MU-NLPC/Calc-aqua_rat huggingface dataset:
Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
Options:
A) 20% B) 80% C) 100% D) 180% E) 200%

Solution: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).   [(2 - 1)/1] * 100% = 100%   ANSWER:100% (2 - 1)/1  * 100= 
 (2 - 1)/1  * 100 = 100
100%   ANSWER:100%
Answer: C
What is the rate percent when the simple interest on Rs.900 amount to Rs.160 in 4 Years?
Choose the correct choice from the following:
A) 5%
B) 7%
C) 9%
D) 4.4%
E) 4%

Solution: 160 = (900*4*R)/100   R = 4.4%   Answer: 4.4%
Answer: D
A school having four classes only have student strength of 10, 50, 30 and 10 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?
Select the correct option:
A) 56%
B) 76%
C) 34%
D) 66%
E) 45%

Solution: 20% of 10+30% of 50+60% of 30+100% of 10   =2+15+18+10= 
2+15+18+10 = 45
now 45 of 100= 45%   ANSW45%R:45%
Answer: E
In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-nine students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes? Choose the correct choice:
A) 13	B) 10	C) 15	D) 8	E) 7

Solution: A U B U 15 = A + B + 15 - AB-B15-A15 + AB15   68 = 25 + 25+ 39 -AB-B15-A15 +3 => AB+B15+A15 = 24   Exactly Two classes = AB+B15+A15 - 3AB15 = 24 -3*3= 
24 -3*3 = 15
15   Hence 15
Answer: C
What is the place value of 7 in the numeral 2734? Select
A) 450
B) 460
C) 480
D) 500
E) 700

Solution: Option '700'    7 * 100= 
 7 * 100 = 700
700
Answer: E
SI on a certain sum of money for 3 yrs at 8 percent /annum is 1/2 the CI on Rs.4000 for 2 yrs at 10 percent/ annum. The sum placed on SI is?  Choose the correct choice from the following options:	A) Rs. 1650	B) Rs. 1700	C) Rs. 1750	D) Rs. 1950	E) Rs. 1980

Solution: C.I.   = Rs. 4000 x 1 + 10 2 - 4000   100   = Rs. 4000 x 11 x 11 - 4000   10 10   = Rs. 840.   Sum = Rs. 420 x 100 = Rs. 1750.   3 x 8   Rs. 1750
Answer: C
A retailer bought a hat at wholesale and marked it up 70% to its initial price of $34. By how many more dollars does he need to increase the price to achieve a 100% markup?  Pick one
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Let x be the wholesale price.   Then 1.7x= 34 and x = 34/1.7= 
34/1.7 = 20
20.   To achieve a 100% markup, the price needs to be $40.   The retailer needs to increase the price by $6 more.   The answer is 6.
Answer: C
There are 6 books on a shelf, of which 2 are paperbacks and 4 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?	Select the correct option.
A) a) 40 B) b) 14 C) c) 50 D) d) 55 E) e) 60

Solution: approach 1   at-least 1 paper back = total - no paper back   6c4-4c4 = 14   approach 2   at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back   = 2c1*4c3+2c2*4c2 = 14   Answer is b) 14
Answer: B
If you are given $2, and the amount doubles every day, how much money will you have after 12 days? Choose the correct choice from the following options.
A) $256 B) $512 C) $1024 D) $2048 E) $4096

Solution: 2^12=4096   The answer is $4096.
Answer: E
Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?	Answers.
A) -33 B) 33 C) 32 D) -31 E) 24

Solution: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.   Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.   So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.   Solving this equation for d+ed+e gives d+e=−66d+e=−66.   Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.   Hence, the answer is -33: -33
Answer: A
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is: Choose the most appropriate option.
A) 5 km/hr	B) 15 km/hr	C) 50 km/hr	D) 20 km/hr	E) 25 km/hr

Solution: Let Abhay's speed be x km/hr.   Then,(30/x - 30/2x)= 3   6x = 30   x = 5 km/hr.   5 km/hrNSWER 5 km/hr
Answer: A
The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin? Choices:  A) 23%  B) 18.75%  C) 30%  D) 50%  E) 100%

Solution: Explanatory Answer   Let the wages earned by Erica be $100   Then, wages earned by Robin and Charles will be $130 and $160 respectively.   Charles earns $30 more than Robin who earns $130.   Therefore, Charles' wage is 30/130*100 = 23.07%.   correct choice is (23%)
Answer: A
In a certain lottery, the probability that a number between 1 and 15, inclusive, is drawn is 1/3 . If the probability that a number 1 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 15 is drawn?	Choose the correct choice from the following answers: A) 2 by 3 B) 1/3 C) 1/4 D) 1/6 E) 2/5

