MU-NLPC/Calc-aqua_rat huggingface dataset:
Company KW is being sold, and both Company A and Company B were considering the purchase. The price of Company KW is 30% more than Company A has in assets, and this same price is also 100% more than Company B has in assets. If Companies A and B were to merge and combine their assets, the price of Company KW would be approximately what percent of these combined assets? Select:  A) 66%  B) 79%  C) 86%  D) 116%  E) 150%

Solution: Let the price of Company A's assets be 100   Price of assets of KW is 30% more than company A's assets which is 130   Price of assets of KW is 100% more than company 79%'s assets which means price of Company 79%'s assets is half the price of KW = 65   A+79% = 165   KW = 130   KW/(A+79%)*100 = 130/165*100 = 78.78% or 79%   79%
Answer: B
Find the distance covered by a man walking for 72min at a speed of 10km/hr? Select the correct option.
A) 12 km B) 3km C) 4km D) 5km E) 6km

Solution: Distance = 10*72/60= 
10*72/60 = 12
12 km   12 kmnswer is 12 km
Answer: A
The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be?  Options:  A) (x- 37)  B) 2x−(37+z)  C) (x−37)/2 + z  D) x/2 - 37 + z  E) (2x−37)/z

Solution: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:   h1 + h2 = x   and h1 = h2 + 37 =>   h2 + h2 + 37 = x => 2h2 = x-37 =? h2 = (x-37)   CORRECT (x- 37)NSWER (x- 37)
Answer: A
If (a-5)(y+2) = 0 which of the following must be true? Options.
A) a = y	B) a > y	C) a < y	D) ay = -10	E) None of the above

Solution: From (a-5)(y+2) = 0 it follows that either a=5 or y=-2.   (A) a = y --> not necessarily true. Consider a=5 and y=0.   (B) a > y --> not necessarily true. Consider a=5 and y=10.   (C) a < y --> not necessarily true. Consider a=5 and y=0.   (D) ay = -10 --> not necessarily true. Consider a=5 and y=0.   Thus, none of the statements must be true.   Answer: None of the above.
Answer: E
There are two decks of 10 cards each. The cards in each deck are labeled with integers from 10 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?	Choose the correct choice from the following answers
A) 0.23 B) 0.36 C) 0.4 D) 0.42 E) 0.46

Solution: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:   11 = 11   12 = 2*2*3   13 = 13   14 = 7*2   15 = 5*3   16 = 2*2*2   17 = 17   18 = 3*2*3   19 = 19   20 = 5*2*2   0.4ombos that have a 2 and a 3 as factors (first + second card):   12 + anything - 19 of these possibilities (we count 12 + 12 only once)   14 + 15 - 2 of these possibilities   15 + 16 - 2 of these possibilities   15 + 20 - 2 of these possibilities   18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities   Total possibilities that will be a multiple of 6: 42   Total possibilites:   10*10= 
  10*10 = 100
100   Probability= 42/100 = 0.40   Answer:0.4
Answer: C
What is the difference between the C.I. on Rs. 6000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? Choices
A) s.2.04	B) s.2.08	C) s.2.02	D) s.2.83	E) s.2.45

Solution: C.I. when interest is compounded yearly   = [6000 * (1 + 4/100) * (1 + (1/2 * 4)/100]   = 6000 * 26/25 * 51/50 = Rs. 6364.8   C.I. when interest is compounded half-yearly   = [6000 * (1 + 2/100)2]   = (6000 * 51/50 * 51/50 * 51/50)   = Rs. 6367.25 Difference   = (6367.25 - 6364.8)   = Rs.2.45.   Answer: s.2.45
Answer: E
Cistern may be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled ? Pick one.
A) 8 hrs
B) 8.5 hrs
C) 7 hrs
D) 7.2 hrs
E) 9 hrs

Solution: filled in 1 hr = 1/4   empties in 1 hr = 1/9   net filled in 1 hr = 1/4-1/9   ==>filled in 36/5 ==> 7.2 hrs   ANSWER 7.2 hrs
Answer: D
A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?
Pick
A) 40% B) 45% C) 50 % D) 60 % E) 55 %

Solution: Another method to solve this question using equations:   1 kg of Brand A will have 400g millet and 600g sunflower.   1 kg of Brand B will gave 650g millet and 350g sunflower.   Suppose,x kg of Brand A and y kg of Brand B are in the mixture.   Then total weight of millet = 400x+650 y g   Total weight of mixture = 1000x + 1000 y g   Given that millet is 500% hence   (400x+650y)/(1000x + 1000y) = 1/2   or, 800x + 1300 y = 1000x+1000y   or 300y=200x   or, x/y = 3/2   % of Brand A = (3/(3+2))*100= 
(3/(3+2))*100 = 60
60%   Hence answer is 60 %
Answer: D
A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son? Choose the correct option:
A) 23 years
B) 22 years
C) 21 years
D) 20 years
E) 19 years

