mathewhe/aqua_rat huggingface dataset:
Question: A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit?
(A) 28000
(B) 30000
(C) 32000
(D) 34000
(E) None of these
Rationale: Explanation :
Suppose B's investment = x. Then A's investment= 3x
Suppose Bs period of investment = y, then A's period of investment = 2y
A : B = 3x * 2y : xy
= 6 : 1
Total profit * 1/7 = 4000
=> Total profit = 4000*7 = 28000. Answer : Option A
Answer: (A) 28000
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.2,40,000 earned at the end of 3 years from the start of the business in 1999 ?
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.80,000
(E) None of these
Rationale: Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(24000x2/6) = Rs. 80,000. Answer D
Answer: (D) Rs.80,000
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 7500
(B) 8500
(C) 9000
(D) 8000
(E) 9500
Rationale: Explanation:
A : B : C
=20000Ã—24:15000Ã—24:20000Ã—18=20Ã—4:15Ã—4:20Ã—3=4Ã—4:3Ã—4:4Ã—3=4:3:3=20000Ã—24:15000Ã—24:20000Ã—18=20Ã—4:15Ã—4:20Ã—3=4Ã—4:3Ã—4:4Ã—3=4:3:3
B's share = 25000Ã—310=7500
ANSWER IS A
Answer: (A) 7500
Question: Robert walks from point A to point B at an average speed of 10 kilometers per hour. At what speed, in kilometers per hour, must Robert walk from point B to point A so that her average speed for the entire trip is 12 kilometers per hour?
(A) 15km/hr
(B) 21km/hr
(C) 16km/hr
(D) 20km/hr
(E) 17km/hr
Rationale: Let's suppose that speed while returning was x km/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
12= 2*10*x/10+x
x= 15 km/hr
answer is A
Answer: (A) 15km/hr
Question: A radio station has to choose six days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
(A) 7
(B) 15
(C) 21
(D) 35
(E) 56
Rationale: Behind the story, we are really being asked to evaluate 7C6. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C6, the third entry of the seventh row, is 7. Answer = A.
Answer: (A) 7
Question: If p and q are both negative and pq < q^2, which of the following must be true?
(A) p < q < p^2 < q^2
(B) q < p< p^2 < q^2
(C) p < q < q^2 < p^2
(D) p^2 < q^2 < q < p
(E) q^2 < p^2 < q < p
Rationale: Because pq < q^2 and both are negative, I thought p < q. So I crossed off answers c), d), and e).
And because p < q , p^2 < q^2
ans B
Answer: (B) q < p< p^2 < q^2
Question: The average (arithmetic mean) of four distinct positive integers is 5. If the average of the smaller two of these four integers is 6, which of the following represents the maximum possible value of the largest integer?
(A) 2
(B) 4
(C) 3
(D) 8
(E) 1
Rationale: Let the distinct number be A,B,C, and D
Its given A > B > C > D
also A + B + C + D =20 and A + B = 6 means C + D = 14
Since the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 8
Answer : D
Answer: (D) 8
Question: 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 54 km/hr. What is the length of the platform?
(A) 288
(B) 240
(C) 881
(D) 1277
(E) 121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: (B) 240
Question: If it is true that x > -2 and x < 9, which of the following must be true?
(A) x > 2
(B) x > -9
(C) x < 2
(D) -9 < x < 2
(E) none of the above.
Rationale: the range is -2 < x < 9
A. x > 2 - no because x can be between -2 < x < 2
B. x > -9 -- the answer is true, because the values of x are always >-9
C. x < 2 - no because x can be between 2 < x < 9
D. -9 < x < 3 - no because x can be between 2 < x < 9
E. none of the above.
Answer: B
Answer: (B) x > -9
Question: Jerry bought a bottle of perfume for a gift for his wife.
The perfume cost $92 before tax.