Solution: You can simply use sets concept in this question. The formula   Total = n(A) + n(B) - n(A and B) is applicable here too.   Set 1: Number 1 or larger   Set 2: Number 15 or smaller   1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or less OR both)   2/3 + P(Set 2) - 1/3 = 1   P(Set 2) = 2/3   2 by 3nswer 2 by 3
Answer: A
When positive integer x is divided by 8, the quotient is y and the remainder is 2. When 2x is divided by 7, the quotient is 2y and the remainder is 4. What is the value of 6y – x?	Choose the correct choice
A) -1	B) 1	C) -2	D) 2	E) -3

Solution: (1) x = 8y+2   (2) 2x = 14y+4   (2)-(1): x=6y+2   6y-x=-2   The answer is -2.
Answer: C
If the range of the set of numbers {140, 90, 135, 110, 170, 145, x, 100, 140} is 100, which of the following could be x? Choose the correct choice from the following answers.
A) 170
B) 190
C) 210
D) 230
E) 250

Solution: The range of the other 8 numbers is 170-90= 
170-90 = 80
80, so x must be either the smallest number or the largest number in the set.   Then x= 170-100= 
170-100 = 70
70 or x= 90+100= 
90+100 = 190
190   The answer is 190.
Answer: B
Sum of two numbers is 50. Two times of the difference of first and seceond is 20. Then the numbers will be?  Choose the correct choice from the following answers
A) 10, 40  B) 20, 30  C) 35, 15  D) 30, 20  E) 15, 35

Solution: Explanation:   x + y = 50   2x Ã¢â‚¬â€œ 2y = 20   x = 30 y = 20   Answer: 30, 20
Answer: D
B, C and D invested Rs.6400, Rs.1600 and Rs.2400 respectively, in a partnership business. Find the share of D in profit of Rs.26000 after a year? Pick one:
A) 6400	B) 6300	C) 6100	D) 6000	E) 6200

Solution: Explanation:   6400:1600:2400   8:2:3   3/13 * 26000= 
3/13 * 26000 = 6_000
6000   6000)
Answer: D
A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
Choose the correct choice from the following
A) Rs.10,500, Rs. 13,500, Rs. 16,500 B) Rs.10,500, Rs. 13,500, Rs. 16,580 C) Rs.10,500, Rs. 13,500, Rs. 16,560 D) Rs.10,500, Rs. 13,500, Rs. 16,509 E) Rs.10,500, Rs. 13,503, Rs. 16,501

Solution: A:B:C = 35000 : 45000 : 55000 = 7:9:11   A's share = 40500 * 7/27 = Rs. 10500   B's share = 40500 * 9/27 = Rs. 13500   C's share = 40500 * 11/27 = Rs. 16500   Rs.10,500, Rs. 13,500, Rs. 16,500nswer: Rs.10,500, Rs. 13,500, Rs. 16,500
Answer: A
Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?	Choose the correct choice from the following answers:
A) 1/3
B) 1/6
C) 1/8
D) 1/7
E) 1/1

Solution: 3h = 5c   6c = 10s   1/3 = 21h*3 + 15c*2   = 63h + 30c   = 105c + 30c = 135c   B 105  + 30= 
105  + 30 = 135
135c   B= 15c*6 + 40s*7 1/2   = 90c + 300s   = 90c + 180c = 270c   1/3:B 90  + 180= 
90  + 180 = 270
270c   1/3:B= 135:270   27:52   1/3 = 27/79 = 1/3   1/3nswer: 1/3
Answer: A
Jerry had an average score of 85 on his first eight quizzes. He had an
average score of 81 on his first nine quizzes. What score did he receive on
his ninth quiz?	Choose the correct choice.
A) 49  B) 51  C) 53  D) 55  E) 57

Solution: The sum of Jerry’s first 8 scores is 8 · 85 and the sum of his first 9 scores is 9 · 81, so he received   9 · 81 − 8 · 85 on his 9th quiz. You can do the arithmetic or note that the answer ends in a 9.   correct answer 49
Answer: A
E is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of E, and y is the minimum value of the sum of k distinct members of E, what is x + y? Select the correct option:
A) kn B) kn + k^2 C) kn + 2k^2 D) 2kn – k^2 E) 2kn

