MU-NLPC/Calc-aqua_rat huggingface dataset:
In a 500 m race Dishu beats Abhishek by 100 m or 5 seconds. In another race on the same track at the same speeds. Abhishek and Prashant start at one end while Dishu starts at the opposite end. How many metres would Abhishek have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant.
Select
A) 250 m
B) 560 m
C) 100 m
D) 320 m
E) 240 m

Solution: Explanation :   Abhishek's speed = 100/5= 
100/5 = 20
20 m/s.   Time taken by Abhishek to cover 500 m=500/20= 
500/20 = 25
25 seconds.   Dishu's speed= 500/20 or 25 m/s   Prashant's speed = 15 m/s   Time taken by Dishu to meet Prashant in 500m race in opposite direction:   Distance covered by Abhishek:   =>500/(15+25).   =>12.5 sec.   =>12.5(20)= 250 m.   250 mnswer : 250 m
Answer: A
Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?	Choices:
A) 10%	B) 18%	C) 19%	D) 12%	E) 13%

Solution: Let the rate of interest during the second year be R%. Given,   4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544   R = 10%   10%nswer:10%
Answer: A
The speed of a boat in upstream is 20 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?	Pick one:
A) 10 kmph.
B) 17 kmph.
C) 18 kmph.
D) 41 kmph.
E) 30 kmph.

Solution: Speed of the boat in still water = (20+80)/2= 
(20+80)/2 = 50
50 kmph. Speed of the stream= (80-20)/2= 
(80-20)/2 = 30
30 kmph.   Answer:30 kmph.
Answer: E
in what proportion water to be mixed with spirit to gain 12.5% by selling it at cost price?  Pick one
A) 1:2	B) 1:3	C) 1:4	D) 1:8	E) 1:16

Solution: If the total quantity=100   Actual quantity of spirit to be sold to get 12.5% gain=100*100/112.5=800/9   So the water =100-(800/9)=100/9   Proportion of water:spirit =100/9 : 800/9= 1:8   ANSWER:1:8
Answer: D
The length of a rectangle is doubled while its width is doubled. What is the % change in area? Pick one:
A) 250% B) 300% C) 500% D) 650% E) 700%

Solution: The original area is L*W   The new area is 2L*2W = 4*L*W   2 *2= 
  2 *2 = 4
4*L*W= L*W + 3*L*W   The area increased by 300%.   The answer is 300%.
Answer: B
The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 60
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes? Choose the correct choice from the following:
A) 51 B) 98 C) 90 D) 125 E) 162

Solution: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics   No. of total students = 60 + (35-15) + (40-10-12) = 60+20+18= 
60+20+18 = 98
98   Hence, Answer will be 98.
Answer: B
Students of three different classes appeared in common examination. Pass average of 10 students of first class was 65%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?	Choose one:
A) 74%
B) 75%
C) 69%
D) 71%
E) None

Solution: Solution:   Sum of pass students of first, second and third class,   = (65% of 10) + (60% of 15)+ (80% of 25)   = 6.5+9+20= 
6.5+9+20 = 35.5
35.5   Total students appeared,= 10+15+25= 
10+15+25 = 50
50   Pass average,= 35.5*100/50= 
35.5*100/50 = 71
71%.   Answer: Option 71%
Answer: D
Bhanu spends 30% of his income on petrol on scooter 30% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent? Choose the correct choice from the following answers:	A) 2287	B) 140	C) 128	D) 210	E) 123

Solution: Given 30% (Income ) = 300 ⇒⇒ Income = 1000   After having spent Rs.300 on petrol, he left with Rs.700.   His spending on house rent = 30% (700) = Rs.210   Answer:210
Answer: D
A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 4 km/h that day, what was its approximate downstream speed?	Choose the correct choice from the following answers:
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Another way will be:   Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed   If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D   =>5D/4 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)   => 5/4 = 1/4 + 2/3 +2/x (div. both sides by D)   => 1.25 = .25+.66 +.33/x => x=5.99 ~6   option 6
Answer: C
A batsman makes a score of 80 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
Choose the most appropriate option:
A) 40 B) 50 C) 62 D) 30 E) 56

Solution: Let the average after 11th inning = x   Then, average after 10th inning = x-5   10(x-5)+80 = 11x   x = 80-50= 
80-50 = 30
30   Answer is 30
Answer: D
For what values of k is the system of equations independent? The equations are as follows:
kx + 5y = 3; 3x + 4y = 9
Choose the correct option:
A) 15/9
B) 15/2
C) 15/1
D) 15/4
E) 15/7

