divelab/Sys2Bench huggingface dataset:
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Six years from today, the difference between the age of the boy and the combined ages of the girls will be
Options:
A)1
B)2
C)-3
D)–5
E)–1
Rationale: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 6 years there ages are
7 ....................... 7 ............................ 9
Difference = 9 - (7+7) = 9 - 14 = -5
Answer = D
Answer: D
Question: What is the product of the prime numbers between 10 and 20
Options:
A)10^1
B)10^2
C)10^3
D)10^4
E)10^5
Rationale: E)
Answer: E
Question: 1852 - 1230 ÷ 10.00 = ?
Options:
A)62.2
B)2000
C)1700
D)1729
E)None
Rationale: Answer
Given expression = 1852 - 1230 ÷ 10.00
= 1852 - 123
= 1729
Correct Option: D
Answer: D
Question: A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold?
Options:
A)a) 2m/300
B)b) m/300
C)c) 5m/900
D)d) m/300 + 50
E)e) 350/m
Rationale: Let Cost of 300 shares be $ 3000
So, Cost of 1 shares be $ 10 =>m/300
Selling price per share = (100+60)/100 * m/300
Or, Selling price per share = 5/3 * m/300 => 5m/900
Hence answer will be (C)
Answer: C
Question: The speed of a car is 140 km in the first hour and 40 km in the second hour. What is the average speed of the car?
Options:
A)72 kmph
B)75 kmph
C)30 kmph
D)90 kmph
E)82 kmph
Rationale: S = (140 + 40)/2
= 90 kmph
ANSWER:D
Answer: D
Question: A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased?
Options:
A)7
B)6
C)5
D)2
E)3
Rationale: Explanation:
The equation for this problem can be made as:
5x + 7y =38
Where x is the number of watermelons and y is the number of pineapples.
Now test for 2, 3 and 4:
For y = 2
5x + 14 =38
x is not an integer
For y = 3
5x = 17
X not an integer
For y =4
X = 2
So 4 pineapples and 2 watermelons can be bought by 38 Rs.
ANSWER:D
Answer: D
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 30 percent during the third year. What is the value of the account today?
Options:
A)$10,350
B)$8,050
C)$10,500
D)$11,500
E)$12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.7 = 10,395
Answer B is correct.
Answer: B
Question: A train 125 m long passes a man, running at 3 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)48
B)50
C)28
D)26
E)29
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 3) km/hr. x - 3 = 45 ==> x = 48 km/hr
Answer: A
Answer: A
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
Options:
A)1987
B)2799
C)3288
D)3000
E)2982
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer: D
Answer: D
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 24 candies so that now Rebecca has four times as many candies as Tina has. Rebecca has now how many candies initially?
Options:
A)36
B)48
C)54
D)55
E)40
Rationale: T = R
T - 24 ;R + 24
R + 24 = 4 ( T - 24 )
R + 24 =4T - 96
R - 4T = - 120
We knowR = T, so
R - 4T = - 120
Or, R - 4R = -120
Or, - 3R = - 120
Or, R = 40( This is the initital no of Candies Rebecca had)
Answer will be E 40
Answer: E
Question: A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2¢ envelopes and 3¢ envelopes. If the company requested 1 more 2¢ envelopes than 3¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
Options:
A)(7x-4)/2
B)5x+7
C)4x-1
D)(3x+22)/2
E)(9x-4)/2
Rationale: We can take
X+1 = 5
X= 4
So 2c envelopes will be 3
and 3c envelopes will be 2
So total cost will be 12
Then that is our target
Plug x =4 in answer choices
Only A works
Correct Answer : A
Answer: A
Question: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x?
Options:
A)17
B)19
C)21
D)23
E)25
Rationale: The median is (6+8)/2 = 7
The mean is (4+5+6+8+10+x)/6 = (33+x)/6
(33+x) /6 * 3/4 = 7
x = 56-33 = 23
The answer is D.
Answer: D
Question: Evaluate 49 / .07
Options:
A)400
B)500
C)700
D)None of these
E)506
Rationale: Explanation:
49/.07 = 4900/7 = 700
Option C
Answer: C
Question: What is the remainder when 43^91 is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
91 has the form 4k+3 so the units digit of 43^91 is 7.
The remainder when dividing by 5 is 2.
The answer is C.
Answer: C
Question: If x = 5 - q and y = 3q - 1, then for what value of q, x is three times to y ?
Options:
A)0
B)1
C)-1
D)-8
E)8
Rationale: Explanation:
x = 3y <=> 5 - q = 3 (3q - 1) <=> 5 - q = 9q - 3 <=> 8q = 8 <=> q = 1.
