MU-NLPC/Calc-aqua_rat huggingface dataset:
A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 2km on foot. His total journey is  Answers:
A) 16km	B) 10km	C) 12km	D) 24km	E) 25km

Solution: Explanation:   Let the journey be x km   Then, 1x/2 + 1x/3 +2 =x   5x +12 =6x   X = 12km   Answer: Option 12km
Answer: C
An electric wire runs for 1 km b/w some no: of poles. If one pole is removed the distance b/w each pole increases by 1 2/6 (mixed fraction). How many poles were there initially?  Pick one.
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: let there be x no. of poles   distance b/w them= 1/(x-1)   now when one pole is removed   distance bw each pole=1/(x-2)   now according to the question   1/(x-2) =8/6 (1/x-1)   on solving you will get x=5   ANSWER:5
Answer: B
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between 6* + 2 and 6* + 6, inclusive? Choose the most appropriate option
A) None	B) One	C) Two	D) Three	E) Four

Solution: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.   Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes in this range.   Nonenswer: None.
Answer: A
A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?  Choose the correct choice:
A) 102	B) 60	C) 75	D) 90	E) 95

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 544   16x = 544   x = 34.   Hence, total number of notes = 3x = 102   102nswer: Option 102
Answer: A
Two numbers have a H.C.F of 9 and a product of two numbers is 1800. Find the L.C.M of the two numbers?  Pick
A) 200	B) 150	C) 160	D) 170	E) 180

Solution: L.C.M of two numbers is given by   (Product of the two numbers) / (H.C.F of the two numbers) = 1800/9= 
1800/9 = 200
200.   200NSWER:200
Answer: A
eight books consisting of 5 financial management, 2 marketing management and Since the denominator will be 11! . And there is no way to divide 11 from numerator and denominator. Use a multiple of 11 in the denominator only answer 1 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.	Choose the correct choice from the following answers.
A) 1/1155
B) 1/5040
C) 1/256
D) 1/2255
E) 1/1455

Solution: Since the denominator will be 8! . And there is no way to divide8 from numerator and denominator. Use a multiple of 8in the denominator only answer   1/256
Answer: C
The cost of 3 kg of sugar is $ 60. What will the cost of 8 kg of sugar be?
Choose the correct choice:  A) 20  B) 40  C) 80  D) 160  E) 180

Solution: This is a situation of direct variation, now we solve using unitary method.   Cost of 3 kg of sugar = $ 60   Cost of 1 kg of sugar = $ 60/3= 
60/3 = 20
$ 20   Cost of 8 kg of sugar= $ 20 × 8   Therefore, cost of 8 kg of sugar = $ 160   ANSWER -160
Answer: D
Nancy works 4 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? Choose the correct answer:  A) a) 3y(7x+2xy)  B) b) 3x+12y  C) c) 3xy(7x+2)  D) d) 3x(2y+7)  E) e) 2x(3y+4)

Solution: Payment of a week for 3 days a week = $4x   Payment of 4 weeks for 3 days a week = $4x*4 = $16x   Payment of a week for y days overtime a week 4 *4= 
4 *4 = 16
$16x   Payment of a week for y days overtime a week= $4x+$2xy   Payment of 3 weeks for y days overtime a week = ($4x+$2xy)*3   Total e) 2x(3y+4)arnings = $16x + ($4x+$2xy)*3 = 28x+6xy =2x(3y+14)   Answer: option e) 2x(3y+4)
Answer: E
If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
Choose the correct choice from the following answers:
A) 2
B) 4
C) 6
D) 3
E) 8

Solution: D   3   Given number = 97215x6   (6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.   x = 3
Answer: D
If y = ||x – 3| – 2|, for how many values of x is y = 5?	Choose the correct choice from the following choices:
A) 2  B) 1  C) 3  D) 4  E) 5

Solution: y = ||x – 3| – 2| can be 4 only and only when X-3= +/-7. so there are 2 values of X   2nswer : 2
Answer: A
Sid left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?
Choose the correct choice from the following.
A) 40
B) 200
C) 266
D) 267
E) 600

Solution: In order not to lose money because of the change Sid's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.   Answer: 267.
Answer: D
An error 6% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?  Choose the correct option: A) 14.05% B) 14.02% C) 14% D) 13% E) 12.36%

