MU-NLPC/Calc-aqua_rat huggingface dataset:
In a house, there are dogs, cats and parrot in the ratio 3:7:5. If the number of cats was more than the number of dogs by a multiple of both 9 and 7. What is the minimum number of pets in the house?  Choose the correct choice from the following: A) 945 B) 630 C) 252 D) 238 E) None of these

Solution: Explanation :   Let, the number of Dogs, Cat and Parrots be 3k, 7k and 5k respectively.   Then, According to the question,   =>7k−3k=63p. (where p is any positive integer).   As the number is a multiple of both 9 and 7, it has to be multiple of 63.   =>k=63p/4.   Minimum value of p for which k is a natural number is 4.   Thus, k=63.   Hence, the number of pets are (63x5) + (63x3) + (63x7) i.e 315 +189+ 441= 945.   945nswer : 945
Answer: A
A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?	Choose the correct choice from the following options.
A) $15,200	B) $15,500	C) $15,800	D) $16,000	E) $16,400

Solution: Let the salary for each person be 14. Thus, the bakery ends up getting  2 + 3*3= 
 2 + 3*3 = 11
11 as extra. This again has to be divided among 6 people. 12/6= 2 which makes it  14+2= 
 14+2 = 16
16. Thus, as it is 11/6, it will be somewhere close to 16 and less than that. Also, 1/6= 0.166. Thus 10/6 = 1.66 which gives the final salary after redistribution as 15.66. Correct answer is C.   _________________
Answer: C
One water pump can fill half of a certain empty tank in 4 hours. Another pump can fill half of the same tank in 4.5 hours. Working together, how long will it take these two pumps to fill the entire tank?  Choices
A) 1 7/13 B) 4 5/8 C) 3 1/4 D) 4 4/17 E) 3 1/2

Solution: One pump can fill a tank in 4 hours and another in 4.5 hours   so the rate at which both can half fill the tank is (1/4+1/4.5) => 17/36   Thus half of the tank can be filled in 36/17   so for filling the complete tank => 36/17*2 = 72/17 =4 4/17   ANSWER:4 4/17
Answer: D
Two numbers are less than third number by 35% and 37% respectively. How much percent is the second number less than by the first
Select
A) 8%
B) 10%
C) 33%
D) 41%
E) 42%

Solution: Let the third number is x.   then first number = (100-35)= 
(100-35) = 65
65% of x=65x/100   Second number is (63x/100)   Difference =65x/100 - 63x/100 = x/50   So required percentage is, difference is what percent of first number   (x/50 * 100/65x * 100 )% = 33% ANSWER :33%
Answer: C
Which of the following is closest to the difference between sum of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?	Choose the correct choice from the following answers:
A) 2.82
B) 2.72
C) 1.82
D) 1.72
E) 0.82

Solution: First term = 1/2 +1/3 +1/4 +1/5 +1/6 +1/7 +1/8 + 1/9   Second term = 1/2 * 2/3 * 3/4 * 4/5 * 5/6 * 6/7 * 7/8 * 8/9 * 9/10 = 1/10   First term - Second term = 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 +1/8 + 1/9 - 1/10   Now rearrange the above equation for simplification:   = (1/2 + 1/5 - 1/10) +( 1/3 + 1/6 + 1/9) + (1/4 + +1/8) +1/7   = 6/10 + 11/18 + 3/8 +1/7   6/10 , 11/18, 3/8 are approximately equal to 0.5   =0.5+0.5+0.5+0.14= 
0.5+0.5+0.5+0.14 = 1.64
1.64   The closest answer choice is 1.72
Answer: D
What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?  Choose the correct choice from the following answers:
A) Rs.325
B) Rs.545
C) Rs.560
D) Rs.550
E) None of these

Solution: Explanation:   Let each instalment be Rs.x .   Then, [x + (x × 12 × 1)/100] + [ x + (x × 12 × 2)/100] + x =1092   ( 28x/25 ) + ( 31x/25 ) + x = 1092   (28x + 31x + 25x) = (1092 * 25)   x = (1092 × 25)/84= 325   ∴ Each instalment = Rs. 325   Rs.325nswer: Rs.325
Answer: A
Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 29 have long fur, 17 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?  Choose one
A) 26  B) 19  C) 11  D) 8  E) 9

Solution: No of dogs=45   Long fur=29   Brown=17   Neither long fur nor brown=8   Therefore, either long fur or brown=45-8= 
45-8 = 37
37   37=29+17-Both   Both=9   Answer 9
Answer: E
A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?	Choose one
A) 234354  B) 243435  C) 243445  D) 245667  E) 220030

