000
C) s 1,050
D) s 1,100
E) s 14,000

Solution: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.   Simran's share = Rs.2450 x	3/7	= Rs. 1,050.   ANSWER :s 1,050
Answer: C
If a, f, and c are consecutive even integers and a < f < c, all of the following must be divisible by 4 EXCEPT	Pick
A) a + c B) f + c C) ac D) (bc)/2 E) (abc)/4

Solution: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.   The 3 numbers can be written as   a, (a + 2)(a + 4).   If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.   A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.   C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.   D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.   E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.   B - f + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.   As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.f + c
Answer: B
If 6^t is a factor of (10!)^2, What is the greatest possible value of t ?	Choose the correct choice from the following.
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: t 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7   6= 2*3   Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice 8
Answer: D
The successive discounts 20% and 15% are equal to a single discount of?
Choose one
A) 15
B) 58
C) 32
D) 27
E) 21

Solution: Let the CP of an article be Rs. 100   Given that successive discounts are 20% and 15%.   SP = 85% of 80% of 100 = (85/100)(80/100)(100)   => SP = Rs. 68   Clearly, single discount is 32%.   Answer: 32
Answer: C
What is the smallest positive integer x, such that 6000x is a perfect cube? Choose the correct choice
A) 4	B) 6	C) 36	D) 12	E) 18

Solution: Take out the factors of 6000 that will come 2*3*10^3. for perfect cube you need every no. raise to the power 3. for 6000x to be a perfect cube, need two 2 and 2 3 that means 36 or 6^2   36 is the answer.
Answer: C
The ratio of two quantities is 2 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities?
Select the correct option
A) 2/5
B) 5/8
C) 7/13
D) 22/25
E) It cannot be determined from the information given.

Solution: Correct Answer: E   Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.   For example, if x = 2 and y = 5, then (x+6)/(y+6) = (2+6)/(5+6) = 8/11. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+6)/(y+6) = (4+6)/(10+6) = 10/16. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (It cannot be determined from the information given.).
Answer: E
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?  Pick one.
A) 0.5908  B) 0.5904  C) 0.5906  D) 0.5904  E) 0.5901

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904   Answer: 0.5904
Answer: B
If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 25000 sheets of xerox paper?  Choose the correct choice from the following answers.
A) $1250	B) $1060	C) $1350	D) $900	E) $1000

Solution: For first 2000 pages - cost 5 cents/paper   For 2001 - 10000 - cost 4.5 cents/paper   For 10000+ - 4 cents/paper   So Cost = (5 cents * 2000 ) + (4.5 cents * 8000 ) + (4 cents * 15000) = $1060   alternatively, (0.05 x 2000)+(0.045x8000)+(0.04x 15000) = 1,060   ANSWER:$1060
Answer: B
Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 500 nuts and 500 bolts?	Choose the correct choice from the following choices:
A) 250 seconds
B) 500 seconds
C) 750 seconds
D) 2,000 seconds
E) 3,000 seconds

Solution: To minimize the amount of time, we should make both machines work all the time while producing 500 nuts and 500 bolts.   Two machines to produce 500 bolts will need   (500*1)/2= 
  (500*1)/2 = 250
250 seconds.   Two machines to produce 500 nuts will need  (500*2)/2= 
 (500*2)/2 = 500
500 seconds.   Total= 250+500= 
250+500 = 750
750.   Answer: 750 seconds
Answer: C
Two trains, traveling towards each other, left from two stations that are 900 miles apart, at 4 pm. If the rate of the first train is 72 mph and the rate of the second train is 78 mph, at whatt time will they pass each other?  Select the correct option
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: After t hours, the two trains will have traveled distances D1 and D2 (in miles) given by   D1 = 72 t and D2 = 78 t   After t hours total distance D traveled by the two trains is given by   D = D1 + D2 = 72 t + 78 t = 150 t   When distance D is equal to 900 miles, the two trains pass each other.   150 t = 900   t = 6 hours.   Answer:6
Answer: C
After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?	Choose the correct choice from the following options:
A) 3377
B) 268
C) 1200
D) 2877
E) 1681

Solution: 1200P* (76/100) = 912   1200P1200 * (76/100)= 
1200 * (76/100) = 912
912   1200P= 12 * 100= 
12 * 100 = 1_200
> 1200P= 1200   Answer: 1200
Answer: C
Find the compound interest on $ 66,000 at 20% per annum for 9 months, compounded quarterly  Choose the correct choice from the following answers
A) 2532.12 B) 2552.2 C) 9524.32 D) 10403.25 E) 20512.54