Solution: Probably the easiest way to solve this question would be to assume some values for n and k.   Say n=3, so E, the set of the first n positive odd numbers would be: E={1, 3, 5};   Say k=1, so E, the maximum value of the sum of K distinct members of Z would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of E would simply be 1.   X+Y=5+1= 
5+1 = 6
6.   Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1= 
2*3*1 = 6
6.   Answer: 2kn.
Answer: E
Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans?
Pick
A) 5.5  B) 11  C) 47.5  D) 66  E) 49.5

Solution: Total price of six cans = 6*36.5= 
6*36.5 = 219
219   Total price of 4 cans= 4*30= 
4*30 = 120
120   Total rice of two cans= 219 - 120= 
219 - 120 = 99
99   Average price of two cans= 99/2= 
99/2 = 99/2 = around 49.5
49.5 c   Another way to do it is this:   Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans.   So cost of the two cans= 2*36.5 + 4*6.5= 
2*36.5 + 4*6.5 = 99
99   Avg cost of the two cans= 99/2= 
99/2 = 99/2 = around 49.5
49.5c   Answer (49.5)
Answer: E
What is difference between biggest and smallest fraction among 2/5, 3/4, 4/5 and 5/6
Choose the correct choice from the following answers:
A) 2/5
B) 3/5
C) 1/6
D) 1/7
E) None of these

Solution: None of thesexplanation:   2/5= 
2/5 = 2/5 = around 0.4
.4, 3/4= .75, 4/5 = .8 and 5/6 = .833   So biggest is 5/6 and smallest is 2/5   Their difference is 5/6 - 2/5 = 13/30   Option None of these
Answer: E
In how many ways can 5 boys be allotted four different sofas such that none of the sofas are empty and all the 5 boys are accommodated? Choices
A) 300
B) 290
C) 280
D) 260
E) 240

Solution: 4 boys can be selected from 5 boys in 5C4 ways = 5   4 boys can be arranged in 4 rooms in 4! ways   and since 1 boy has to share a room with one of the 4 boys, therefore total ways = 2! = 2   Hence total number of ways in which allocation can be done = 5C4 * 4! * 2! = 5*2*4! =240   240
Answer: E
There are 9 books on a shelf that consist of 2 paperback books and 7 hardback books. If 5 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?	Pick one
A) 85
B) 95
C) 105
D) 115
E) 125

Solution: The total number of ways to select 5 books is 91055 = 126   The number of ways which do not include any paperbacks is 71055 = 21   The number of combinations with at least one paperback is  126-21= 
 126-21 = 105
105   The answer is 105.
Answer: C
Power saving (in %) of a bulb is directly proportional to square root of its efficiency. By how much % is power saving of bulb-1(efficiency 0.8) greater than power saving of bulb-2 (efficiency 0.2)?	Choose the correct choice from the following choices
A) 60%  B) 70%  C) 80%  D) 90%  E) 100%

Solution: Power, P1=k∗sqrt(0.8)   Power, P2=k∗sqrt(0.2)   Difference = P1−P2=k∗sqrt(0.8)−k∗sqrt(0.2)   % greater =k∗sqrt(0.8)−k∗sqrt(0.2)/k∗sqrt(0.2)∗100   = 100%.   Hence, 100%
Answer: E
The speed at which a man can row a boat in still water is 18 kmph. If he rows downstream, where the speed of current is 6 kmph, what time will he take to cover 100 metres? Choose the correct choice: A) 6.67seconds B) 18 seconds C) 26 seconds D) 14.99 seconds E) 6 seconds

Solution: Speed of the boat downstream = 18 +6= 
18 +6 = 24
24 kmph= 24 * 5/18 = 6.67m/s   Hence time taken to cover 100 m = 100/6.67   = 14.99 seconds.   Answer:14.99 seconds
Answer: D
By selling 14 pencils for a rupee a man loses 22%. How many for a rupee should he sell in order to gain 22%?	Choose the correct choice from the following answers:
A) 10	B) 9	C) 7	D) 6	E) 4

Solution: 88% --- 14   122% --- ?   88/122 * 14 = 10   10nswer: 10
Answer: A
A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 8 Gallons of water and 16 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?	Choose the correct option
A) 120  B) 75  C) 100  D) 150  E) 175