Solution: Let present age of the son =x years   Then, present age the man =(x+24) years   Given that, in 2 years, man's age will be twice the age of his son   ⇒(x+24)+2=2(x+2)   ⇒x=22   ANSWER:22 years
Answer: B
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 32 kmph. Of how many minutes does the train stop per hour?  Choose the correct answer.
A) 17 B) 83 C) 12 D) 83 E) 28

Solution: Explanation:   T = 13/45 * 60 = 17   17nswer: Option 17
Answer: A
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Pick:
A) Rs.3600	B) Rs.3700	C) Rs.3800	D) Rs.3900	E) Rs.4900

Solution: Area = (l + b – d) d   (80 + 60 – 10)10 => 1300 m2   1300 * 3 = Rs.3900   ANSWER:Rs.3900
Answer: D
In how many different ways can the letters of the word JUDGE be arranged so that the vowels always come together? Choose the correct answer.
A) 36 B) 48 C) 52 D) 30 E) 24

Solution: Required number = 4!2! = 48   Answer is 48
Answer: B
What number comes next in this Number series.
4 4 6 9 7 8 8 ?
*Hint: check calende Pick
A) 1	B) 3	C) 6	D) 7	E) 8

Solution: A   7 (the number of letters in the month January)   June : 4 letters   July : 4 letters   August: 6 letters   September : 9 letters   October : 7 letters   November : 8 letters   7ecember : 8 letters
Answer: D
If the price of petrol increases by 32, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? Select:
A) 25%
B) 20%
C) 24.2%
D) 33.33%
E) None of these

Solution: Explanation :   let us assume before increase the petrol will be Rs. 100.   After increase it will be Rs (100+32) i.e 132.   Now, his consumption should be reduced to :-   =(132−100)/132 ∗ 100.   Hence, the consumption should be reduced to 24.2%.   Answer : 24.2%
Answer: C
In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 8 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can?	Choose the correct answer
A) 56 B) 60 C) 64 D) 68 E) 72

Solution: Let C be the capacity of the can.   (5/8)*(C-8)+8=(2/3)*C   15C-120+192=16C   C=72   The answer is 72.
Answer: E
Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 16 such machines produce in 4 minutes ? Choose the correct answer.
A) 2880	B) 1800	C) 2700	D) 10800	E) None of these

Solution: Solution   Let the required number of bottles be x.   More machines,More bottles (Direct Proportion)   More minutes,More bottles (Direct Proportion)   âˆ´ 6 Ã— 1 Ã— x = 16 Ã— 4 Ã— 270 â‡” x = 16x4x270/6= 2880 . 2880nswer 2880
Answer: A
If x^2 = y^3 , where x and y are non negative and non zero integers, what is the greatest possible value of x * y from options below?	Choose the correct choice from the following options
A) 343
B) 625
C) 243
D) 921
E) 741

Solution: C. x=27, y=9   27^2=729   9^3=729   x * y = 27 * 9= 
27 * 9 = 243
243   My answer is (243) 243
Answer: C
The ratio between the speeds of two trains is 7: 9. If the second train runs 540 kms in 3 hours, then the speed of the first train is ? Choose one.
A) 140 km/hr	B) 130 km/hr	C) 110 km/hr	D) 120 km/hr	E) None of these

Solution: Explanation:   Let the speeds of two trains be 7X and 9X km/hr.   9/X=540/3=>X=20Km/hr   So speed of first train is   20*7= 
  20*7 = 140
140 km/hr   Option 140 km/hr
Answer: A
Vehicle X is 22 miles ahead of Vehicle Y, which is traveling the same direction along the same route as Vehicle X. If Vehicle X is traveling at an average speed of 36 miles per hour and Vehicle Y is traveling at an average speed of 45 miles per hour, how long will it take Vehicle Y to overtake and drive 23 miles ahead of Vehicle X?
Choose the correct choice.
A) 5 hours B) 7 hours 20 minutes C) 4 hours D) 3 hours 45 minutes E) 2 hours 30 minutes

