MU-NLPC/Calc-aqua_rat huggingface dataset:
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 50 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?  Answers:
A) 18/79	B) 1/6	C) 1/25	D) 1/250	E) 1/900

Solution: So there are 900 cars that they have to search.. Each takes 50mins, total of 45000 mins.. Have to find in 180 mins.. Prob180/45000 = 1/250 (ANSWER 1/250)
Answer: D
The largest two digit number which is a perfect cube, is:
Choose one.
A) 25	B) 36	C) 49	D) 64	E) 81

Solution: Explanation:   4*4*4= 
4*4*4 = 64
64   Answer: 64
Answer: D
A certain candy store sold lollipops for $0.90 each and pieces of individually wrapped saltwater taffy for $0.20 each. If a customer purchased both lollipops and taffy from the store, and spent a total of $3.90, what total number of lollipops and saltwater taffy did the customer purchase?	Choose the correct answer:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: we can take numbers, as price of lollipop 9, 2 for taffy and 39 total for ease.   Now we can determine quickly that total number should range between 39/9 <= N <=39/2, so ans should be between 4 and 20.   Now solving the expression 9A+2B =39   first possibility with 1 lollipop, 15 taffy we get $3.90 total amount, but   1+15= 
  1+15 = 16
16, and 16 is not an option.   So next choice, for 9A+2B=39 would come by decreasing 39 in multiple of 9 and checking divisibility of that number by 2. this way we get   3 lollipop, 6 taffy would be $3.90 total, 3*0.90 + 6*0.20= 3.90   Hence total number is  3 + 6= 
 3 + 6 = 9
9   Ans 9
Answer: D
A train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min. Find the length of train?
Choose the correct choice from the following answers:
A) 100.1 m
B) 223.1 m
C) 111.1 m
D) 120.3 m
E) 133.4 m

Solution: EXPLANATION:   We know,   Speed =	Distance / Time   Speed =	10/50	x 60 = 40 x 5/18 m/sec = 11.1 m/sec   Length of train = (Speed x Time)   = (11.11 x 10)   = 111.1 m   ANSWER IS 111.1 m
Answer: C
In N is a positive integer less than 200, and 2N/108 is an integer, then N has how many different positive prime factors?
Choose the correct choice from the following options
A) 2  B) 3  C) 5  D) 6  E) 8

Solution: (B).   2n/108 must be an integer. => n/54 must be an integer. Hence n must be a multiple of 2*3*9.   => n has 3 different prime integers.
Answer: B
A salt manufacturing company produced a total of 100 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year? Choose the correct choice from the following options:
A) 700	B) 650	C) 750	D) 800	E) 725

Solution: Total production of salt by the company in that year = 100 + 200 + 300 + .... + 1200 = 7800.   Average monthly production of salt for that year = 7800/12= 
7800/12 = 650
650.   Answer: 650
Answer: B
If a and b are positive integers such that a/b = 5.75, which of the following must be a divisor of a	Choices:
A) 6  B) 5  C) 4  D) 1  E) 7

Solution: a/b = 5.75   a/b = 575/100   a/b = 23/4   a = 23/4*b   We require to find from the available 5 options that must be a divisor of a"   This also means which of the following 5 options can divide 23 evenly   (Ignore b as its value unknown; Ignore 4 as in denominator)   Only option 1 = 1 best fits in   Answer = 1   ANSWER:1
Answer: D
If 213 × 16 = 3408, then 1.6 × 2.13 is equal to : Select:
A) 0.3408
B) 3.408
C) 34.08
D) 340.8
E) None of these

Solution: Solution   1.6 × 2.13 = (16/10x 213/100)= (16x 213/1000) = 3408/100 = 3.408. Answer 3.408
Answer: B
Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 457?
Choices: A) 26.4% B) 21% C) 20% D) 19% E) None of these

Solution: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621   SP = Rs. 457, Discount = 621 - 457= 
621 - 457 = 164
164   Discount %= 164/621 * 100 = 26.4%   26.4%NSWER:26.4%
Answer: A
Which of the numbers below is the odd one out
1,4,10,19,21,31,46. Choose the correct choice.
A) 4  B) 21  C) 10  D) 19  E) 31

