MU-NLPC/Calc-aqua_rat huggingface dataset:
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?  Choose the correct choice from the following:
A) 5
B) 4
C) 7
D) 9
E) None of these

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km = 954×60954×60 = 10 min.   Option(None of these) is correct
Answer: E
Four bells commence tolling together and toll at intervals of 2, 3, 4 and 5 seconds respectively. In 10 minutes, how many times do they toll together ?
Choose the correct choice from the following choices:
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: LCM of 2, 3, 4, and 5 is 60.   So, after each 60 seconds, they would toll together.   Hence, in 10 minutes, they would toll 10*60 seconds / 60 seconds = 10 times   But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second).   So, total tolls together = 10+1= 
10+1 = 11
11   Answer: 11
Answer: B
If 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 20% of m is equal to what percent of 100% of j ? Choose the correct choice from the following options.
A) 0.35  B) 3.5  C) 35  D) 350  E) 700

Solution: IMO answer should be 350...   consider j=10, then k=50, l=150 and m=350....   20% of 350, comes out to be 70....   100% of 10 is 10....   (70*100)/10=700....   Ans : 700
Answer: E
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?  Choose the correct choice from the following options.
A) 22 seconds  B) 65 seconds  C) 24 seconds  D) 12 seconds  E) 21 seconds

Solution: Speed of the boat downstream   = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 120/5= 
120/5 = 24
24 seconds.   Answer:24 seconds
Answer: C
A straight pipe 6 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?	Choose the correct choice:
A) 1/6 and 1/4 only	B) 1/4 and 1/3 only	C) 1/6, 1/4, and 1/3	D) 1/12, 1/6 and 1/4	E) 1/12, 1/6, and 1/3

Solution: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.   In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).   Distinct lengths would be: 3=3/12=1/4, 4-3=1=1/3 meters long pieces.   Answer: 1/4 and 1/3 only.
Answer: B
The average height of 20 students is 20 cm and the average height of 11 students is 20 cm . What is the average height of the 31 students?	Answers
A) 40 cm	B) 20 cm	C) 30 cm	D) 25 cm	E) 35 cm

Solution: The total height of the 31 students =(20 * 20) + (11 * 20) = 400 + 220= 
400 + 220 = 620
620 cm The required average height=620/31= 
620/31 = 20
20 cm Answer :20 cm
Answer: B
A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train? Choose the correct choice from the following answers
A) 187 m	B) 287 m	C) 279 m	D) 270 m	E) 197 m

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 250)/26 = 20   x = 270 m.   Answer: 270 m
Answer: D
A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? Choices:
A) Rs.10000
B) Rs.12800
C) Rs.6000
D) Rs.8000
E) Rs.9000

Solution: 16*8: x*4 = 5:2   x = 12.8 => Rs.12800   ANSWER:Rs.12800
Answer: B
What is K's position with respect to P?	Choose the correct choice from the following answers:
A) Fifth to the LEFT	B) 7	C) Fifth to the right	D) 8	E) 72

Solution: Answer: Option Fifth to the right
Answer: C
IF A'S INCOME IS 25%LESS THAN B'S.BY WHAT % B'S INCOME IS GREATER THAN A? Choose the correct choice from the following answers:  A) 11  B) 12  C) 33  D) 15  E) 36

Solution: If B 's income is rs 100,   A's income = Rs 75   % B'S IN33OME IS GREATER THAN A = 100*25/75= 33.33 %   ANSWER:33
Answer: C
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Choices:
A) 27 liters
B) 18 liters
C) 10 liters
D) 11 liters
E) 14 liters

Solution: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P = 10 liters.   Answer:10 liters
Answer: C
The area of a triangle is with base 4m and height 5m?  Choose the correct choice from the following options
A) 11 m2 B) 10 m2 C) 54 m2 D) 86 m2 E) 42 m2

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer:10 m2
Answer: B
a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (5/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?	Choose the correct option.
A) 3/8
B) 1/2
C) 9/16
D) 5/7
E) 3/4