Solution: Percentage error in calculated area   =(6+6+(6Ã—6)/100)%   =12.36%   ANSW12.36%R:12.36%
Answer: E
A group of men decided to do a work in 50days, but 10 of them became absent. If the rest of the group did the work in 60days, Find the original number of men? Choose the correct choice from the following answers:
A) 60 B) 50 C) 40 D) 100 E) 25

Solution: Original number of men = 10*60 / (60-50)= 
10*60 / (60-50) = 60
60   60nswer is 60
Answer: A
What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?
Choose one.
A) 72 * 8!
B) 144 * 8!
C) 36 * 8!
D) 9!
E) None of these

Solution: Solution:   As every girl friend should get one gift.   The number of ways 8 distinct gifts can be selected is: 9C8 = 9 ways.   The number of ways each GF gets one gift each out of these 8 selected gifts 8!   Total number of ways 8 gifts can be distributed is 9 *8!.   Now the last one gift can be given to any of the 8 GF hence, the total number of ways of distributing =(9 *8! *82)= 36 * 8! ways.   Answer: Option 36 * 8!
Answer: C
The area of a rectangle is 63 sq m. The width is two meters shorter than the length. What is the width?  Choose the correct choice from the following choices
A) 9	B) 7	C) -9	D) 11	E) 6

Solution: a = l x w   w = l - 2   l = w + 2   a = (w + 2 ) x w   a = w^2 + 2 x w   63 (  + 2 )= 
(  + 2 ) = 2
w^2 + 2 x w   63= w^2 + 2w   0 = w^2 + 2w - 63   0 = (w + 9)(w - 7)   w = -9 and w = 7, width cannot be negative so w = 7   Answer is 7
Answer: B
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 30 ps per meter is? Choose the correct choice from the following choices
A) s.122	B) s.105	C) s.125	D) s.120	E) s.121

Solution: 3x * 2x = 3750 => x = 25   2(75 + 30) = 210 m   210 * 1/2 = Rs.105   Answer:s.105
Answer: B
In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest? Answers:
A) 8 1/3 B) 8 1/9 C) 8 1/6 D) 8 1/2 E) 8 1/1

Solution: (4000*3*R)/100 = (5000*5*4)/100   R = 8 1/3   8 1/3nswer: 8 1/3
Answer: A
In one hour a boat goes 11 km long the stream and 5 km against the stream.The speed of the boat in still water is? Choose the correct answer: A) 7 B) 8 C) 6 D) 5 E) 1

Solution: Speed in still water 7 = ½ ( 11+5) km/hr 7= 8 kmph   7nswer: 7
Answer: A
what is the value of y if the greatest common divisor of (y-4)!,(y+1)!, and (y+2)! is 720.  Choose the correct option:  A) 12  B) 10  C) 9  D) 7  E) 8

Solution: GCD of (y-4)!,(y+1)!, and (y+2)! is 720. Find y.   Best way to find n is substitute each of the answer and find out the correct one.   Only option B gave the correct answer.   Option B: 10 and find GCD or 6!, 11! and 12!. 6! itself is 720 and 6! which is contained in the other two factorials. This satisfies the condition, hence answer is 10.   Answer is 10.
Answer: B
The monthly rent of a shop of dimension 18feet × 22feet is Rs.2244. What is the annual rent per square foot of the shop? (a) Rs. 5(2/3) Choose the correct answer:
A) 43 B) 56 C) 68 D) 87 E) 92

Solution: Sol. Monthly rent per square feet = 2244/(18*22)   & Annual rent per square feet   =12*(2244/(18*22))= 
12*(2244/(18*22)) = 68
68   68
Answer: C
A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?	Choose the correct choice from the following options:  A) 202  B) 200  C) 209  D) 207  E) 201

Solution: The number of ways to select two men and three women = ⁵C₂ * ⁶C₃   = (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)= 
(5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2) = 200
200   Answer:200
Answer: B
What will be the fraction of 50%  Choose the most appropriate option
A) 1/4 B) 1/2 C) 1/10 D) 1/11 E) None of above

Solution: Explanation:   It will 50*1/100 = 1/2   Option 1/2
Answer: B
The average of six integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers? Choose the correct choice from the following.
A) 45
B) 62
C) 75
D) 83
E) 90