Solution: For the equations to be independent, conditions is a1a2≠b1b2a1a2≠b1b2   k3≠54k/3≠5/4 or k ≠15/4   Answer:15/4
Answer: D
If it is 4:37 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.)	Select the correct option
A) 4:40 B) 4:44 C) 4:47 D) 4:30 E) 4:32

Solution: 4:37minus 2,880,717in any way must end with 0, the only answer choice which ends with 0 is A.   4:40nswer: 4:40.
Answer: A
The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is? Choose the correct choice from the following choices:
A) 2 B) 4 C) 6 D) 3 E) 8

Solution: 4.5 4.5   30% 70%   30% ----- 4.5   70% ------? => 10.5 - 4.5= 
10.5 - 4.5 = 6
6 ml   ANSWER 6
Answer: C
A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?
Choose one.
A) 72  B) 67  C) 28  D) 126  E) 27

Solution: Length = Speed * time   Speed = L/T   S = 700/20= 
700/20 = 35
35 M/Sec   Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 126 Kmph   Answer:126
Answer: D
What is the 28th digit to the right of the decimal point in the decimal form of 5/11?	Choose the correct choice from the following answers:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: 5/11 = 0.45454545...   The even numbered positions in the decimal expansion are all 5.   The answer is 5.
Answer: C
If E:F = 3:1 and F:G = 5:2 then E:F:G is
Choose the correct choice from the following choices
A) 15:5:3 B) 15:5:2 C) 16:5:2 D) 15:4:2 E) 5:5:2

Solution: Solution:   E/F = 3/1;   F/G = 5/2;   E:F:G = 3*5:1*5:1*2 = 15:5:2.   Answer: Option 15:5:2
Answer: B
If a trader sold two cars each at Rs. 325475 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is?  Choose the correct option:
A) 1.44% B) 1.74% C) 1.84% D) 1.97% E) 2.25%

Solution: SP of each car is Rs. 325475, he gains 15% on first car and losses 15% on second car.   In this case, there will be loss and percentage of loss is given by   = [(profit%)(loss%)]/100   = (15)(15)/100 % = 1.44%   Answer:2.25%
Answer: E
If the first day of a year (other than leap year) was Wednesday, then which was the last day of that year? Choose the correct choice from the following options:
A) Saturday  B) Wednesday  C) Tuesday  D) Monday  E) None of these

Solution: Explanation :   Given that first day of a normal year was Wednesday   Odd days of the mentioned year = 1 (Since it is an ordinary year)   Hence First day of the next year = (Wednesday+ 1 Odd day) = Thursday   Therefore, last day of the mentioned year = Wednesday. Answer : Option Wednesday
Answer: B
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is	Options
A) 2 km/hr B) 3 km/hr C) 4 km/hr D) 5 km/hr E) None of these

Solution: Explanation:   Let the speed of the stream be x km/hr. Then,   Speed downstream = (15 + x) km/hr,   Speed upstream = (15 - x) km/hr   So we know from question that it took 4(1/2)hrs to travel back to same point.   So,   30/15+x−30/15−x=4 1/2   30/15+  30/15= 
30/15+  30/15 = 4
4 1/2=>900/225−x2=9/2   =>9x2=225   =>x=5km/hr   Option 5 km/hr
Answer: D
A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice? Choose the correct choice from the following answers.
A) 1/16	B) 5/16	C) 2/5	D) 13/16	E) 27/32

Solution: Fair coin is tossed 5 times . Hence total number of outcomes = 2^5 = 32.   Problem asks for probability of getting atleast heads twice. Hence if we calculate probability of getting Heads exactly once and probability of not getting Heads at all and subract it from the total probability of the event which is 1 (As total probability of certain event will be always 1) we can get the probability of getting atleast heads twice.   Probability of getting exactly one head and no heads= (Number of possible outcomes [ HTTTT , THTTT, TTHTT, TTTHT, TTTTH , TTTTT] = 6)/ (Total possible outcomes = 32)   => 6/32 = 3/16   Hence probability of getting atleast heads twice = 1 - (3/16) = 13/16 => Choice [13/16]
Answer: D
If 8a = 9b and ab ≠0, what is the ratio of a/9 to b/8?
Choose one:	A) 64/81	B) 8/9	C) 1	D) 9/8	E) 81/64

Solution: if ab ≠0   then a and b has two integer sets of pair   if a=9 then b=8   and if a=-9 then b=-8   also in fraction if a=1/8 then b=1/9   any of the pair we check the ratio 8a/9b=1   ANSWER:1
Answer: C
The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A?	Choose the correct choice:  A) 81  B) 65  C) 75  D) 89  E) 90