Solution: (555 + 445) * 2 * 110 + 30 = 220000 + 30= 
220000 + 30 = 220_030
220030   220030
Answer: E
The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = \\frac{22}{7}\\) in your calculations.
Choose the correct choice from the following answers:
A) 1696 sq m
B) 1694 sq m
C) 1594 sq m
D) 1756 sq.m
E) 1896 sq.m

Solution: Explanatory Answer   The cow can graze the area covered by the circle of radius 19m initially, as the length of the rope is 19m.   Area of a circle = π * (radius)2   Therefore, the initial area that the cow can graze = 22/7 * 19(2) sq m.   When the length of the rope is increased to 30m, grazing area becomes = 22/7 * 30(2) sq m.   The additional area it could graze when length is increased from 19m to 30m   = 22/7 * (30square - 19square) sq m.   22/7 * (30 + 19)(30 - 19) = 22/7 * 49 * 11= 
22/7 * 49 * 11 = 1_694
1694 sq m.   Choice 1694 sq m
Answer: B
A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 20 per kg, then his gain percent is	Select:
A) 7%	B) 13%	C) 14%	D) 15%	E) 16%

Solution: Explanation:   Suppose he bought 5 kg and 3 kg of tea.   Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.   Selling price = Rs. (8 x 20) = Rs. 160.   Profit = 160 - 150= 
160 - 150 = 10
10   So, Profit %= (10/150) * 100 = 7%   Option 7%
Answer: A
If a man can cover 24 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Choose the correct choice from the following answers
A) 118 km
B) 162 km
C) 324 km
D) 1887 km
E) 177 km

Solution: 24 m/s = 24 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 24 * 18/5 * 15/4= 
24 * 18/5 * 15/4 = 324
324 km.   Answer: 324 km
Answer: C
If 7 cats can kill 7 rats in 7 minutes, how long will it take 100 cats to kill 100 rats?
Select the correct option.
A) 5 minutes
B) 6 minutes
C) 7 minutes
D) 8 minutes
E) 9 minutes

Solution: It will take 7 minutes for 100 cats to kill 100 rats.   1 cat can kill 1 rat in 7 minutes, so 100 cats can kill 100 rats in 7 minutes   Answer 7 minutes
Answer: C
An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?	Choose one:
A) 4%
B) 4.04%
C) 4.15%
D) 4.34%
E) 5%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = 404 x 100 % = 4.04%   100 x 100   4.04%
Answer: B
A shopkeeper sold an article for Rs 2564.36. Approximately what was his profit percent if the cost price of the article was Rs 2300 Choose the correct choice from the following.
A) 4%	B) 5%	C) 6%	D) 7%	E) 12%

Solution: 12%xplanation:   Gain % = (264.36*100/2300) = 11.49 % = 12% approx   Option 12%
Answer: E
A train covers a distance of 12 km in 10 min. If it takes 11 sec to pass a telegraph post, then the length of the train is?	Choose the correct choice from the following choices:	A) 177 m	B) 189 m	C) 220 m	D) 178 m	E) 188 m

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 11= 
20 * 11 = 220
220 m.   Answer: 220 m
Answer: C
A cricketer scored 152 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
Choose one: A) 46.2% B) 54.54 % C) 60.52% D) 70% E) None of these

Solution: Explanation :   Number of runs made by running = 152 - (12 x 4 + 2 x 6)   = 152 - (60)= 
152 - (60) = 92
92   Now, we need to calculate 92 is what percent of 152.=> 92/152 * 100 = 60.52 %   Answer : 60.52%
Answer: C
Michael is interested in dividing all of his boxed food equally among the shelves in his pantry. Unfortunately, the boxes don't divide evenly. It turns out that Michael will need to add three more shelves to the pantry and throw away four boxes of food. Which of the following can describe the initial number of boxes of food and the initial number of pantry shelves (in the order boxes of food; shelves)?
Choose the correct choice from the following choices:
A) 71; 4. B) 28; 6. C) 65; 7. D) 53; 4. E) 45; 6.