Solution: The answer isC: 11/16.   The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.   For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:   (a+b)/2 = (3/4)*b   a = b/2   For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 5/8*c:   (b+c)/2 = (5/8)*c   b = (1/4)*c   For set R, consisting of numbers (a, a+1,...c), the median needs to be found:   a = b/2 = (1/4*c)/2 = (1/8)*c   Median = (a + c)/2 = (1/8*c + c)/2 = (9/8)*c/2 = (9/16)*c (ANSWER 9/16)
Answer: C
A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required? Choose the correct choice from the following choices.
A) 95  B) 92  C) 88  D) 82  E) 85

Solution: Explanation:   Solution 1   Area of the field =680 sq. feet.   Length of the adjacent sides are   20 feet and  680/20= 
 680/20 = 34
34 feet.   Required length of the fencing=20+34+34= 
20+34+34 = 88
88 feet   Answer: Option 88
Answer: C
Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 500 funds on the list have 3-star ratings, how many funds are on the list?  Pick.
A) 500 B) 750 C) 1,000 D) 1,250 E) 1,500

Solution: 1,250   Fraction of 5- and 4-star funds: 1/3 + (2/5)*(2/3) = 5/15 + 4/15 = 9/15   Fraction of 3-star funds = 1 - 9/15 = 6/15   (6/15)*Total = 500   Total = 1250
Answer: D
The length of a rectangle is twice its breadth. If its length is decreased by 10 cm and breadth is increased by 10 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle? Answers:
A) 25 cm B) 35 cm C) 30 cm D) 45 cm E) 55 cm

Solution: Let breadth =x cm   Then, length =2x cm   Area =x×2x=2x^2 sq.cm.   New length =(2x−10) cm   New breadth =(x+10) cm   New area =(2x−10)(x+10) sq.cm.   Given that, new area = initial area +75 sq.cm.   ⇒(2x−10)(x+10)=2x^2+75   ⇒2x^2+20x−10x−100=2x^2+75   ⇒10x−100=75   ⇒10x=75+100= 
75+100 = 175
175   ⇒x=175/10= 
175/10 = 35/2 = around 17.5
17.5 cm   Length=2x=2×17.5=35 cm   ANSWER:35 cm
Answer: B
Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has twuenty iron coins and thuenty copper coins, how many different sums from 1¢ to 140¢ can he make with a combination of his coins?	Pick one:
A) 137  B) 140  C) 166  D) 136  E) 2

Solution: The total sum is 20*2 + 20*5= 
20*2 + 20*5 = 140
140¢. If you can make each sum from 1 to 140 (1¢, 2¢, 3¢, ..., 140¢), then the answer would be 140 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 139¢ and 137¢ (since total sum is 140¢ we cannot remove 1¢ or 3¢ to get 139¢ or 137¢).   So, out of 140 sums 4 are for sure not possible, so the answer must be   140 - 4= 
  140 - 4 = 136
136 sums or less. Only A fits.   Answer: 136.
Answer: D
A man sitting in a train which is traveling at 55 kmph observes that a goods train, traveling in opposite direction, takes 10 seconds to pass him. If the goods train is 320 m long, find its speed	Choose the correct choice from the following answers:
A) 52 kmph B) 56 kmph C) 60 kmph D) 62 kmph E) 72 kmph

Solution: Explanation:   Relative speed = 320/10 m / sec = ((320/10)×(18/5)) kmph = 115 kmph.   Speed of goods train = (115 - 55)= 
(115 - 55) = 60
60 kmph   Answer: Option 60 kmph
Answer: C
Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 12 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?  Choose the correct choice from the following choices:
A) 54	B) 66	C) 80	D) 36	E) 96

Solution: 36   36   It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 12 MPH = 36 miles
Answer: D
Find the largest number of four digits which is exactly divisible by 27,18,12,16
Select:
A) 9906
B) 9916
C) 9936
D) 9736
E) 9746

Solution: Explanation:   LCM of 27-18-12-16 is 432.   After dividing 9999 by 432 we get 63 remainder.   So answer will be 9999-63= 
9999-63 = 9_936
9936   Option 9936
Answer: C
Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 8 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?  Pick: A) 13 B) 24 C) 18 D) 19 E) 12

Solution: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/8   => 1/x = 1/6 - 1/8 = (4 - 3)/24 = 1/24   => x = 24.   Answer: 24
Answer: B
A train 700 m long passes a man, running at 20 km/hr in the same direction in which the train is going, in 40 sec. The speed of the train is?  Choose the correct choice from the following options:
A) 40 km/hr
B) 41 km/hr
C) 42 km/hr
D) 43 km/hr
E) 44 km/hr