Solution: Principal = $ 66000; Time = 9 months =3 quarters;   Rate = 20% per annum = 5% per quarter.   Amount = $ [66000 x (1+(5/100))^3] = $ 76403.25   CI. = $ (76403.25 - 66000)= 
(76403.25 - 66000) = 10_403.25
$ 10403.25   Answer 10403.25.
Answer: D
10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt. Options.
A) 1/12
B) 7/12
C) 5/12
D) 11/12
E) 13/12

Solution: You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.   You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2= 
5*4/2 = 10
10 ways.   So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.   So probability of picking at least one printed t-shirt= 110/120 = 11/12   Answer is 11/12
Answer: D
All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 152 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?  Pick one.
A) 1216 B) 1723 C) 1129 D) 2613 E) 1372

Solution: A   B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.   Quantity of milk in B = 8k - 5k = 3k.   Quantity of milk in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of milk in container C= 8k - 3k = 5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 152 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 152 8  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 152 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 152= 3k + 152 => 2k = 304 => k = 152   The initial quantity of milk in 1216 = 8k = 8 * 152= 
8 * 152 = 1_216
1216 liters.
Answer: A
A walks at 10 kmph and 4 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?	Choose the correct answer.
A) 100km  B) 150km  C) 80km  D) 120km  E) 200km

Solution: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.   x/10 - x/20 = 4   x = 80 km   Answer is 80km
Answer: C
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/6 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?
Select:
A) 7
B) 9
C) 11
D) D.13
E) 18

Solution: rate of bob to paint n rooms is n/T(bob)   rate of Albert to paint n rooms is n/T(albert).   albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1   Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time   Therefore   n/x + n/x-1 = (3n/5)/(4/3) =   n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic   4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.   6*3 = 3n   18 = 3n.   Answer is 18
Answer: E
A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Thursday at 11 AM, what will be the time at the end of 10 days?  Choose the correct choice from the following answers:  A) 11:54:24 AM  B) 11:56:24 AM  C) 12:16:40 PM  D) 11:54:40 AM  E) 12:06:36 PM

Solution: Clock loses: 1 minute in 3 hours = 8 minutes in 24 hours = 32 minutes in 4 days.   Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;   Net gain in 10 days = 86.40 - 32= 
86.40 - 32 = 54.4
54.4 minutes.   11AM + 54.4 minutes= 11:54 and 4/10th of a minute or 24 seconds.   11:54:24 AMnswer: 11:54:24 AM
Answer: A
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Select
A) 40	B) 56	C) 41	D) 42	E) 34

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40nswer: Option 40
Answer: A
If the average marks of three batches of 40, 50 and 60 students respectively is 45, 55, 65, what is the average marks of all the students? Select the correct option
A) 56.33 B) 34.89 C) 23.67 D) 54.65 E) 43.98

Solution: 56.33verage marks of batch1 = 45   Students in batch1 = 40   Total marks of batch1 = 40*45   56.33verage marks of batch2 = 55   Students in batch2 = 50   Total marks of batch2 = 50 × 55   56.33verage marks of batch3 = 65   Students in batch3 = 60   Total marks of batch3 = 65 × 60   Total students = 40 + 60 + 50= 
40 + 60 + 50 = 150
150   56.33verage marks of all the students=((40*45)+(50×55)+(65×60))/150   =169/3   =56.333   56.33nswer is 56.33.
Answer: A
a, b are positive integers. The remainder of a to be divided by 5 is 2 and the remainder of b to be divided by 7 is 3.
Which is possible to be the remainder of a*b to be divided by 48	Choose the correct choice from the following answers:	A) a) 2	B) b) 6	C) c) 8	D) d) 12	E) e) 20

Solution: Two ways to do it...   a=5x+2..   b=7y+3..   1) convenient way..   Take x and y as 0, and you will get a*b as   2*3= 
  2*3 = 6
6   Answer : b) 6
Answer: B
What is the length of a bridge (in meters), which a train 156 meters long and travelling at 45 km/h can cross in 40 seconds?	Options.
A) 308 B) 320 C) 332 D) 344 E) 356

Solution: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s   In 40 seconds, the train can travel  25/2 * 40= 
 25/2 * 40 = 500
500 meters   500= length of train + length of bridge   length of bridge = 500 - 156= 
500 - 156 = 344
344 meters   The answer is 344.
Answer: D
10 groups have applied for funding from the rec board. After dividing the budget equally among the 10, the rec board finds that there are 4 dollars left over, as funding allocations must be in whole numbers of dollars.
The next semester, the rec board has 4 times as much money to allocate to the 10 groups. How much money will be left over this semester?
Choices:  A) 2  B) 4  C) 6  D) 8  E) 0

Solution: We can put m=10*k+4.   So 4*m=40*k+16 ---> 40*k+16 = 10*(4*m+1) +6 ---> The remainder is 6.   The answer is, therefore, (6).
Answer: C