Solution: A + B + C = 3 *70= 
3 *70 = 210
210   A + B + C + D= 4 * 70= 
4 * 70 = 280
280 ---- (i)   So, D= 70& E = 70 + 3= 
70 + 3 = 73
73   B + C + D +E=68 * 4= 
68 * 4 = 272
272 --- (ii)   From Eq. (i) & (ii)   81-E= 280 –272 = 8   81 = E +8 = 73 + 8= 
73 + 8 = 81
81   81nswer : 81
Answer: A
How many legs are there if each sheep has 4 legs and there are total 250 of that kind?	Choose the correct choice from the following answers
A) A)700 B) B)800 C) C)1000 D) D)10000 E) of the above

Solution: Sol.   Total of 250 each has 4 legs   = 250 * 4= 
250 * 4 = 1_000
1000   Answer : 1000
Answer: C
A, B and C rents a pasture for Rs.1073. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Choices:
A) 270 B) 289 C) 267 D) 255 E) 333

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 1073= 
9/29 * 1073 = 333
333   Answer: 333
Answer: E
A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient? Choose the correct choice from the following answers:
A) 10 days B) 20 days C) 5 days D) 25 days E) 15 days

Solution: 400 --- 31   400 --- 3   120 --- ?   400*3 = 120*x => x =10 days   10 daysNSWER 10 days
Answer: A
If 14 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?	Options
A) 78 days. B) 154 days. C) 149 days. D) 148 days. E) 167 days.

Solution: B   154 days.   From the above formula i.e (m1*t1/w1) = (m2*t2/w2)   so (14*6*88/1) = (6*8*d/1)   on solving, d = 154 days.
Answer: B
Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
A. 3 4/9 days	Choose one:
A) 9 3/7 days B) 9 7/8 days C) 9 3/8 days D) 9 3/8 days E) 2 3/8 days

Solution: 1/15 + 1/25 = 8/75   75/8   = 9 3/8 days   Answer:9 3/8 days
Answer: C
. Data sufficiency question:
What will be the percentage profit of selling one liter milk.?
1) 16 liter of milk is sold at cost price after adding 20% water to it.
2) the cost price of one liter milk is Rs.16. Options
A) 23	B) 29	C) 27	D) 1291	E) 11

Solution: Explanation:   Let us assume one liter costs Rs.1. So C.P = Rs.16   When 20% water is added, then total volume = 20 liters. So SP = 20. Profit can be calculated.   Statement 1 is sufficient.   Statement 2 is not required.   Answer:29
Answer: B
Amy's sells kale at x dollar per pound for the first 20 pounds and .5x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?  Choose the most appropriate option:
A) 24
B) 25
C) 26
D) 21.5
E) 28

Solution: For Amy's deal to be better, the cost has to be less or equal to Lucia's   Assuming 'n' is the number of pounds of kale, the equation is   20x + (n-20) (0.5x) <= 14x + (n-14)(0.9x)   Resolve it:   ==> 20x + 0.5nx - 10x <= 14x + 0.9nx - 12.6x   ==> 8.6x <=0.4nx   ==> 21.5x < =nx   ==> x (n-21.5) > = 0   as x cannot be 0,   ==> n - 21.5>=0   ==> n > = 21.5   so the minimum value is 21.5   '21.5' would be the correct answer
Answer: D
If 12x = 16y = 28z, then what is a possible sum of positive integers x, y, and z?	Choose the correct choice
A) 52 B) 58 C) 122 D) 84 E) 168

Solution: 12x = 16y = 28z   3x = 4y = 7z   3(4*7) = 4(3*7) = 7(3*4)   Addition = 28+21+12= 
28+21+12 = 61
61   Answer would be multiple of 61 which is 122   Answer :122
Answer: C
A certain essay consists of 12 paragraphs. Each paragraph contains at least 110 words but not more than 120 words. Which of the following could be the total number of words in the essay?	Choose the correct choice from the following choices
A) 1430	B) 1540	C) 1640	D) 1740	E) 1840

Solution: lets consider minimum no of words ... 12 * 110 = 1320   Lets consider maximum no of words .... 12*120= 1440   answer should be one of these two values or should lie between these two values ...   only 1 option 1430 - 1430
Answer: A
A square marked 1, 2, 3 and 4 on its four sides. Four colors pink, purple,brown and yellow are used to paint the four sides of the square. If the adjacent sides are painted with the different colors, in how many ways can the sides be painted?	Choices
A) 4	B) 12	C) 9	D) 27	E) 6