Solution: 21 is the odd man.. diff between sucessive no.s are multiples of 3   ANSWER:21
Answer: B
The average (arithmetic mean) of a normal distribution of a school's test scores is 62, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
Choices
Select
A) 63rd percentile	B) 68th percentile	C) 84th percentile	D) 96th percentile	E) 98th percentile

Solution: (78-65)/6.5= 
(78-65)/6.5 = 2
2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2= 84th percentile   84th percentile
Answer: C
A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent E should the number of hours worked be increased?
Choose the correct choice from the following options:
A) 12.5% B) 20% C) 25% D) 50% E) 100%

Solution: Correct Answer: C   Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked E will be 25% greater than the original number. The answer is 25%.
Answer: C
If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
Choose the correct option:
A) 157.55	B) 157.76	C) 157.5	D) 157.57	E) 157.87

Solution: (3500*1.5*3)/100= 
(3500*1.5*3)/100 = 157.5
> 157.50   Answer: 157.5
Answer: C
Four dice are thrown simultaneously. Find the probability that all of them show the same face.	Choose the correct answer.
A) 1/215
B) 1/216
C) 1/217
D) 2
E) 2/215

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64   n(S)=64   Let X   be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6   Hence required probability,   =n(X)n(S)=664   =1/216   Answer is 1/216
Answer: B
If x^4 + y^4 = 650, then the greatest possible value of x is between: Choose the correct choice from the following options.
A) 1 to 2  B) 2 to 3  C) 3 to 4  D) 5 to 6  E) 7 to 8

Solution: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.   We're told that X^4 + Y^4 = 100. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....   X^4 = 650   Looking at the answers, it makes sense to see what 5^4 equals....   5^4 = 625   Since that is BELOW 650, and 6^4 will clearly be MORE than 650, we have the correct answer.   Final Answer:   5 to 6
Answer: D
If * stands for /, / stands for -, + stands for * and - stands for +, then
9/8*7+5-10 = ?
Choose the correct choice from the following options.
A) 13.3  B) 10.8  C) 10.7  D) 11.4  E) 12.5

Solution: 9/8*7+5-10 this expression becomes 9-8/7*5+10 after exchanging the symbols then the values for it would be   9-1.142*5+10= 
  9-1.142*5+10 = 13.29
13.290(app)=13.3   13.3NSWER:13.3
Answer: A
Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?	Choose the correct choice: A) 120 B) 150 C) 190 D) 110 E) 140

Solution: Let the number be x.   Then, 4*x/5 –(65% of x) = 21   4x/5 –65x/100 = 21   5 x = 2100   x = 140.   Answer is 140.
Answer: E
If a and b are nonzero integers such that 2a/5 = b, then each of the following must be true EXCEPT Choose the correct choice from the following answers: A) 0 < b/a < 1 B) ab is positive. C) On the number line, b lies between 0 and a. D) The ratio of a to b is equivalent to 10/4. E) a – b is positive.

Solution: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.   We're told that A and B are NONZERO INTEGERS and that 2a/5 = b or 2a = 5b. We're told that each of the answer is always true EXCEPT for one of them...   Before we get to the actual work, it's important to note a few details:   1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...   2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.   Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...   A = 5   B = 2   AND   A = -5   B = -2   Answer A: 0 < B/A < 1   2/5 and -2/-5 both = 2/5. Answer A appears true.   Answer B: AB is positive   (2)(5) and (-2)(-5) both = +10. Answer B appears true.   Answer C: B is between 0 and A on the number line   0....2....5   -5....-2....0   Answer C appears true.   Answer D: A/B = 10/4   5/2 = -5/-2   10/4 = 5/2   Answer D appears true.   Answer E: A - B is positive     5 - 2= 
  5 - 2 = 3
3   -5 - (-2)= -3 *****This is NOT always true.   Final Answer:   a – b is positive.
Answer: E
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?	Choose the correct choice from the following answers.
A) Rs.340	B) Rs.282	C) Rs.739	D) Rs.400	E) Rs.538