Solution: Option D.) Initially 53 boxes of food then reduced to 49 boxes of food; and Initially 4 pantry shelves then increased to 7 pantry shelves.   49 / 7= 
49 / 7 = 7
7 boxes of food per pantry shelf.
Answer: D
X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 44 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is : Choose the most appropriate option:
A) 39.6	B) 43	C) 40	D) 38	E) 29

Solution: Solution: 39.6verage speed = 2XY / X+Y   = 2*44*36 / 44+36   = 39.6   39.6nswer : 39.6
Answer: A
If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
6 = 36
Then 24 = ?
Hint: Its a logic Riddle not a mathematical riddle Choose the correct choice from the following answers:
A) 1
B) 2
C) 4
D) 6
E) 8

Solution: 4   24   As stated   4=24 => 24=4   Answer is 4
Answer: C
What amount does Kiran get if he invests Rs.7680 at 8% p.a. compound interest for two years, compounding done annually? Choose the correct choice from the following.
A) 8957  B) 8978  C) 7890  D) 3408  E) 2886

Solution: 8957= P{1 + R/100}n   => 7680{1 + 8/100}2   = Rs.8957   8957nswer: 8957
Answer: A
A pool which was 3/4 full to begin with, was filled at a constant rate for 5/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?	Choose the correct choice from the following options.
A) 8 hrs 45 mins.  B) 9 hrs.  C) 9 hrs 30 mins.  D) 11 hrs 40 mins.  E) 15 hrs 33 mins

Solution: The pool was 3/4 full initially.   In 5/3 hrs, it was filled to 6/7 of its capacity.   Therefore, in 5/3 hrs, 6/7 - 2/3 was the amount of volume filled.   So, 5/3 hrs = 6/7 - 3/4 = 3/28   Therefore, for filling the vessel from empty to full, you would require 5/3 * 28/3 = 35/4 = 15 Hrs 33 Mins.   Hence 15 hrs 33 mins
Answer: E
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 294, what is the least possible value of n? Choose the correct choice from the following answers:
A) 8
B) 10
C) 12
D) 14
E) 16

Solution: 294 = 2*3*7*7, so n must be at least 14.   The answer is 14.
Answer: D
If y = 30p, and p is prime, what is the greatest common factor of y and 20p, in terms of p?  Pick: A) p B) 2p C) 5p D) 10p E) p^2

Solution: y = 30p = 2*3*5*p   20p = 2^2*5*p   The greatest common factor of 30p and 20p is the product of all the common prime factors, using the lower power of repeated factors. The greatest common factor is 2*5*p = 10p   The answer is 10p.
Answer: D
If A`s salary is 20% less then B`s salary , by how much percent is B`s salary more than A`s ?  Choose one
A) 15% B) 41% C) 37% D) 25% E) 23%

Solution: Required percentage = [(20*100)/(100-20)= 
(20*100)/(100-20) = 25
25%.   Answer is 25%.
Answer: D
The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
Choose the correct choice:
A) 76 B) 28 C) 23 D) 98 E) 32

Solution: Let the initial number of members in the group be n.   Initial total weight of all the members in the group = n(48)   From the data,   48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23   Therefore there were 23 members in the group initially.   Answer:23
Answer: C
15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container M? Choose the correct choice
A) A:45
B) B:25
C) C:37.5
D) D:36
E) E:42

Solution: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.   1st Replacement   After the first replacement you have 37.5-15= 
37.5-15 = 22.5
22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.   The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.   Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.   Final Replacement   The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.   Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. C:37.5hoice C:37.5 is correct.
Answer: C
A train 150 m long crosses a platform 130 m long in 20 sec; find the speed of the train?  Choose the most appropriate option:
A) 50
B) 60
C) 55
D) 45
E) 53

Solution: D = 150 + 130= 
150 + 130 = 280
280   T= 20   S = 280/20 * 18/5 = 50 kmph.   50nswer: 50
Answer: A
If 5 - 5/X = 4 + 4/X, then X =  Choose the most appropriate option:
A) 1
B) 9
C) -1
D) 5/4
E) -4/5

Solution: We're given the equation 5 - 5/X = 4 + 4/X. We're asked for the value of X.   The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...   5X - 5X/X = 4X + 4X/X   We can then eliminate that denominator, which gives us....   5X - 5 = 4X + 4   9 = X   9
Answer: B
A dice is rolled twice. What is the probability of getting sum 9?  Choose the correct answer.
A) 1/9	B) 1/8	C) 1/7	D) 1/5	E) 1/2

Solution: Explanation:   Possible event = 6*6= 
6*6 = 36
36   Favourable outcomes= {(3, 6), {4, 5}, {5, 4}, (6, 3)}   Thus probability; favourable/total   = 4/36   => 1/9   1/9NSWER: 1/9
Answer: A
A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
Options
A) 20%  B) 25%  C) 33.33%  D) 40%  E) 35%