Solution: If the base of the square is pink, then in order the adjacent faces to be painted with the different colors, the top must also be pink. 4 side faces can be painted in Brown-Purple-yellow Brown-Purple-Yellow OR Purple-yellow- Brown-Purple-yellow- Brown (2 options).   But we can have the base painted in either of the four colors, thus the total number of ways to paint the square is 2*2= 
2*2 = 4
4.   4nswer: 4.
Answer: A
If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 Select the correct option:  A) 800  B) 700  C) 750  D) 850  E) 900

Solution: cost P = 125/100 * 115/100 * 110/100 = 1265   253/160p=1265==> p =800   800NSWER 800
Answer: A
The ages of Raju and Biju are in the ratio 3:1. Fifteen years hence, the ratio will be 2:1. Their present
ages are:
Answers.
A) 30yrs, 10yrs
B) 45 yrs, 15yrs
C) 21 yrs, 7 yrs
D) 60yrs, 20yrs
E) None of these

Solution: Expl : Let the ages of raju and Biju is 3x and x years respectively.   Then, (3x +15)/ (x+15) = 2/1; -> 2x + 30 = 3x + 15 -> x = 15   So Raju’s age = 3*15= 
3*15 = 45
45 and 45 yrs, 15yrsiju’s age= 15 years   Answer:45 yrs, 15yrs
Answer: B
If a number E between 0 and 1 is selected at random, which of the following will the number most likely be between? Pick: A) 0 and 3/20 B) 3/20 and 1/5 C) 1/5 and 1/4 D) 1/4 and 3/10 E) 3/10 and 1/2

Solution: The number E will most likely be between the largest range.   A. 0 and 3/20 --> range 3/20;   B. 3/20 and 4/20 --> range 1/20;   C. 4/20 and 5/20 --> range 1/20;   D. 5/20 and 6/20 --> range 1/20;   E. 6/20 and 10/20 --> range 4/20.   Answer: 3/10 and 1/2.
Answer: E
If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B ?  Choose the correct choice
A) 108  B) 120  C) 132  D) 144  E) 156

Solution: Two two-digit positive integers have the same digits but in reverse order   So they must be in the form 10x+y and 10y+x   Adding both of them will give us 11x+11y -----------> 11(x+y) -----------> that means 11 is the factor of sum   Among the answer choices only 132(choice 132) has 11 as its factor and it is the possible sum of two integers A and B   ANSWER:132
Answer: C
A cab driver 5 days income was $600, $250, $450, $400 , $800. Then his average income is?	Choose the correct choice:  A) $460  B) $480  C) $500  D) $520  E) $540

Solution: avg = sum of observations/number of observations   avg income=(600+250+450+400+800)/5= 
(600+250+450+400+800)/5 = 500
500   Answer is $500
Answer: C
A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 9 minutes?	Choose the correct choice from the following options:
A) 486 B) 54 C) 108 D) 216 E) 324

Solution: ONE Veggiematik machine can chop 36 carrots in 4 minutes   So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes   In other words, ONE Veggiematik machine can chop 54 carrots in4minutes   So,SIXVeggiematik machines can chop (9)(54) carrots in9minutes   In other words, SIX Veggiematik machines can chop 486 carrots in9minutes   486nswer 486
Answer: A
A box contains 5 red, 4 blue, and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red? Choose the correct choice from the following choices: A) 235 B) 270 C) 280 D) 285 E) 240

Solution: Explanation:   You decline to mention whether balls of the same color are identical. If they are, then you have only 99 ways to do so. Why? Two positions are dedicated to red. For the remaining two, you can have red, blue or white (all are sufficiently numerous to allow that) and so that's 3×3=93×3=9 ways.   If, on the other hand balls of the same color are non-identical, then you can select four balls of any color is (5+4+3/4)=495(5+4+34)=495 ways. No red ball is selected in (4+3/4)=35 ways. Exactly one red ball is selected in 5×(4+3/3)175 ways. Thus, you select at least two red balls in 495−(35+175)=285 ways   Answer is 285
Answer: D
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.35000?
Choose the correct choice:
A) 11585	B) 11879	C) 12779	D) 12672	E) 12782

Solution: 11585 = 35000(11/10)^3   = 46585   = 35000   ----------   11585   11585nswer: 11585
Answer: A
Using all the letters of the word "THURSDAY", how many different words can be formed? Choose the correct choice from the following.
A) 7  B) 8!  C) 7  D) 5  E) 2

Solution: Total number of letters   = 8   Using these letters the number of 8 letters words formed is ⁸P₈   = 8!.   Answer: 8!
Answer: B
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 60 revolutions. How many revolutions does the second wheel make in covering d feet?
Select
A) 60x-y  B) 30x+y  C) 30x-y  D) 60x+y  E) 60x/y