Solution: Relative speed = 45-36= 
45-36 = 9
9 miles per hour   Dist required= 22+23= 
22+23 = 45
45 miles   Time taken to overtake= 45/9= 
45/9 = 5
5 hours. 5 hours is the answer.
Answer: A
If the personal income tax rate is lowered from 38% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $36500?
Answers.
A) $1825	B) $5000	C) $3150	D) $7000	E) $10000

Solution: Saving = (38-33)% of 36500 = 1825.   $1825nswer:$1825
Answer: A
Currently guavas cost 30 cents/pound. Due to a disease affecting the guava trees it is expected that next month guavas will cost 50% more than they do currently. How much are guavas expected to cost next month? Choose the correct answer
A) 50 cents /pound
B) 45 cents /pound
C) 55 cents /pound
D) 60 cents /pound
E) 65 cents /pound

Solution: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).   In this case, (new cost) = 30 cents/pound + (50/100)(30 cents/pound)   = 30 cents/pound + 15 cents/pound   = 45 cents /pound   Answer : 45 cents /pound
Answer: B
There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible? Choose the correct choice from the following answers.
A) 100
B) 90
C) 50
D) 45 different pairs
E) 25

Solution: 1. first child out of 0 - 10 possibilities   2. second child out of 9 - 9 possibilities. the total number of pairs = 9*10= 
9*10 = 90
90   3. exclude xy yx cases:  90/2= 
 90/2 = 45
45   Second way   N=10C2=10!/(8!2!) =10*9/2= 
10*9/2 = 45
45   ANS:45 different pairs
Answer: D
8.008/4.004	Pick
A) 2  B) 0.02  C) 0.2  D) 20  E) 2

Solution: Answer is 2, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/4004= 
8008/4004 = 2
2   2nswer 2
Answer: A
If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?  Choose the correct option
A) 4:3	B) 4:0	C) 4:5	D) 4:7	E) 4:2

Solution: Explanation:   a1:a2 = 4:3   d1:d2 = 4:3   4:3nswer: Option 4:3
Answer: A
A rectangular garden is to be twice as long as it is wide. If 150 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?	Select
A) 40 B) 50 C) 60 D) 70 E) 80

Solution: ALTERNATE APPROACH   Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.   Given Perimeter is 150   So, 2 ( L + 50 ) = 150   Or, L + 50 = 75   Now use the answer options ( Given Length ; 50reath will be half the length)   (A) 40   L = 40 ; 50 = 20   L + b = 60   (50) 50   L = 50 ; 50 = 25   L + b = 75   (C) 60   L = 60; 50 = 30   L + b = 90   (D) 70   L = 70; 50 = 35   L + b = 105   (E) 80   L = 80; 50 = 40   L + b = 120   Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (50)
Answer: B
Find the roots of quadratic equation: 3x2 - 7x - 6 = 0?  Choose the correct choice from the following choices
A) -6, 3 B) 3, -2/3 C) -5, 2 D) -9, 2 E) None of these

Solution: 3x2 - 9x + 2x - 6 = 0   3x(x - 3) + 2(x - 3) = 0   (x - 3)(3x + 2) = 0 => x = 3, -2/3   ANSWER:3, -2/3
Answer: B
While purchasing one item costing Rs. 400, I had to pay the sales tax at 7% and on another costing Rs. 6400, the sales tax was 9%. What percent of the sales tax I had to pay, taking the two items together on an average ?	Choose the correct choice from the following answers.
A) 8 + 15/17
B) 8 + 15/18
C) 8 + 15/12
D) 8 + 15/11
E) 8 + 15/110

Solution: Explanation:   Total sales tax paid = 7% of Rs, 400 + 9% of Rs. 6400   == Rs. (28 + 576) = Rs. 604.   Total cost of the items = Rs. (400 + 6400) = Rs. 6800.   Required percentage =% =%.   8 + 15/17nswer: 8 + 15/17) 8 + 15/17
Answer: A
In a ground there are men and dogs. In all, there are 20 heads and 72 feet. How many men and how many horses are in the ground?
Options
A) 8 men and 14 dogs.  B) 7 men and 14 dogs.  C) 6 men and 14 digs.  D) 5 men and 14 dogs.  E) 4 men and 14 dogs.