Solution: 100 * (b + f) - 100 * b = (25/100) * 100 * b   b = 4 * f   Percentage of f = (f / (b + f)) * 100 = (f/5f) * 100 = 20%   20%NSWER:20%
Answer: A
What number is obtained by adding the units digits of 734^98 and 347^81? Pick one.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: The units digit of 734^98 is 6 because 4 raised to the power of an even integer ends in 6.   The units digit of 347^81 is 7 because powers of 7 end in 7, 9, 3 or 1 cyclically. Since 81 is in the form 4n+1, the units digit is 7.   Then   6+7= 
  6+7 = 13
13.   The answer is 13.
Answer: D
If five boxes of fruit contain six different fruit in each box, and a fruit is randomly selected from each box, what is the probability of getting at least one pair of the same fruit?	Select the correct option:
A) 31/32	B) 4/9	C) 1/2	D) 5/49	E) 49/54

Solution: AT LEAST one pair of matching fruit.   First solve for NO matching fruit:   1st box = any fruit = 6/6   2nd box = not a match to the first = 5/6   3rd box = not a match to the 1st or 2nd = 4/6   4th box = not a match to the 1st, 2nd or 3rd = 3/6   5th box = not a match to the 1st, 2nd, 3rd or 4th = 2/6   (6/6)(5/6)(4/6)(3/6)(2/6) =   (1)(5/6)(2/3)(1/2)(1/3) = 60/648   5/54   5/54 is the probability of NO matching fruit, so...   1 - 5/54 = 49/54 = the probability of getting at least one matching pair of fruit.   Answer: 49/54
Answer: E
If c is 25% of a and 50% of b, what percent of a is b? Choose one.
A) 2.5% B) 50% C) 25% D) 35% E) 250%

Solution: Answer = 50%   25a/100 = 50b/100   b = 25a/50 = 50a/100 =50%
Answer: B
A is twice as fast as B. If B alone can do a piece of work in 10 days, in what time can A and B together complete the work?
Select.
A) 10/3 B) 8 C) 9 D) 7/3 E) 12

Solution: A can do the work in10/2 i.e., 5 days.   A and B's one day's work = 1/5+ 1/10 = (2 + 1)/10 = 10/3   So A and B together can do the work in 10/3 days.   10/3nswer: 10/3
Answer: A
If a carpenter completes 3/8th of his work in 6 days, then how many more days will he require completing his remaining work?  Answers
A) 10	B) 99	C) 77	D) 66	E) 72

Solution: Explanation:   As 3/8th of the work is completed, the work remaining is 5/8th of the total.   (3/8):6::(5/8):x   x = 6*(5/8)/(3/8)= 
6*(5/8)/(3/8) = 10
10   10NSWER: 10
Answer: A
A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $141 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist? Choose the correct choice from the following answers.
A) 5
B) 7
C) 9
D) 11
E) 13

Solution: $141 = 27*$5 + 2*$3   We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).   The number of $5 chocolates can be 27, 24, 21, 18, 15,...,3 for a total of 9 combinations.   The answer is 9.
Answer: C
Evaluate:59- 12*3*2 =?
Select:
A) 42	B) 51	C) 62	D) 72	E) 82

Solution: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right   12**2 = 4* 2= 
4* 2 = 8
8   Hence   59 - 12*3*2= 59- 8= 
59- 8 = 51
51   correct answer 51
Answer: B
Meg and Bob are among the 3 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
Answers.
A) 24
B) 30
C) 3
D) 90
E) 120

Solution: Total # of ways the race can be finished is 3!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 3!/2=3.   Answer: 3.
Answer: C
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the smallest sector?
Choose the correct answer:
A) 1/72
B) 1/36
C) 1/18
D) 1/12
E) 1/9

Solution: Largest angle = 80   Let, Difference between any two angles in A.P. = d   i.e. Sum of all angles will be   80 + (80-d) + (80-2d) + (80-3d) + (80-4d) + (80-5d) + (80-6d) + (80-7d) = 640 - 28d   But sum of all central angles in a circle = 360   i.e. 640 - 28d = 360   i.e. d = 280/28= 
280/28 = 10
10   Smallest Sector= (80-7d) = 80-7*10= 
80-7*10 = 10
10   Smallest sector as Fraction of entire circle= 10/360 = 1/36   Answer: option 1/36
Answer: B
If the equation x^2−6x=-k has at least one solution, which of the following must be true?
Pick one:
A) k > 9  B) k < −9  C) k = 9  D) k ≤ 9  E) k ≥ −9

Solution: x^2−6x=-k   => x^2−6x + k = 0   For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.   b^2-4ac ≥0   => 36 - 4*1*(-k) ≥0   => 36 - 4k ≥0   => k ≤9   Answer k ≤ 9
Answer: D
Look at this series: 544, 509, 474, 439, 404 ... What number should come next? Pick one.
A) 206 B) 408 C) 369 D) 507 E) 404

Solution: 369   This is a simple subtraction series. Each number is 35 less than the previous number.   369
Answer: C
If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 40 men in 3 days?
Options:
A) 65mtr.
B) 52mtr
C) 70mtr.
D) 112mtr.
E) 17mtr.