Solution: A wheel covers 2πr distance in one revolution. where r= diameter/2   First wheel covers d feet in 60 rev. => d= 60* 2π * (x/2)   Second wheel covers d feet in let's say P revolutions; => d = P* 2π * (y/2)   comparing both equations:-   => p= (60∗2π∗x/2)/(2π∗y/2)   => 60x/y   Answer :- 60x/y
Answer: E
12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?  Choices
A) 18 B) 15 C) 16 D) 12 E) None

Solution: Sol.   Capacity of each bucket = 9 litres.   Number of buckets needed = (162/9)= 
(162/9) = 18
18.   18nswer 18
Answer: A
If log1087.5 = 4.9421, then the number of digits in (875)10 is? Options:
A) 60
B) 28
C) 27
D) 26
E) 25

Solution: X = (875)10 = (87.5 x 10)10   Therefore, log10X = 10(log4087.5 + 1)   = 10(4.9421 + 1)   = 10(5.9421) = 59.421   X = antilog(59.421)   Therefore, number of digits in X = 60.   60NSWER:60
Answer: A
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 25% greater than any other employee, what is the lowest possible salary that any one employee earned? Choose the correct choice from the following answers.
A) $40,384.61	B) $41,667	C) $42,000	D) $50,000	E) $60,000

Solution: Employee 1 earned $x(say)   Employee 2 will not earn more than $1.25x   Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees   (1.25x*20)+x=1,050,000   Solving for x=$40,384.61   $40,384.61nswer $40,384.61
Answer: A
A man buys 56 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? Select
A) 7.6 %  B) 7.7 %  C) 20.52 %  D) 23.62 %  E) 27.82 %

Solution: Explanation:   Let Marked price be Re. 1 each   C.P. of 56 pens = Rs. 46   S.P. of 56 pens = 99% of Rs. 56 = Rs. 55.44   Profit % = (Profit /20.52 %.P.) x 100   Profit% = (9.44) x 100 = 20.52 %   ANSWER: 20.52 %
Answer: C
What is the rate percent when the simple interest on Rs.800 amount to Rs.400 in 2 Years? Choose the correct choice from the following answers:
A) 5%
B) 6%
C) 2%
D) 25%
E) 1%

Solution: Interest for 2yrs = 400   Interest for 1yr = 200   Interest rate = 200/800 x 100 = 25%   Answer : 25%
Answer: D
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?	Pick one
A) 9	B) 10	C) 11	D) 12	E) 13

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km =	9/54	x 60	min	= 10 min.   answer :10
Answer: B
The cost C of manufacturing a product can be estimated by the formula C= 0.03 rs t^2, where r ans s are amounts, in pounds, of two major ingredients and t is production time in hours. if r is increased by 50%, s increased by 20% and t decreased by 30%, by approximately what % will the estimated cost of manufacturing the product change.	Choose one
A) 40% increase  B) 12% increase  C) 4% increase  D) 12% decrease  E) 24% decrease

Solution: Let r=s=t=100   C = 0.03*r*s(t^2)   =0.03*100*100*(100^2)   =3,000,000   r1 = 50% more than r = 150   s1 = 20% more than s =120   t1 = 30% less than t = 70   C1= 0.03 * 150 *120 * 70 * 70   =0.03 * 1800 * 4900   = 54*4900= 
54*4900 = 264_600
264600   12% decreaseecrease= C-C1 = 3,000,000-264600=35400   %12% decreaseecrease = 35400/300000 * 100 = 354/30= 
354/30 = 59/5 = around 11.8
11.8 ~ 12% 12% decreaseecrease   ANSWER:12% decrease
Answer: D
Robet traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. Choose the correct choice from the following:
A) z=3x
B) x=3z
C) y=2x
D) x=2y
E) y=3x

Solution: Robet Travelled for x,y and for z min.   Total Time : x + y + z   Which is equal to : 3y   Equating both sides we get   x+y+z = 3y   => x+z =2y ........ Eqn 1   Looking out at options   D Says x =2y   Using it in Eqn 1   2y + z = 2y   => Z = 0 mins, Which I guess is not possible.   The Ans isx=2y
Answer: D
Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?	Answers
A) 1/13  B) 2/15  C) 4/13  D) 3/17  E) 1/19

Solution: Here, n(S) = 52   There are 13 cards that are diamond (including one king) and there are 3 more kings.   Let E = event of getting a diamond or a king.   Then, n(E) = (13 + 3)= 
(13 + 3) = 16
16   P (E)= 16 / 52 = 4/13   4/13
Answer: C