Solution: 6 men and 14 dogs.   Let M = men and D = dogs. We can come up with 2 equations.   M + D = 20   2M + 4D= 72   Solving the 2 equations will give 6 men and 14 dogs.   Answer 6 men and 14 digs.
Answer: C
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 8:30 am. They shall first cross each other at ?	Choose the correct choice.
A) 7:15 am	B) 7:30 am	C) 8: 42 am	D) 7:50 am	E) 7:60 am

Solution: Explanation:   Relative speed between two = 6-1= 
6-1 = 5
5 round per hour   They will cross when one round will complete with relative speed,   which is 1/5 hour= 12 mins.   So 8:30 + 12 mins = 8:42   Option 8: 42 am
Answer: C
A 28 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? Choose the correct choice from the following:  A) 12  B) 8  C) 88  D) 77  E) 14

Solution: 1: 2/5 = 5: 2   2/7 * 28= 
2/7 * 28 = 8
8   Answer: 8
Answer: B
Speed of a boat in standing water is 9 kmph and the speed of the stream is 1. 5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is Options:	A) 16 hours	B) 18 hours	C) 20 hours	D) 24 hours	E) None

Solution: Solution   Speed upsteram	= 7.5 kmph.   Speed downsteram	= 10.5 kmph.   Total time taken	=[10.5/7.5 + 105/10.5]hours   = 24 hours.   Answer 24 hours
Answer: D
If m = ||n – 3| – 2|, for how many values of n is m = 6?	Choose the correct choice:	A) 1	B) 3	C) 4	D) 5	E) 2

Solution: m = ||n – 3| – 2| can be 4 only and only when n-3= +/-8. so there are 2 values of n   Answer : 2
Answer: E
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed W ?
Options.
A) 6 B) 8 C) 10 D) 12 E) 16

Solution: Let the current speed be x miles per hour.   Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x   Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)   As per question, 96/(x-4) - 96/1.5x = 16   Solving this W we get x = 8.   8.
Answer: B
A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 15% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?  Choose the correct choice.
A) 70 lbs	B) 40 lbs	C) 30 lbs	D) 50 lbs	E) 63 lbs

Solution: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:   A = # of pounds sold at 7% profit   B = # of pounds sold at 15% profit   A+B = 100 pounds   (.07A + .15B)/(A+B) = .10   .07A + .15B = .1A + .1B   .05B = .03A   5B = 3A   5/3 = A/B   So, for every 5 pounds of A, we have 3 pounds of B.   With 100 pounds total, we have 63 pounds of A and 37 pounds of B.   option 63 lbs
Answer: E
The difference between two integers is 5. Their product is 500. Find the numbers.
Choose the correct choice:
A) 15, 20 B) 20, 25 C) 30, 25 D) 21, 26 E) 25, 27

Solution: Explanation:   Let the integers be x and (x + 5). Then,   x(x + 5) = 500   x2 + 5x - 500 = 0   (x + 25)(x - 20) = 0   x = 20   So, the numbers are 20 and 25.   ANSWER IS 20, 25
Answer: B
The sum of the first 60 positive even integers is 3,750. What is the sum of the odd integers from 101 to 200, inclusive?	Choose the correct choice from the following answers
A) 4,700
B) 7,500
C) 10,500
D) 15,000
E) 19,600

Solution: 101+103+.......199   If we remove 100 from each of these it will be sum of 1st 100 odd numbers.   so 101+103+.......199 = 60 * 100 + (1+3+5+7+......)   sum of 1st 100 natural numbers = (100 * 101) / 2= 
(100 * 101) / 2 = 5_050
5050   Sum of 1st 60 positive even integers= 3750   sum of 1st 100 odd numbers = 5050 - 3750= 
5050 - 3750 = 1_300
1300   so 101+103+.......199= 60 * 100 + (1+3+5+7+......) = 6000 + 1300 =4700   4,700 is the answer.
Answer: A
Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 12.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 7 hours?  Choose one
A) 42
B) 84
C) 70
D) 98
E) 140

Solution: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 12.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 12 mph then the maximum distance, in miles, that the cyclist could travel in 7 hours would be  7*12= 
 7*12 = 84
84 miles.   Answer: 84.
Answer: B
Three friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?
Select the correct option.
A) 5%	B) 10%	C) 20%	D) 25%	E) 33%

Solution: Let x be the original price of one ticket.   The total original cost is 3x.   The new cost is 4y, where y is the discounted price of one ticket.   3x = 4y   y = 3x/4 =0.75x which is a discount of 25%.   The answer is 25%.3 /4= 
3 /4 = 3/4 = around 0.75
0.75x which is a discount of 25%.   The answer is 25%.
Answer: D
A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 10 days.In how many days B alone can do the work?	Select the correct option:
A) 5days  B) 15 days  C) 12 days  D) 9 days  E) 10 days