Solution: 2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400   Answer:Rs.400
Answer: D
A 2-digit number is such that the product of the digits plus the sum of the digits
is equal to the number. What is the units digit of the number?  Pick:	A) 1	B) 3	C) 5	D) 7	E) 9

Solution: Assume the 2 digit number is of the form xy, with x 6= 0. The statement indicates   that these two digits satisfy the equation xy + x + y = 10x + y. A quick simplication gives   y = 9.   correct answer 9
Answer: E
What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?	Choose the most appropriate option
A) 76 ways
B) 66 ways
C) 30 ways
D) 56 ways
E) 43 ways

Solution: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women   = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5= 
(4 * 3)/(2 * 1) * 5 = 30
30 ways.   Answer: 30 ways
Answer: C
(935421 x 625) = ?	Select:
A) 575648125 B) 584638125 C) 584649125 D) 585628125 E) None of these

Solution: Explanation:   935421 x 625 = 935421 x 54 = 935421 x(10/2)4   = 584638125   ANSWER IS 584638125
Answer: B
2,3,5,8,13,21,34,?  Choose one.
A) 57 B) 58 C) 55 D) 54 E) 56

Solution: Each number is the sum of the previous two numbers, ie 18 + 29 = 55.   Answer : 55
Answer: C
one person Tharak speed with the current is 10 km/hr and the speed of the current is 3 km/hr. Tharak's speed against the current is:
Choose the correct choice: A) 0 km/hr B) 1 km/hr C) 2 km/hr D) 3 km/hr E) 4 km/hr

Solution: Man's speed with the current = 10 km/hr   => speed of the man + speed of the current = 10 km/hr   speed of the current is 3 km/hr   Hence, speed of the man = 10-3= 
10-3 = 7
7 km/hr   man's speed against the current= speed of the man - speed of the current   = 7-3= 
7-3 = 4
4 km/hr   ANSW4 km/hrR:4 km/hr
Answer: E
The price of electricity in the area where the Smith family lives is scheduled to increase by 20% next year. Since the Smith family cannot afford an increase in their electric bill, how much will they have to reduce consumption to keep their cost the same?
Choose the correct choice from the following options:
A) 30%
B) 25%
C) 16.7%
D) 20%
E) None

Solution: Solution: Let the current year's electrical expense be represented by Rs. 100.   The price of electricity rises 20%. So, to buy same amount of electricity, they need to increase their expense,   = (100 + 20% of 100) = Rs. 120.   But, they want to keep electricity expense the same, so they have to cut Rs. by 20 to keep it to Rs. =100.   The % decrease in consumption is,   (20/120)*100 = 20%.   Mental Calculation Method;   100-----20%↑---→120------X%↓---→100.   Here, X = (20/120)*100 = 16.7%.   Answer: Option 16.7%
Answer: C
A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability T of generating an odd prime digit is between
Pick one:  A) 0 and 1/6  B) 1/6 and 1/3  C) 1/3 and 1/2  D) 1/2 and 2/3  E) 2/3 and 5/6

Solution: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1   Note that 1/10 is least value and is equal to 0.1 so we can write above series as   K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1   K=1/3+   P (3 or 5 or 7) =K*13/24   Required probability T= 13/24 × 1/3+ = 4+/24 > 1/6   Answer should be B   P.s. 3+ denotes a value little greater than 3 .   Same for 4+.
Answer: B
When integer Q is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3l
II. 4l+10
III. 5l
IV. 2l
V .6l  Options
A) I B) II C) IV D) V E) III

Solution: III
Answer: E
Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 80, what is his shoe size?	Choose the correct choice from the following answers:
A) 80 B) 70 C) 75 D) 40 E) 50

Solution: Solution -   Given that, G = 2B and Life expectancy(L) = 80   L=2SB/G -> 80 = 2SB/2B --> S=80.   80NS 80
Answer: A
The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from c to d, inclusive, where 0<c<d?  Answers
A) d(d+1)/2 - (c+1)(c+2)/2	B) d(d+1)/2 - c(c+1)/2	C) d(d+1)/2 - (c-1)c/2	D) (d-1)d/2 - (c+1)(c+2)/2	E) (d-1)d/2 - c(c+1)/2