If the total price including tax was $98.90, find the tax rate
(A) 7.5%
(B) 5%
(C) 12%
(D) 8%
(E) 10%
Rationale: Total price including tax is $98.90
Perfume cost before Tax is = 92
ie 92 *7.5% +98.90
Answer is 7.5%
Answer: (A) 7.5%
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 30%, then find the population of city atthe end of the year 2007
(A) 976374
(B) 971750
(C) 980241
(D) 2356677
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 30/100)
= 971750
B
Answer: (B) 971750
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 220 m in 18 sec. then find the length of the train?
(A) 200m
(B) 180m
(C) 272m
(D) 210m
(E) 267m
Rationale: Length of the train be ‘X’
(X + 150)/15 = (X + 220)/18
5X + 1100 = 6X + 900
X = 200m
Answer: A
Answer: (A) 200m
Question: Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 150 meters. They next meet after Sally has run 200 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
(A) 250
(B) 300
(C) 350
(D) 400
(E) 500
Rationale: Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 100 meters, thus second time she runs 2*150 = 300 meters.
Since second time (when they run full circumference) Brenda runs 300 meters and Sally runs 200 meters, thus the circumference is 300 + 200 = 500 meters.
Answer: E.
Answer: (E) 500
Question: In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets W can be created from this process?
(A)  35
(B)  105
(C)  210
(D)  420
(E)  630
Rationale: W=7C4 * 3C2 = 105 Answer B.
7C4 ways to choose 4 numbers for Box 1
3C2 ways to choose 2 numbers for Box2
1 way for Box 3 .
every combination will give a different product and can be arranged least to highest only in one way .B
Answer: (B)  105
Question: 852.68 âˆ’ 4.5 + 288.98 = ? âˆ’ 2132.54
(A) 6078.58
(B) 5225.9
(C) 6258.58
(D) 6088.58
(E) None
Rationale: Option 'C'
Answer: (C) 6258.58
Question: If the average (arithmetic mean) of the four numbers 3, 16, 33, and (N + 1) is 20, then N =
(A)  19
(B)  20
(C)  21
(D)  27
(E)  29
Rationale: 3+16+33+N+1= 20 x 4 = 80
=>N +53 = 80
=>N=27
Answer D
Answer: (D)  27
Question: Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 240 square feet. How many feet offence does Frank use?
(A) 14
(B) 52
(C) 54
(D) 180
(E) 240
Rationale: Area = Length x Breadth
240 = 40 x Breadth
So, Breadth = 6 Units
Fencing required is -
Breadth + Breadth + Length
6 + 6 + 40 => 52 feet
Answer must be (B) 52
Answer: (B) 52
Question: A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 800 m long?
(A) 42
(B) 44
(C) 46
(D) 48
(E) 50
Rationale: Speed = 120/6 = 20 m/sec.
Required time = (120 + 800)/20
= 46 sec.
Answer:C
Answer: (C) 46
Question: The cost price of 14 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/15
(B) 27 3/11
(C) 36 2/14
(D) 32 2/16
(E) 12 2/12
Rationale: 14 CP = 11 SP
11 --- 2 CP
100 --- ? =>27 3/11%.Answer: B
Answer: (B) 27 3/11
Question: If 10 litres of an oil of Rs.40 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?
(A) Rs.48.66
(B) Rs.51.03
(C) Rs.54.17
(D) Rs.55.33
(E) None of the above
Rationale: 40*10 = 400
66*5 = 330
730/15 = 48.66
ANSWER:A
Answer: (A) Rs.48.66
Question: A and B go cycling in the same direction with speeds of 6 km/hr and 12 km/hr. A car from behind passes them in 9 and 10 seconds respectively. What is the speed of the car?
(A) 22 km/hr
(B) 33 km/hr
(C) 66 km/hr
(D) 44 km/hr
(E) None of these
Rationale: Explanation:
The relative speed of A and B is 6 km/hr = 1.67 m/s
As the car passes A after 10s, the distance between A and B after 10s (i.e. at 11th second) is the distance covered by car in 1 second.