Solution: 20 men is 6 days can build 112 metres   25 men in 3 days can build = 112*(40/20)x(3/6)   = 112 meters   Answer: 112mtr..
Answer: D
Sherlock Homes and Dr. Watson have to travel from Rajeev Gandhi chowk to Indira
Gandhi International Airport via the metro. They have enough coins of 1, 5, 10 and 25
paise. Sherlock Homes agree to pay for Dr. Watson only if he tells all the possible
combinations of coins that can be used to pay for the ticket.
How many combinations are possible if the fare is 50 paise ?	Answers.
A) 52	B) 49	C) 45	D) 44	E) 42

Solution: Let the number of 1, 5, 10 and 50 paise coins required are x, y, z and w respectively.   So when paid total amount is: x + 5y + 10z + 25w, which is equal to the fare paid.   So, x + 5y + 10z + 25w = 50   The number of non negative integral solution of this equation will be equal to the   number of ways the fare can be paid.   x + 5y + 10z + 25w = 50   In this equation w can be either 0, 1 or 2   Case 1: When w is 2   No other coins are required to pay   So there is only one way to pay: (0, 0, 0, 2)   Total no of ways : 1   Case 2: When w is 1   x + 5y + 10z = 25   In this case z can have only three values possible: 0, 1 or 2   Case I: When z is 0   x + 5y = 25   possible values are: (25, 0, 0, 1), (20, 1, 0, 1), (15, 2, 0, 1), (10, 3, 0, 1),   (5, 4, 0, 1), (0, 5, 0, 1)   Case II: When z is 1   x + 5y = 15   possible values are: (15, 0, 1, 1), (10, 1, 1, 1), (5, 2, 1, 1), (0, 3, 1, 1)   Case III: When z is 2   x   + 5= 
  + 5 = 5
5   possible values are: (5, 0, 2, 1), (0, 1, 2, 1)   Total no of ways : 12   Case 3: When w is 0   x + 5y + 10z= 50   In this case z can have only three values possible: 0, 1, 2, 3, 4 or 5   Case I: When z is 0   x + 5y = 50   possible values are: (50, 0, 0, 0), (45, 1, 0, 0), (40, 2, 0, 0), (35, 3, 0, 0),   (30, 4, 0, 0), (25, 5, 0, 0), (20, 6, 0, 0), (15, 7, 0, 0), (10, 8, 0, 0), (5, 9, 0, 0),   (0, 10, 0, 0)   Case II: When z is 1   x + 5y = 40   possible values are: (40, 0, 1, 0), (35, 1, 1, 0), (30, 2, 1, 0), (25, 3, 1, 0),   (20, 4, 1, 0), (15, 5, 1, 0), (10, 6, 1, 0), (5, 7, 1, 0), (0, 8, 1, 0)   Case III: When z is 2   x + 5y = 30   possible values are: (30, 0, 2, 0), (25, 1, 2, 0), (20, 2, 2, 0), (15, 3, 2, 0),   (10, 4, 2, 0), (5, 5, 2, 0), (0, 6, 2, 0)   Case IV: When z is 3   x + 5y = 20   possible values are: (20, 0, 3, 0), (15, 1, 3, 0), (10, 2, 3, 0), (5, 3, 3, 0), (0,   4, 3, 0)   Case V: When z is 4   x + 5y = 10   possible values are: (10, 0, 4, 0), (5, 1, 4, 0), (0, 2, 4, 0)   Case VI: When z is 5   1 2 3 4 5 6 7 8 9   x + 5y = 0   possible values are: (0, 0, 5, 0)   Total no of ways : 36   So total no of ways = 1 + 12 + 36= 
1 + 12 + 36 = 49
49   ANSWER:49
Answer: B
Nirmal and Kapil started a business investing Rs. 9000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Rs. 4600, what was Kapil’s share initially ? Choose the correct answer:
A) Rs 2300 B) Rs 2400 C) Rs 2500 D) None of above E) Rs 3500

Solution: Explanation:   Nirmal:Kapil = 9000*12:(12000*6+6000*6) = 1:1   Kapils share = Rs. [4600 *(1/2)) = Rs. 2300   Option Rs 2300
Answer: A
There are t members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of t?  Choose one:
A) 11
B) 12
C) 15
D) 18
E) 22

Solution: Combinations of two persons, in which Michael was not selected = 55   number of ways two persons can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11   Thus, t = m + 1(Michael) = 12   option 12
Answer: B