Solution: When it comes to averages, we know thataverage value = (sum of n values)/n   We can rewrite this into a useful formula:sum of n values = (average value)(n)   The average of five integers is 63   So, the sum of ALL 5 integers = (63)(6) =378   The average of three of the integers is 65   So, the sum of the 3 integers = (65)(3) =195   So, the sum of the 2 REMAINING integers =378-195= 
378-195 = 183
183   If the sum of the 2 REMAINING integers=183, and we want to minimize one value, we must MAXIMIZE the other value.   100 is the maximum value so let 1 integer = 100, which means the other must equal 83   Answer: 83
Answer: D
Pipe A can fill a tank in 3 hours. Due to a leak at the bottom, it takes 6 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank? Select the correct option:
A) 67	B) 88	C) 4.5	D) 26	E) 12

Solution: Let the leak can empty the full tank in x hours 1/3 - 1/x = 1/6   => 1/x = 1/2 - 1/6 = 1/4.5   => x = 4.5 Answer:4.5
Answer: C
Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?	Choose the correct answer
A) 8 1/9	B) 8 1/0	C) 8 1/4	D) 8 1/3	E) 8 1/1

Solution: 3/12 + (3 + x)/15 = 1   x = 8 1/4   Answer: 8 1/4
Answer: C
If mn ≠ 0 and 25 percent of n equals 37 1/2 percent of m, what is the value of 12n/m? Select the correct option
A) 18  B) 323323  C) 8  D) 3  E) 98

Solution: Given : 25 percent of n equals 37(1/2) percent of m => (25/100)*n = (75/200)*m => 2n = 3m.   12n/m = 6*2n/m = 6*3m/m = 18. Hence 18.
Answer: A
In a group of 3 boys and 7 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?  Choose the correct choice from the following choices
A) 145	B) 175	C) 205	D) 235	E) 265

Solution: Number of ways to select four children is 10C4 = 210   Number of ways to choose only girls is 7C4 = 35   Number of ways that at least one boy is selected is  210 - 35= 
 210 - 35 = 175
175   The answer is 175.
Answer: B
what is the compound interest on rs:30,000 for 4 months at the rate of 5% per annum
Choose the correct answer:
A) 501.13	B) 502.13	C) 503.13	D) 504.13	E) 505.13

Solution: it is monthly compound   rate=5/12% per month   30000*(1+5/1200)^4-30000=503.13   ANSWER:503.13
Answer: C
A company has 15 managers and 75 associates. The 15 managers have an average salary of $120,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?	Options
A) $35,000 B) $45,000 C) $55,000 D) $65,000 E) $75,000

Solution: The 15 managers have an average salary of $120,000. The sum of their salaries is:   sum = (average)*(number of salaries) = $120,000*15 = $1,800,000   The 75 associates have an average salary of $30,000. The sum of their salaries is:   sum = (average)*(number of salaries) = $30,000*75 = $2,250,000   When we add those two sums, we get the total payroll of all 90 employees.   $1,800,000 + $2,250,000 = $4,050,000   So, we have 90 employees, and together they earn $4,050,000, so the average is   average = $4,050,000 ÷90 = $45,000   Answer: $45,000.
Answer: B
The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio o  Choose the correct choice from the following answers:
A) 6:5  B) 4:7  C) 3:5  D) 5:7  E) 8:9

Solution: 4:5   3:2   -------   12:15:10   12:10   ==>6.5   6:5NSWER 6:5
Answer: A
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction Q of the sum of the 21 numbers in the list?  Choices
A) 1/20	B) 1/6	C) 1/5	D) 4/21	E) 5/21

Solution: This is how I used to calculate which I think works pretty well:   if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)   n + 20a = S   the question tells us that   n = 4a   plug this back into the first equation and you get that the sum is 24a   4a + 20a = 24a   therefore fraction Q of n to the total would be   4a/24a or 1/6   answer 1/6 4  + 20= 
 4  + 20 = 24
24a   therefore fraction Q of n to the total would be   4a/24a or 1/6   answer 1/6
Answer: B
A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Choose the correct choice from the following choices.
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Speed downstream = d/t = 85/(2 1/2) = 34 kmph   Speed upstream = d/t = 45/(2 1/2) = 18 kmph   The speed of the stream = (34 - 18)/2= 
(34 - 18)/2 = 8
8 kmph   Answer: 8
Answer: D
If p is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT  Choose the correct answer:	A) z - w = 3(y - x)	B) p is divisible by 8	C) The average of w, x, y, and z is odd	D) p is divisible by 4	E) w + x + 8 = y + z