Therefore, at t = 11, d = 1.67 * 11
d = 18.33 m
v = d/t = 18.33/1 = 18.33m/s
v = 66 km/hr
ANSWER C
Answer: (C) 66 km/hr
Question: If the ratio of x to y is 3 to 5, then (y-x)/(x+y)?
(A) -7/3
(B) -2/8
(C) 2/8
(D) 1
(E) 7/3
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 3 to 5 means
(x/y)=(3/5)
Cross-multiply
3x = 5y
x = (3/5)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (3/5)*y) / ((3/5)*y + y)
= ((2/5)*y) / ((8/5)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(2/5) / (8/5)
= (2/5) * (8/5)
The 5s cancel each other out, and you are left with 2/8.
Answer: (C) 2/8
Question: 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
(A) 12 DAYS
(B) 9 DAYS
(C) 20 DAYS
(D) 14 DAYS
(E) 17 DAYS
Rationale: Answer: Option C
16 * 25 = 20 * x => x = 20 days
Answer: (C) 20 DAYS
Question: The average weight of 50 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?
(A) 51 1⁄3
(B) 52 3/5
(C) 52 5⁄3
(D) 43.42
(E) None of these
Rationale: Total weight of 50 students
= 50 × 52 = 2340 kg
Total weight of 5 students who leave
= 5 × 48 = 240 kg
Total weight of 5 students who join
= 5 × 54 = 270 kg
Therefore, new total weight of 50 students
= 2600 – 240 + 270 = 2630
⇒ New average weight = 2630⁄50 = 52 3/5 kg
Answer B
Answer: (B) 52 3/5
Question: A computer manufacturer produces a certain electronic component at a cost of $60 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) $28
(B) $82
(C) $172
(D) $138
(E) $192
Rationale: This question can be solved easily using a equation model.
150*p = 16500(fixed cost) + 150*60+150*2.
= 16500 +9000 +300 =
P= $172.
C
Answer: (C) $172
Question: 2, 5, 10, 17,..
(A) 5
(B) 8
(C) 26
(D) 7
(E) 12
Rationale: Explanation:
Numbers are
(1*1)+1=2
(2*2)+1=5
(3*3)+1=10
(4*4)+1=17
(5*5)+1=26
ANSWER:C
Answer: (C) 26
Question: If (a – b) is 9 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
(A) 6
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (a – b) – (c + d) = 9 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 9 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 9 and (b + d) = (c – a) – 3
=> (a – c) – 9 = (c – a) – 3 => 2(a – c) = 6 => (a – c) = 3
ANSWER:C
Answer: (C) 3
Question: a man can row 14 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
(A) 13 km/hr.
(B) 6 km/hr.
(C) 7 km/hr.
(D) 15 km/hr.
(E) 11 km/hr.
Rationale: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=14 or x=7.
Rate upstream=7 km/hr,rate downstream=21 km/hr.
Hence,rate of stream=1/2(21-7)km/hr=7 km/hr.
Answer is C.
Answer: (C) 7 km/hr.
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Loe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Loe?
(A) 15
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Loe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins.D
Answer: (D) 90
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
(A) Rs. 28000
(B) Rs. 24000
(C) Rs. 30000
(D) Rs. 26000
(E) None of these
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
ANSWER:B
Answer: (B) Rs. 24000
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 45% increase
(E) 50% increase
Rationale: CR = (A^2) * ( 1/B)
put any values
625 = 25*25
B increases by 100% so it becomes 50
CR remains same at 625
1/B becomes 50
so A^2 should be
625/50 = 12.5 or say decreased by 50%
ANSWER:D
Answer: (D) 45% increase
Question: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 1:3
(B) 2:3
(C) 3:1
(D) 4:1
(E) 4:3
Rationale: Let the present ages of A and B be 5x and 3x years respectively.
Then, (5x - 4)/(3x + 4) = 1/1
2x = 8 => x = 4
Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1
ANSWER C
Answer: (C) 3:1
Question: Car Z travels 55 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
(A) 320
(B) 375.2
(C) 400
(D) 408.3
(E) 440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 45 miles/hour, the car will run 55 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 44 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 44 miles/gallon * 10 gallons = 440 miles.