Solution: Speed of the train relative to man = 700/40 = 35/2 m/sec.   = 35/2 * 18/5= 
35/2 * 18/5 = 63
63 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 20) km/hr.   x - 20 = 63 => x = 43 km/hr.   Answer: 43 km/hr
Answer: D
The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 20 on the fourth day, his average earning for the whole week is ?
Choose one
A) Rs . 18.95 B) Rs 16 C) Rs. 20 D) Rs. 25.71 E) None of these

Solution: Answer   Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day   = 4 x18 + 4 x 22 -20   = Rs. 140   ∴ Average earning = 140 / 7   = Rs. 20   Rs. 20orrect Option: Rs. 20
Answer: C
If 15% of 40 is greater than 25% of a number by 2,then find the number is?  Answers:
A) 20
B) 15
C) 16
D) 25
E) 30

Solution: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16   ANSWER 16
Answer: C
Sandy is younger than Molly by 20 years. If the ratio of their ages is 7:9, how old is Sandy?
Choose the correct option
A) 42  B) 49  C) 56  D) 63  E) 70

Solution: Let Sandy's age be 7x and let Molly's age be 9x.   9x - 7x = 20   x = 10   Sandy is 70 years old.   The answer is 70.
Answer: E
A certain company charges $5 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $5 plus $1 per pound. If the company charged $30 to ship a certain package, which of the following was the weight of the package, in pounds?
Choose one.
A) 20	B) 25	C) 30	D) 35	E) 40

Solution: Let the weight of the package be X. Then the cost is 1*X + 5= 30 ---> X=25 ---> X=25   Answer : 25
Answer: B
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Pick
A) 247
B) 249
C) 245
D) 882
E) 279

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer: 245
Answer: C
For a,q,d are the positive integers, and d|a means that “a is divisible by d”, if d|aq, which of the following must be true?
Choose the correct choice from the following choices:
A) d|a
B) d|q
C) d|2aq
D) d|(a+q)
E) d|(a-q)

Solution: d/a means a is divisible by d   d/aq means ab divisible by d.   all are integers so ,   if ab is divisible by d,   1 a can be divisible by d   or   2 q can be divisble by d.   so the question stem asks must true.   so option a and b are could but not must.   option c is 2aq divisible by d. if ab is divisible by d then 2aq is divisible by d.   option d and e we can't predict.   so option d|2aq is correct.
Answer: C
A bus takes 4 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 4/3th of the previous time?	Choose the most appropriate option:
A) 50 Kmph  B) 90 Kmph  C) 95.9 Kmph  D) 95.4 Kmph  E) 90.5 Kmph

Solution: Time = 4   Distance = 480   4/3 of 4 hours = 4 * 4/3 = 5.3 Hours   Required speed = 480/5.3 = 90.5 Kmph   90.5 Kmph
Answer: E
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 8 months, find for how much time did Q invest the money?  Choose the correct choice from the following choices.
A) 11 B) 10 C) 18 D) 16 E) 12

Solution: 7*5: 8*x = 7:10   x = 16   Answer:16
Answer: D
When positive integer f is divided by 6, the remainder is 1. Which of the following must be true?
I. f is a prime number
II. f is odd
III. f is divisible by 7  Choose the most appropriate option: A) I only B) II only C) III only D) I and II only E) II and III only

Solution: f=6q+1   Examine II) put q=0,1,2,3....... we have f=1,7,13,...25 so f must be odd   Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true   Examine I) f= 7 true but while 2 is prime, it does not give reminder 1   Answer: II only
Answer: B
A train 124 m long running at 68 kmph crosses a platform in 19 sec. What is the length of the platform?	Pick one: A) 338 B) 234 C) 240 D) 881 E) 271

Solution: D = 68 * 5/18 = 19 = 358 – 124 = 234   Answer: 234
Answer: B
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Pick.
A) 60 kg	B) 75 kg	C) 80 kg	D) 85 kg	E) 90 kg

Solution: Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (65 + 20)= 
(65 + 20) = 85
85 kg   Option 85 kg
Answer: D
My boss has $243,986 in the business account. What is the least amount of money (in whole number of dollars) that he must add to his account if she wants to split this money evenly among his nine employees? Select:
A) $1  B) $2  C) $3  D) $4  E) $6