Solution: Or try plug-in method: let d=4 and c=3 --> then d+c=7. Let see which option yields 7.   A. d(d+1)/2 - (c+1)(c+2)/2 = 10-10= 
10-10 = 0
0;   B. d(d+1)/2 - c(c+1)/2= 10-6= 
10-6 = 4
4;   C. d(d+1)/2 - (c-1)c/2= 10-3= 
10-3 = 7
7 --> OK;   D. (d-1)d/2 - (c+1)(c+2)/2= 6-10=-4;   E. (d-1)d/2 - c(c+1)/2 = 6-6= 
6-6 = 0
0.   Answer: d(d+1)/2 - (c-1)c/2.
Answer: C
P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?  Pick one
A) 2/7  B) 4/9  C) 6/7  D) 1/2  E) 9 3/5

Solution: 9 3/5xplanation :   Amount of work P can do in 1 day = 1/16   Amount of work Q can do in 1 day = 1/12   Amount of work P, Q and R can together do in 1 day = 1/4   Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48   => Hence R can do the job on 48/5 days = 9 (3/5) days   ANSW9 3/5R:9 3/5
Answer: E
Calculate how many men are needed to finish a specific task in 15 days if it will take 60 men to complete the same task in 80 days. ?
Pick: A) 325 B) 323 C) 310 D) 320 E) 221

Solution: men required to finish the work in 15 days = 60*80/15= 
60*80/15 = 320
320   Answer is 320
Answer: D
A certain country is divided into 8 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/12 the total number of Progressives in the entire country, what fraction of the country is Traditionalist? Pick one.
A) 1/5	B) 1/3	C) 1/2	D) 2/3	E) 3/5

Solution: Let P be the number of Progressives in the country as a whole.   In each province, the number of traditionalists is P/12   The total number of traditionalists is 8P/12 = 2P/3.   The total population is P + 2P/3 = 5P/3   P / (5P/3) = 3/5   The answer is 3/5.
Answer: E
Solve the equation for x : 6x - 47 + 3x = 4 + 9 - x  Choose the correct choice.
A) 4 B) 5 C) 7 D) 9 E) 6

Solution: 6   6   9 x + x = 13 + 47   10 x = 60 => x = 6
Answer: E
If 1/8 of a pencil is black, 1/2 of the remaining is white and the remaining 3 1/2 cm is blue, find the total length of the pencil.  Choose the correct option.
A) 12	B) 9	C) 8	D) 6	E) 5

Solution: Let the total length of the pencil be x cm.   Black part is 1/8 of the length so x/8.   so the Remaining part is x - x/8 ==> 8x/8 - x/8 ==> 7x/8 cm.   white part = 1/2 * 7x/8 = 7x/16 cm.   so the remaining part is 7x/8 - 7x/16 ==> 14x/16 - 7x/16 = 7x/16   which is equal to 3 1/2.   7x/16 = 7/2 cross multiply and we get x = 16/2= 
16/2 = 8
8 cm.   so the total length of the pencil is 8 cm. The correct answer is option 8) 8.
Answer: C
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 9 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art? Choose the correct choice from the following options.
A) 25 B) 32 C) 36 D) 48 E) 62

Solution: Make a venn diagram to get a clear picture. Look at the diagram:   Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.   d + f = 20 (People who take Art and one other class)   b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)   17 + 10 + 9 + b + d + e + f = 100 (Total people)   b + b/3 = 44   b = 33   Number of freshmen who take Art = 33 + 20 + 9= 
33 + 20 + 9 = 62
62   Answer 62
Answer: E
65% of a number is 21 less than 4/5th of that number. What is the number?
Choose the correct choice from the following answers:
A) 100
B) 120
C) 140
D) 130
E) 115

Solution: Let the number be x   Then, 4x/5 - (65% of x) = 21   4x/5-65x/100 = 21   x = 140   Answer is 140
Answer: C
A train crosses a platform of 350 m in 15 sec, same train crosses another platform of length 500m in 20 sec. then find the length of the train?
Choose the correct choice:
A) 100m B) 180m C) 159m D) 250m E) 152m