Answer E.
Answer: (E) 440
Question: The area of a square is equal to five times the area of a rectangle of dimensions 60 cm * 12 cm. What is the perimeter of the square?
(A) 289 cm
(B) 800 cm
(C) 829 cm
(D) 288 cm
(E) 240 cm
Rationale: Area of the square = s * s
= 5(60 * 12)
=> s = 60
= 60 cm
Perimeter of the square
= 4 * 60
= 240cm.
Answer: E
Answer: (E) 240 cm
Question: 57 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 13
(C) 14
(D) 15
(E) 19
Rationale: According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 57 x 12 x 5 = 30 x 6 x X
X = 19
Hence, the number of days = 19.
ANSWER:E
Answer: (E) 19
Question: Of the five numbers in a sequence, the first term is 7,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
(A) 6988.8
(B) 9,750.90
(C) 9,975.15
(D) 9,984.30
(E) 10,736.25
Rationale: 1st number= 7,000
2nd number = 20% of 7,000= 1400
3rd number= 20% of 1400= 280
4th number = 20% of 280= 56
5th number= 20% of 56= 11.2
Range = 7,000-11.2= 6988.8
A is the answer
Answer: (A) 6988.8
Question: what is the smallest integer that is multiple of 3,5,7
(A) A)105
(B) B)35
(C) C)200
(D) D)280
(E) E)140
Rationale: It is the lcm of 3, 5 and 7 which is 105.
The answer is A.
Answer: (A) A)105
Question: The average weight of A, B and C is 43 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 17 kg
(B) 20 kg
(C) 26 kg
(D) 31 kg
(E) 25 kg
Rationale: let d sum of a, b, c is 3*43=129
and sum of a and b s 2*40=80
sum of b and c is 3 *43=86
hence 80+86-129=25
ans=31
ANSWER:E
Answer: (E) 25 kg
Question: In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what Z percent of all the people in Smithtown are left-handed women?
(A)  50%
(B)  40%
(C)  25%
(D)  20%
(E)  10%
Rationale: looking at the ratio we can take total number of people=20..
ans 5/20 or 25% C
Answer: (C)  25%
Question: Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 20 times smaller, from source B alone?
(A) 6 hours and 40 minutes
(B) 15 minutes
(C) 20 minutes
(D) 10 minutes
(E) 3 minutes
Rationale: Let the movie size be 400 u.
Given,A+C=4 hrs.
A+C=100 u/hr
And A+B+C=2.5 hrs or 400/2.5=160 u/hr
B alone=160-100=60 u/hr
Trailer=20 times smaller or400/20=20 u
B will take 20/60 hrs or 20 minutes.
Ans C
Answer: (C) 20 minutes
Question: If a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh 104 kilograms. What is the student's present weight in kilograms?
(A) 70
(B) 71
(C) 72
(D) 73
(E) 74
Rationale: Let x be the weight of the sister.
Then the student's weight is 2x+5.
x + (2x+5) = 104
3x = 99
x = 33 kg
Then the student's weight is 71 kg.
The answer is B.
Answer: (B) 71
Question: A 12% stock yields 8%.The market value of the stock is :
(A) Rs. 72
(B) Rs. 150
(C) Rs. 112.50
(D) Rs. 116.50
(E) None of these
Rationale: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 12, investment = Rs.(100/8X12)= Rs. 150
∴ Market value of Rs. 100 stock = Rs.150
Answer B
Answer: (B) Rs. 150
Question: In a certain city each of 25 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors or a combination of 3 colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)
(A) 7
(B) 3
(C) 6
(D) 4
(E) 5
Rationale: E.5:
if we have 5 colors we can choose pairs in 5C2 + 5C3 ways = 10 + 10 and single color flags are 5. Therefore total number of flags = 25.