Solution: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.   p = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12   Focus on the easiest options first. You see that p is not divisible by 8. Answer (p is divisible by 8)
Answer: B
A wildlife preserve is being planned for 8,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population?  Choose the correct choice:
A) 340 B) 330 C) 320 D) 310 E) 890

Solution: Number of rhinos = 8000   Watering area = 10,000 acres   Number of rhino to increase by 10 percent ,then number of rhino = 8800   Grazing area for a rhino = 100   Total grazing area for 8800 rhinos= 8800 * 100 = 8,80,000   Total area required for the wildlife preserve = 8,80,000 + 10,000 = 8,90,000 = 890 * 1000   Answer 890
Answer: E
A train 560 m long, running with a speed of 63 km/hr will pass a tree in? Choose the correct answer.
A) 15
B) 16
C) 17
D) 28
E) 32

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 560 * 2/35= 
560 * 2/35 = 32
32 sec   Answer: Option 32
Answer: E
An old priest fell on a bottom of the well of a church.
The well is 17 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ? Choose the correct answer
A) 13-days B) 14-days C) 11-days D) 19-days E) 10-days

Solution: 13-days   13-days   In 12-days, he will climb 12-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: A
Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Choose the correct option:	A) 5.8%	B) 5.5%	C) 5.6%	D) 2.6%	E) 5.3%

Solution: C.P. of 1 toy = 375/12 = Rs. 31.25   S.P of 1 toy = Rs. 33   Profit = 1.75/31.25 * 100 = 28/5= 
28/5 = 28/5 = around 5.6
5.6%   Answer: 5.6%
Answer: C
A piece of cloth cost Rs 35. if the length of the piece would have been 4m longer and each meter cost Re 1 less , the cost would have remained unchanged. how long is the piece? Pick one
A) 5 mtrs  B) 10 mtrs  C) 12 mtrs  D) 15 mtrs  E) 18 mtrs

Solution: If length of piece is x and cost per mtr is C, then   x*C = 35 or C =35/x   (x+4)*(C-1) = 35 or x*C +4C-x -4 =35 or 35+4C-x -4 = 35   4C-x =4   4*(35/x)-x =4   x= 10 mtrs   ANSWER:10 mtrs
Answer: B
I was x years old 5 years ago. How old shall I be 7 years hence ?  Choose the correct choice: A) x +5 B) x + 7 C) x + 12 D) x + 13 E) None of these

Solution: given that my age 5 years ago is x years   hence my present age be x+5 years   so my age after 7 years from now = x+5+7   which is equal to x+12   ANSWER:x + 12
Answer: C
What is the lowest possible common multiple of 2 distinct integers, each greater than 64? Choose the correct choice from the following answers.
A) 68
B) 69
C) 130
D) 68^2
E) 68·69

Solution: In order to get the lowest LCM, we have to take the first number as 65 and the next number as its multiple.   So, I can take 65 and 130 as two distinct numbers, such that Lowest LCM = 130.   Answer should be 130.
Answer: C
By selling a bat for Rs.360/- a man loses 10% what is that bat cost price
Answers
A) s.400/-	B) s.630/-	C) s.700/-	D) s.780/-	E) s.800/-

Solution: 90 % ------> 360 (90 * 4 = 360)   100 % ------>400 (100 * 4 = 400)   Cost price = Rs.400/-   s.400/-)
Answer: A
An equity analyst needs to select 3 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 6, in how many ways can she choose and rank her top 3 picks?  Choices:
A) 210  B) 150  C) 120  D) 420  E) 840

Solution: Number of ways of choosing 3 stocks = 61203   Number of ways of ranking the chosen stocks = 3!   Hence total ways of chosing and ranking = 61203 * 3!= 120   120orrect Option: 120
Answer: C
In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg? Pick one:
A) 5/6  B) 4/9  C) 5/7  D) 5/2  E) 5/8

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6   5/6nswer:5/6
Answer: A
An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 6. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
Choose the correct choice from the following answers:
A) s 1200	B) s 1500	C) s 1600	D) s 1900	E) s 900