Solution: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.   Original mixture has 20% salt and 80% water.   Total = x   Out of which Salt = 0.2x and water = 0.8x   Now, 1/4 water evaporates and all salt remains.   So what remains is 0.2x salt and 0.6x water.   Now 16 gallons salt is added and 8 gallons of water is added.   So salt now becomes -> (0.2x + 16) and water --> (0.6x+8)   Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.   So (0.2x+16) = (0.6x+8)/2 => 0.2x= 24   Solving, x = 120   120nswer : 120
Answer: A
The distance between towns A and B is 300 km. One train departs from town A and another train departs from town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find the speeds of both trains if 2 hours after their departure the distance between them is 40 km.
Choose the correct choice:
A) 22  B) 27  C) 236  D) 90  E) 81

Solution: Let the speed of the slower train be xx km/hr. Then the speed of the faster train is (x+10)(x+10) km/hr. In 2 hours they cover 2x2x km and 2(x+10)2(x+10)km, respectively. Therefore if they didn't meet yet, the whole distance from A to B is 2x+2(x+10)+40=4x+602x+2(x+10)+40=4x+60 km. However, if they already met and continued to move, the distance would be 2x+2(x+10)−40=4x−202x+2(x+10)−40=4x−20km. So we get the following equations:   4x+60=3004x+60=300   4x=2404x=240   x=60x=60 or   4x−20=3004x−20=300   4x=3204x=320   x=80x=80   Hence the speed of the slower train is 60 km/hr or 80 km/hr and the speed of the faster train is 70 km/hr or 90 km/hr.   Answer:90
Answer: D
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda?
Answers
A) 4/7	B) 3/7	C) 15/64	D) 4/28	E) 28/135

Solution: using Binomial. theorem   n15/64r (p)^r (q)^n-r   615/644 (1/2)^4 (1/2)^r   which is 15/64   Answer is 15/64.
Answer: C
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform?  Pick one:
A) 240  B) 188  C) 177  D) 260  E) 320

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Length of the train= 20 * 20= 
20 * 20 = 400
400 m.   Let the length of the platform be x m . Then,   (x + 400)/36= 20 => x = 320.   Answer: 320
Answer: E
Divide $500 among Y,Z in the ratio 2:8. How many $ that Z get? Choices: A) $100 B) $200 C) $300 D) $500 E) $400

Solution: Sum of ratio terms = 2+8= 
2+8 = 10
10   Z= 500*8/10= 
500*8/10 = 400
$400   Answer is $400
Answer: E
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?
Choose the correct choice from the following
A) 5/36 B) 5/24 C) 1/12 D) 1/6 E) 1/4

Solution: 2/3 * (2X-1) / (3X-1) = 5/ 12 => X = 3   So total gems = 9   and probability of ruby = 1/3 * 2/8 = 1/12   answer 1/12 1/12
Answer: C
A set of numbers has the property that for any number t in the set, t - 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -5
II. 11
III. 6	Select the correct option
A) I only B) II only C) I and II only D) II and III only E) I, II, and III

Solution: The question is which of the followingmustbe in the set, notcouldbe in the set.   If -1 is in the set so must be -1-2=-3, as -3 is in the set so must be -3-2=-5, as -5 is in the set so must be -5-2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers less than -1 are also in the set.   I onlynswer: I only.
Answer: A
At exactly what time past 9:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?	Choose one:  A) 20 13/21 minutes past 7:00  B) 20 13/17 minutes past 7:00  C) 21 3/23 minutes past 7:00  D) 21 9/11 minutes past 9:00  E) 22 4/9 minutes past 7:00

Solution: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?   That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 9:00. At 9:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.   So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of   210-90= 
  210-90 = 120
120 degree at the rate of 5.5 degrees per minute ---> 120/5.5= 21 9/11 minutes.   Thus, 21 9/11 minutes past 9:00 is the correct answer.
Answer: D
Three numbers are in the ratio 3:5:7. The largest number value is 63. Find difference between Smallest & largest number is?  Choose the correct choice.
A) 20  B) 24  C) 30  D) 34  E) 36

Solution: == 3:5:7   Total parts = 15   = The largest number value is 63   = The largest number is = 7   = Then 7 parts -----> 63 ( 7 * 9 = 63 )   = smallest number = 3 & Largest number = 7   = Difference between smallest number & largest number is = 7 - 3= 
7 - 3 = 4
4= Then 4 parts -----> 36 (4 * 9 = 36)   36
Answer: E
Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 16, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?  Choose one
A) 7/4  B) 10/3  C) 12/5  D) 15/7  E) 18/11