ANS E.
Answer: (E) 5
Question: In what time will a train 600 meters long cross an electric pole, if its speed is 144 km/hr
(A) 5 seconds
(B) 4.5 seconds
(C) 3 seconds
(D) 15 seconds
(E) None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 144*(5/18) = 40 m/sec
Time = Distance/speed
= 600/40 = 15 seconds
Answer: D
Answer: (D) 15 seconds
Question: Six bells commence tolling together and toll at the intervals of 2,4,6,8,10,12 seconds resp. In 60
minutes how many times they will toll together.
(A) 15
(B) 16
(C) 30
(D) 31
(E) None of these
Rationale: Explanation:
LCM of 2-4-6-8-10-12 is 120 seconds, that is 2 minutes.
Now 60/2 = 30
Adding one bell at the starting it will 30+1 = 31
Answer: Option D
Answer: (D) 31
Question: If 28 less than five times a certain number is 232. What is the number?
(A) 32
(B) 42
(C) 52
(D) 62
(E) 72
Rationale: 5x−28 Subtraction is built backwards,multiply the unknown by 5
5x−28=232 Is translates to equals
+28+28 Add 28 to both sides
5x=260 The variable ismultiplied by 5
5 5 Divide both sides by 5
x=52 The number is 52.
correct answer C
Answer: (C) 52
Question: The sum of the mean, the median, and the range of the set {2, 4, 6,8,10} equals which one of the following values?
(A) 21
(B) 42
(C) 61
(D) 84
(E) 10
Rationale: set {2, 4, 6, 8, 10}
Mean = (2+4+6+8+10)/5 = 6
Meadian = Middle term = 6
Range = Highest - Lowest = 10-1 = 9
Mean+Median+Range = 6+6+9 = 21
Answer: Option A
Answer: (A) 21
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for?
(A) 160
(B) 175
(C) 180
(D) 195
(E) 215
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 X 8 X 4) = 160.
160 X 2.40 + x X 3.20 = 432
3.20 X = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175
Answer: Option B
Answer: (B) 175
Question: How many diagonals does a 60-sided convex polygon have?
(A) 960
(B) 1280
(C) 1710
(D) 2560
(E) 3420
Rationale: A 60-sided convex polygon has 60 vertices.
If we examine a single vertex, we can see that we can connect it with 57 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 60 vertices can be connected with 57 vertices to create a diagonal then the total number of diagonals would be (60)(57) = 3420
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3420 by 2 to get 1710.
The answer is C.
Answer: (C) 1710
Question: Find the number of days required by z number of workers, working z hours a day to complete z units of work, if x workers, working x hours a day complete x units of work in x days.
(A) x3/z
(B) x2/z
(C) x3/z2
(D) x2/z2
(E) None of these
Rationale: Explanation :
M1D1T1W2 = M2D2T2W1
Where, M – number of men
D – number of days
T – time duration
W – amount of work
x*x*x*z = z*D2*z*x
D2 = x2/z
Answer : B
Answer: (B) x2/z
Question: How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?
(A) 16
(B) 27
(C) 31
(D) 32
(E) 64
Rationale: The solution offered counted it differently.
So I just want to clear it up whether I am also thinking in the right direction.
Number of subset
Since we have 5 digits other than 0, we can take any numbers from the set of 5 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
5c1+5c2+5c3+5c4+5c5=31
And one set is the NULL set having no elements in it so
31+1=32
ANSWER:D
Answer: (D) 32
Question: A number is increased by 50% and then decreased by 50%, the final value of the number is ?
(A) decrease by 20%
(B) decrease by 22%
(C) decrease by 23%
(D) decrease by 21%
(E) decrease by 25%
Rationale: Here, x = 50 and y = - 50
Therefore, the net % change in value
= ( x + y + xy/100)%
= [50 - 50 + (50 * -50)/100]% or - 25%
Since the sign is negative, there is a decrease in value by 25%.
ANSWER: E
Answer: (E) decrease by 25%