Solution: Explanation :   Let P = Faruk, Q = Vasim, R = Ranjith   Let P = 3x, Q = 5x and R = 6x.   Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 1800.   Hence, (R - p) = (1800 - 900)= 
(1800 - 900) = 900
900   Answer : s 900
Answer: E
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
Choose the most appropriate option.
A) 84.33%	B) 83.39%	C) 83.93%	D) 83.93%	E) 83.33%

Solution: Explanation:   Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.   Answer: Option 83.33%
Answer: E
A bag contains 4 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
Answers:
A) 19/20
B) 17/20
C) 3/5
D) 8/10
E) 9/40

Solution: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.   Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.   P(A) = (4/7) x (3/5) =12/35.   P(B) = (3/7) x (2/5) = 6/35.   Hence, the required probability is P(A) + P(B) which is nothing but 3/5.   ANSWER:3/5
Answer: C
P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
Select:	A) 5 days	B) 10 days	C) 14 days	D) 22 days	E) 26 days

Solution: Explanation :   Work done by P in 1 day = 1/20   Work done by Q in 1 day = 1/12   Work done by P in 4 days = 4 × (1/20) = 1/5   Remaining work = 1 – 1/5 = 4/5   Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15   Number of days P and Q take to complete the remaining work = (4/5) / (2/15)= 
(4/5) / (2/15) = 6
6   Total days= 4 + 6= 
4 + 6 = 10
10   Answer : Option 10 days
Answer: B
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 5.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?  Choose the correct choice from the following answers:
A) (320 - y)/(5x)
B) (y +200)/(5x)
C) 5(80 - y)/(4x)
D) (y + 400)/(4x)
E) (4y + 320)/(5x)

Solution: Ans (y +200)/(5x)   Plug some numbers   Let y = 40 houses and x (  +200)/(5 )= 
(  +200)/(5 ) = 40
40 houses and x= 20   then they painted 20 houses per week   as painters were added to the group , the rate of the group increased to 5.25 x => 5.25 * 20= 
5.25 * 20 = 105
105 houses per week   total time they took= (40/20) + (40/1055) = 2.4 weeks   Putting the values of x and y in equation (y +200)/(5x)   (y +200)/(5x) = (40+200)/5*20 = 240/100= 
240/100 = 12/5 = around 2.4
2.4
Answer: B
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Pick one:
A) 2345  B) 3456  C) 2334  D) 3456  E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
On dividing a number by 357, we get 42 as remainder.On dividing the same number by 17, what will be the remainder ?
Choose the correct choice from the following answers:  A) 4  B) 5  C) 8  D) 7  E) 2

Solution: Let x be the number and y be the quotient.Then,   x=357*y+42   =(17*21*y)+(17*2)+8   =17*(21y+2)+8.   Required number =8.   Answer is 8
Answer: C
A can do a piece of work in 80 days. He works at it for 10 days B alone finishes the remaining work in 42 days. In how much time will A and B working together, finish the work?  Pick one:
A) 25	B) 30	C) 20	D) 32	E) None of them

Solution: Work done by A in 10 days =(1/80*10)=1/8   Remaining work = (1- 1/8) =7/ 8   Now,7/ 8 work is done by B in 42 days.   Whole work will be done by B in (42 x 8/7) = 48 days.   A’s 1 day's work = 1/80 and B's 1 day's work = 1/48   (A+B)'s 1 day's work = (1/80+1/48)=8/240=1/30   Hence, both will finish the work in 30 days.   Answer is 30.
Answer: B
X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 16days. How long will Y take to complete the work?  Choose the correct choice
A) 10 B) 12 C) 15 D) 18 E) 20

Solution: Work done by X in 8days = 8*1/40 = 1/5   Remaining work = 1 - 1/5 = 4/5   4/5 work is done by Y in 16days   Whole work will be done by Y in 16*5/4= 
16*5/4 = 20
20days   Answer is 20
Answer: E
It has 20L mixutre conatins milk and water in the ratio 3:5,replace 4 litres of mixture with 4 litres of water what is the final ratio of milk and water.
Choose the correct choice.
A) 2:7  B) 3:7  C) 4:7  D) 5:7  E) 6:7

Solution: Full mixture has 7.5L milk 12.5L water if we fetch 4L mixture according to ratio it will be 1.5L milk & 2.5L water,replace this mixture from the water then it will be 6L milk and 14L water then ratio will be 6/14=3:7.   ANSWER:3:7
Answer: B