Solution: The time it takes printer X is 16 hours.   The combined rate of Y and Z is 1/10 + 1/20 = 3/20   The time it takes Y and Z is 20/3   The ratio of times is 16 / (20/3) = 3*16/20 = 12/5   The answer is 12/5.
Answer: C
Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
Choices
A) 2.05%  B) 2.10%  C) 2.25%  D) 2.30%  E) 2.34%

Solution: Generally in such cases, there is always loss.   So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.   Loss% = 2.25%ommon loss and gain% 2	= x 2   10 10   Therefore, here common loss and gain % = 15%   Hence,   Loss% = 15 2	= 2.25%   2.25%
Answer: C
A person is traveling at 35km/hr and reached his destiny in 5hr find the distance?	Choose the correct choice from the following choices:
A) A)100km  B) B)95km  C) C)175km  D) D)80km  E) E)125km

Solution: speed = 35km/hr   time = 5hr   distance = 35*5= 
35*5 = 175
175km   Answer is 175km
Answer: C
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
Answers:
A) 70/3 sec  B) 80/3 sec  C) 40/3 sec  D) 60/3 sec  E) 90/3 sec

Solution: C   Relative speed = (36 + 72)* 5/18 = 6 * 5= 
6 * 5 = 30
30 mps.   The time required= d/s = (100 + 100 + 200)/35   = 400/30 = 40/3 sec.
Answer: C
Find the value of x from the below equation? : 3x^2+5x+2 = 0  Choose the correct choice from the following options.
A) -1  B) 1  C) -2  D) 2  E) -3

Solution: a = 3, b = 5, c = 2   x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6   x1 = (-5 + 1)/6 = -4/6 = -2/3   x2 = (-5 - 1)/6 = -6/6 = -1   -1
Answer: A
A sum of money place at compound interest doubles itself in 5 years. In how many years will it amount to eight times itself?	Choose the most appropriate option:
A) 15 years	B) 11 years	C) 12 years	D) 18 years	E) 19 years

Solution: 100 ---- 200 ---- 5   400 ---- 5   800 ---- 5   ------   15 years   15 yearsnswer: 15 years
Answer: A
A software programmer does 10% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X? Choose the correct choice from the following choices.
A) 13x /15  B) 15x/15  C) 7x/15  D) 2x/30  E) 13x/30

Solution: Take X=30 lines   80% of 30 = 24 lines   20% of 30 = 6 lines   W - R - T   6 lines - r1 - 24 (first 80% of the 30 days)   24 lines - r2 - 6 ( last 20% of the 20 days)   r1 = 1/4r2 = 4   Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1   => 6 * 4 + 8 * 1/4 = 24 + 2= 
24 + 2 = 26
26   Insert, X=30 in all options => 7x/15 is the answer.
Answer: C
On flipping 3 coins together what is the outcomes for exactly one head and one tail?	Select:
A) {HHH, HTH, THH, TTH, THT, HTT}
B) {HHT, HTH, THH, TTH, THT, TTT}
C) {HHT, HTH, THH, TTH, THT, HTT}
D) {HHT, HTH, THH, TTH, THT, TTT}
E) None

Solution: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}   Favorable outcomes for at least two heads   = favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail.   = {HHT, HTH, THH, TTH, THT, HTT}   {HHT, HTH, THH, TTH, THT, HTT}
Answer: C
What is the lowest possible common multiple of 2 distinct integers, each greater than 67? Choose the correct choice
A) 68  B) 69  C) 136  D) 68^2  E) 68·69

Solution: In order to get the lowest LCM, we have to take the first number as 68 and the next number as its multiple.   So, I can take 68 and 136 as two distinct numbers, such that Lowest LCM = 136.   Answer should be 136.
Answer: C
A work which could be finished in 11 days was finished 3 days earlier after 10 more men joined. The number of men employed was?  Select:  A) 22  B) 20  C) 88  D) 71  E) 12

Solution: x ------- 11   (x + 10) ---- 6   x * 11 = (x + 10)6   x = 12   \Answer: 12
Answer: E
A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?	Choose one
A) 12 1/2 years	B) 2 1/2 years	C) 12 1/5 years	D) 12 6/2 years	E) 13 1/2 years

Solution: 100 ---- 200 ---- 5   200 ---- 5   100 ---- 2 1/2   ------------------   600 ---- 12 1/2 years   12 1/2 yearsnswer: 12 1/2 years
Answer: A