Solution: To find the least amount he should add to his saving account to split the money evenly among his employees,   he needs to make the total divisible by 9   Simply add the individual digits of the total = 2+4+3+9+8+6 =   If you add 4 , the number is divisible by 9 (32+ 4)   Correct Option : $4
Answer: D
If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q?  Choose the correct choice:
A) 6	B) 4	C) 3	D) 2	E) 1

Solution: 4500+10q+d+8737=13003+100q+10d   13237+10 q+d=13003+100q+10d   234=90q+9d   26=10 q+d   d=6 ^ q=2   ==> d-q= 4   ANSWER 4
Answer: B
Two bags are randomly selected from a flight at the airport to be searched, one at a time, then sent through after being searched (this means: without return). Five smugglers are watching this and they each have three bags with contraband. There are 20 bags on the flight. What is the probability that they will get away? (Answer in lowest terms).  Choices
A) 5/75 B) 3/12 C) 5/76 D) 2/19 E) 1/2

Solution: The flight has 20 bags total. There are (5 smugglers)(3 bags) = 15 bags with contraband, and   20 - 15= 
  20 - 15 = 5
5 with no contraband, so the probability of getting a bag with no contraband is P(N)= 5/20 on the first selected bag.   Because selection is (without return), the P(N) has changed for following selections. Now, there are 19 bags, but the number bags with contraband stay the same; since, we are only calculating for success as no bag with contraband... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:   Formula = P(A\B) = P(A and B)/P(B).   2 bags are selected; so,   P(A\B) = (5/20)(5/19) = 25/380 = 5/76   Answer: 5/76
Answer: C
A, B, C, D and E are 5 consecutive points on a straight line. If BC = 2CD, DE = 4, AB = 5 and AC = 11, what is the length of AE?	Pick one:	A) 21	B) 26	C) 30	D) 18	E) 16

Solution: A-----B----C--------18----E   Given: 18E = 4 - (i)   AB = 5 - (ii)   AC = 11 - (iii)   BC = 2C18 - (iv)   From (ii) and (iii), BC = 6   From (iv), C18 = 3   Length of AE = AC + C18 + 18E = 11 + 3 + 4= 
11 + 3 + 4 = 18
18   Correct Option: 18
Answer: D
The top and bottom of a tower were seen
to be at angles of depression 30° and 60° from the top of a
hill of height 100 m. Find the height of the tower	Choose the correct answer.
A) 64.67 m  B) 66.67 m  C) 68.67 m  D) 56.67 m  E) 46.67 m

Solution: 66.67 my making A diagram   AC represents the hill and DE represents the pole   Given that AC = 100 m   angleXAD = angleAD66.67 m = 30° (∵ AX || 66.67 mD )   angleXAE = angleAEC = 60° (∵ AX || CE)   Let DE = h   Then, 66.67 mC = DE = h, A66.67 m = (100-h) (∵ AC=100 and 66.67 mC = h), 66.67 mD = CE   tan 60°=ACCE=>3√=100CE=>CE = 1003√--- (1)   tan 30°=A66.67 m66.67 mD=>13√=100−h66.67 mD=>13√=100−h(1003√)   (∵ 66.67 mD = CE and Substituted the value of CE from equation 1 )=>(100−h)=13√×1003√=1003=33.33=>h=100−33.33=66.67 m   i.e., the height of the pole = 66.67 m   ANSWER:66.67 m
Answer: B
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
Choose the correct answer
A) Rs.6725 B) Rs.6727 C) Rs.6908 D) Rs.6725 E) Rs.6728

Solution: CP = SP * (100/(100 + profit%))   = 8339(100/124) = Rs.6725.   Answer: Rs.6725
Answer: D
A customer pays 80 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?  Options:
A) 100	B) 40	C) 70	D) 90	E) 20

Solution: Let x be the original price.   x - 20 = 80   x - 20 + 20 = 80 + 20   x + 0 = 100   x = 100   100nswer is 100
Answer: A
An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.90 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?  Answers
A) 130,000 B) 300,000 C) 380,000 D) 400,000 E) 420,000