Solution: Explanation:   A’s 5 day work = 5*1/15=1/3   Remaining work = 1-1/3=2/3   15 days completes 2/3 work in 6 days   15 days alone can do in x days   2/3*x=10   X=15 days   Answer: Option 15 days
Answer: B
If the sum of 5 consecutive integers is y, which of the following must be true?
I. y is an even number
II. y is an odd number
III. y is a multiple of 5  Select
A) I only
B) II only
C) III and II only
D) I and III
E) III only

Solution: I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.   II. Same as above. This need not be always true.   III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)   = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.   Therefore III only is the answer.
Answer: E
A company consists of 5 senior and 3 junior staff officers. If a committee is created with 1 senior and 2 junior staff officers, in how many ways can the committee be formed? Choose the correct choice from the following choices
A) 15 B) 30 C) 45 D) 80 E) 200

Solution: Choose 1 senior from 5 senior and choose 2 junior from 3 junior:   5C1 * 3C2 = 5 * 3= 
5 * 3 = 15
15   15ns: 15
Answer: A
The average of first ten prime numbers which are odd is?
Choose the most appropriate option:
A) 15.9  B) 15.5  C) 15.2  D) 15.8  E) 13.2

Solution: Sum of first 10 prime no. which are odd = 158   Average = 158/10= 
158/10 = 79/5 = around 15.8
15.8   Answer: 15.8
Answer: D
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 10200, how much money did he borrow?
Pick one:
A) 10000
B) 80288
C) 2668
D) 2600
E) 2781

Solution: Let the sum be Rs. x. Then,   [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 10200   18x + 45x + 39x = (10200 * 100)   102x = 1020000 => x = 10000.   10000nswer:10000
Answer: A
By how much is three-fifth of 600 greater than four- seventh of 210 ? Choose the correct choice from the following answers:
A) 320	B) 240	C) 420	D) None of these	E) Cannot be determined

Solution: Solution   3/5 of 600 - 4/7 of 210 = 240.   Answer 240
Answer: B
If we have 8 people in a meeting, in how many ways they can sit around a table?  Choose the correct choice from the following choices.
A) 10*9!  B) 9*8!  C) 8*7!  D) 7*6!  E) 6*5!

Solution: If there are "n" people sitting around a table, there are "(n-1)!" possible arrangements:   Here, n=8   (n-1)!=7!=7*6!   Ans:"7*6!"
Answer: D
The area of a square is equal to four times the area of a rectangle of dimensions 52 cm * 13 cm. What is the perimeter of the square?
Select the correct option
A) 200 B) 208 C) 210 D) 220 E) 228

Solution: Area of the square = s * s = 4(52 * 13)   => s = 52 cm   Perimeter of the square = 4 * 52= 
4 * 52 = 208
208 cm.   Answer: Option 208
Answer: B
Two employees X and Y are paid a total of Rs. 650 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Options.
A) s.200.45	B) s.250.45	C) s.295.45	D) s.300.45	E) s.310.45

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 650   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 650   ⇒ y[12/10 + 1] = 650   ⇒ 22y/10 = 650   ⇒ 22y = 6500   ⇒ y = 6500/22 = Rs.295.45   s.295.45)
Answer: C
On dividing 52 by a number, the quotient is 16 and the remainder is 4. Find the divisor?
Answers
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: d = (D-R)/Q   = (52 - 4)/16   = 48/16= 
48/16 = 3
3   3)
Answer: B
If s and t are positive integers such that s/t = 4.12, which of the following could be the remainder when s is divided by t ?	Choices:  A) 2  B) 4  C) 8  D) 20  E) 30

Solution: The remainder is 0.12 or 12/100. You can go one step further and say that X/Y=12/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.   One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.   30/Y=12/100   12Y=3000   Y=250   Answer: 30.
Answer: E
A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage
Select the correct option
A) 25% loss  B) 25% gain  C) 15% gain  D) 15% loss  E) None

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (500 - 400)/400 = 25% gain   25% gain
Answer: B
A semicircle has a radius of 11. What is the approximate perimeter of the semicircle? Options.
A) 45	B) 51	C) 57	D) 63	E) 69

Solution: The perimeter of a circle is 2*pi*r.   The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r   The perimeter is pi*11 + 2*11 which is about 57.   The answer is 57.
Answer: C
The cubic f(x) = x3 - 7x - 6 has three distinct roots, a, b, and c. Compute 1/a + 1/b + 1/c .  Choose the correct choice from the following choices:
A) -5/6
B) -6/6
C) -7/6
D) -8/6
E) -9/6

Solution: 1/a+1/b+1/c=ab+bc+ca/abc   =-7/-6   =-7/6   correct answer -7/6
Answer: C