Solution: Length of the train be ‘X’   X + 350/15 = X + 500/20   4X + 1400 = 3X + 1500   X = 100m   100mnswer:100m
Answer: A
P has $63 more than what Q and R together would have had if both B and C had 1/9 of what P has. How much does P have?	Select
A) $69  B) $72  C) $75  D) $78  E) $81

Solution: P = (2/9)*P+63   (7/9)*P=63   P=81   The answer is $81.
Answer: E
A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work? Choose the correct choice from the following.
A) 17 days	B) 19 days	C) 22 days	D) 20 days	E) 18 days

Solution: 18 days   18 days   8/12 + 6/x = 1   X = 18 days
Answer: E
In the next Cricket World Cup T-20, Team R has decided to score 200 runs only through 4s and 6s. In how many ways can the Team R score these 200 runs?
Pick one
A) 13  B) 15  C) 16  D) 17  E) 18

Solution: Team R can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.   So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.   Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1= 
(50 - 2)/3 + 1 = 17
17   Answer: D   Alternate solution: 4x + 6y= 200 --> 2x + 3y = 100   x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.   There are 17 even multiples of 3 between 0 and 100.   Answer: 17
Answer: D
As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, four orange ice pops, and five lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?	Answers:
A) 7/22
B) 17/33
C) 27/44
D) 37/55
E) 47/66

Solution: P(2 cherry) = 3/12 * 2/11 = 6/132   P(2 orange) = 4/12 * 3/11 = 12/132   P(2 lemon) = 5/12 * 4/11 = 20/132   P(2 of the same flavor) = 38/132   P(2 different flavors) = 1 - 38/132 = 94/132 = 47/66   The answer is 47/66.
Answer: E
The sum of all consecutive odd integers from −19 to 29, inclusive, is
Choose the correct choice from the following choices:
A) 125
B) 135
C) 150
D) 175
E) 235

Solution: The sum of the odd numbers from -19 to +19 is 0.   Let's add the remaining numbers.   21+23+25+27+29 = 5(25) = 125   The answer is 125.
Answer: A
In how many ways Chief Minister and Minister be elected from a team of 8 members?  Choose the correct choice from the following answers.
A) 65	B) 56	C) 50	D) 58	E) 60

Solution: To do this, if captain is elected first, then we have 8 ways of doing this.   For election of vice-captain, we have only 7 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 8*7= 
8*7 = 56
56 ways.   56
Answer: B
What is the place value of 8 in the numeral 8729
Choose the correct option:
A) 8000 B) 3400 C) 3500 D) 3000 E) 4000

Solution: Option '8000'    8 * 1000= 
 8 * 1000 = 8_000
8000
Answer: A
Claire has a total of 80 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?  Choose the correct option.
A) 39 B) 50 C) 54 D) 57 E) 36

Solution: G+H =80 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12= 
25*12 = 300
300   G=80-H OR 3(80-H) +4H =300 H = 300-240= 
300-240 = 60
60 TH36N G= 96-60= 
96-60 = 36
36   36
Answer: E
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
Options:
A) 33	B) 16	C) 77	D) 88	E) 11

Solution: Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4   Suppose Tanya takes x days to do the work.   5:4 :: 20:x => x= 16 days.   Hence, Tanya takes 16 days to complete the work.   Answer: 16
Answer: B
Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long E would it take Victor to complete 10 jobs without any supervision?  Choose one:  A) 34  B) 52  C) 60  D) 70  E) 92

Solution: Rate when supervised = (job)/(time) = 1/t.   Rate when unsupervised = (job)/(time) = 1/(t+3).   For  144/2= 
 144/2 = 72
72 days he is supervised and for  144/2= 
 144/2 = 72
72 days he is unsupervised and does 36 jobs:   72/t + 72/(t+3)= 36 --> t=3 days --> t+3 = 6 days.   Victor to complete 10 jobs without any supervision will need E 10(t + 3) = 60 days.   Answer: 60.
Answer: C