Solution: Total royalties for first 100.000 books = .8*100,000= 80,000   Total royalties for the rest of the books = 260,000-80,000 = 180,000   Remaining books = 180,000/0.9 = 200,000   Total books = 200,000+100,000 = 300,000 Answer 300,000
Answer: B
Look at this series: 2, 4, 6, 8, 10, ... What number should come next?
Choose the correct answer.
A) 10
B) 11
C) 16
D) 13
E) 12

Solution: E   12   This is a simple addition series. 12ach number increases by 2.
Answer: E
Nitin ranks 27th in a class of 89 students. What is rank from the last ? Choose the correct option:  A) 63  B) 65  C) 67  D) 87  E) 89

Solution: Explanation:   Number students behind the nitin in rank = (89 - 27)= 
(89 - 27) = 62
62   Nitin is 63th from the last   63nswer: 63) 63
Answer: A
If a woman buys 700 pencils for $70 and sold them for $3 dollars for a 10 pack, determine her profit per pack.  Choose the correct choice
A) 2 B) 3 C) 20 D) 30 E) 70

Solution: Cost of 700 pencils = $70   700 pencils/$70 = 10 pencils for $1   Sold 10 pencils for $3   Profit per 10 pencils = $(3-1)= 
(3-1) = 2
$2 per pack   Therefore, her profit is $2 per 10 pack   answer :2
Answer: A
The average of the daily income of A, B and C is Rs . 60 . If B earns Rs . 20 more than C and A earns double of what C earns. What is the daily income of C ? Choose the correct choice from the following answers
A) Rs. 70	B) Rs. 60	C) Rs. 40	D) None of these	E) Cannot be determined

Solution: Answer   Let C's earning = Rs. y.   Then, B's earning = Rs. (y + 20)   and A's earning = Rs. 2y   ∵ 2y + y + 20 + y= 3 x 60   ⇒ 4x = 160   ∴ x = 40   Rs. 40orrect Option: Rs. 40
Answer: C
Insert the missing number
2, 9, 28, 65, ...
Choose the correct option
A) 126	B) 195	C) 121	D) 103	E) 112

Solution: the series are 2,9,28,65,126   logic is 1cube+1,2cube+1, 3cube+1,4cube+1, 5cube+1   so the answer is 126   126NSWER:126
Answer: A
20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability C that one more throw to this series will increase the mean score? Choose the correct answer: A) 1/6 B) 1/3 C) 1/2 D) 2/3 E) 5/6

Solution: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.   Thus probability 1/2 is 1/2.1/2
Answer: C
Find the total number of prime factors in the expression (4)^13 x (7)^5 x (11)^2	Choose the correct choice from the following answers: A) 26 B) 22 C) 25 D) 27 E) 33

Solution: (4)^13x (7)^5 x (11)^2   = (2 x 2)^13 x (7)^5 x (11)^2   = 2^13 x 2^13 x7^5x 11^2   = 2^26 x 7^5 x11^2   Total number of prime factors = (26 + 5 + 2)= 
(26 + 5 + 2) = 33
33.   Answer is 33.
Answer: E
P is three times as fast as Q and working together, they can complete a work in 6 days. In how many days can Q alone complete the work?
Choices:
A) 16  B) 77  C) 88  D) 55  E) 8

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 6 days, which means Q can do the work in 24 days.   Hence, P can do the work in 8 days.   Answer:8
Answer: E
If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 25 overs in an ideal case scenario?
Options
A) 900 B) 850 C) 828 D) 825 E) None

Solution: Solution:   828   Explanation:   For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:    6 * 5 + 3= 
 6 * 5 + 3 = 33
33   But this will have to go like it only till the 24th over. In the 25th over, he can hit a six in the last ball as well as that will be the last ball of his destination.   Thus runs for the 25th over will be  6 * 6= 
 6 * 6 = 36
36.   Hence the maximum runs= 33 * 24 + 36= 
33 * 24 + 36 = 828
828   Answer 828
Answer: C
Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is:  Choose the correct choice from the following answers.
A) 1000	B) 2000	C) 2300	D) 3400	E) 2830

Solution: Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.   Then, 4x + 9y = 13400 -- (i)   And, 10% of 4x + 20% of 9y = 1880   2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)   Solving (i) and (ii), we get : x = 2000 and y = 600.   Cost price of each horse = Rs. 2000.   Answer: Option 2000
Answer: B