Answer: B
Answer: B
Question: Jimâ€™s Taxi Service charges an initial fee of $2.5 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
Options:
A)$3.15
B)$4.45
C)$4.80
D)$5.65
E)$5.40
Rationale: Let the fixed charge of Jimâ€™s Taxi Service = 2.5 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.5 + (3.6/.4) * .35
= 2.5 + 9*.35
= 5.65 $
Answer D
Answer: D
Question: Which of the following CANNOT be the median E of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?
Options:
A)(w+x)/2 - 1
B)(w+z)/2
C)(x+y)/2
D)(y+z)/2 -1
E)(w+x+y+z)/4
Rationale: Using the properties of consecutive positive integers we could right away eliminate B,C and E.
(B) - The average of first and last terms is the median
(C) - For even number of integers, the median is the average of middle terms
(E) - The average is equal to median if the integers are consecutive
Remaining answer choices are A and D.
For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median E.
Answer (A)
Answer: A
Question: E individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
Options:
A)E-d
B)dx/E
C)dx
D)dx/E(E - d)
E)E-d
Rationale: Number of individuals = E
Amount paid by each individual = n
Total expected amount = Charity's goal = nE = x
n = x/E
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/E --> Additional amount
Number of individuals who are paying = E - d
Additional amount has to be divided among the (E - d) individuals --> dx/E(E - d)
D
Answer: D
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
Options:
A)2888
B)2887
C)2880
D)2886
E)2881
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
Answer:C
Answer: C
Question: A fair 8-sided dice labeled 1 to 8 is tossed three times. What is the probability the value of the dice shown is 3 at least once?
Options:
A)57/512
B)7/512
C)55/512
D)9/512
E)11/512
Rationale: This is a fair dice with 8 fair sides, so the probability of the dice landing on any sides is equal.
The question ask if the value of the dice is shown 3 at least once
So the calculation of the first possible outcomes is 1/8*1/8*1/8 (all of the dice thrown shown the value of 3)
This is follow by the second possible outcomes if the dice thrown show the value of 3 2 times ( 1/8*1/8*7/8) *7 here referring to any number besides 3
The third possible outcomes is that the dice show the value 3 one time ( 1/8*7/8*7/8)
So the answer is 1/512+7/512+49/512= 57/512
Answer: A
Answer: A
Question: The simple interest on a sum of money will be Rs.400 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Options:
A)800
B)3799
C)1200
D)2693
E)1732
Rationale: P --- 10 ---- 400
P --- 5 ----- 200
3P --- 5 ----- 600
------
=> 800
Answer: A
Answer: A
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1200, what is the reduced price for kg?
Options:
A)s.40
B)s.46
C)s.49
D)s.41
E)s.60
Rationale: 1200*(25/100) = 300 ---- 5
? ---- 1
=> Rs.60
Answer: E
Answer: E
Question: If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of the sky ?
Options:
A)Red
B)BLUE
C)PINK
D)ORANCE
E)BLACK
Rationale: Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of the sky is 'Blue' but in coding language, 'Blue' is called 'Red'.
ANSWER: A
Answer: A
Question: c.	What number should replace the letter K?
2, 2, 4, 12, 12, 24, 72, 72, 144, 432, K
Options:
A)866
B)864
C)434
D)432
E)452
Rationale: The sequence progresses x1, x2, x3 repeated; The letter K should be 432 x 1 = 432.
Ans D = 432
Answer: D
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 20, the dividend is:
Options:
A)1000
B)1200
C)1020
D)100
E)120
Rationale: Divisor = (5 * 20) = 100
= 10 * Quotient = Divisor
=> Quotient = 100/10 = 10
Dividend = (Divisor * Quotient) + Remainder
Dividend = (100* 10) + 20 = 1020.
C
Answer: C
Question: Four representatives are to be randomly chosen from a committee of six men and six women. How many different 4-representative combinations contain at least one woman?
Options:
A)400
B)415
C)455
D)480
E)495
Rationale: 12*11*10*9/4*3*2*1=11*5*9=495
Forbidden options
6*5*4*3/4*3*2*1=5*3=15
495-15=480
ANS:D
Answer: D
Question: Tough and Tricky questions: Word Problems.
ACT Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
Options:
A)$4,035
B)$4,036
C)$9,035
D)$16,140
E)$36,140
Rationale: The ACT company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Answer: C
Question: What is the probability of getting a queen or spade from a set of cards?
Options:
A)3/13
B)4/13
C)5/13
D)6/13
E)7/13
Rationale: no. of spade = 13
no. of queen = 3 (excluding queen of spade)
no. of possible outcome = 13+3 = 16
probability = no. of favorable outcome/ total possible outcomes = 16/52 = 4/13
ANSWER:B
Answer: B
Question: In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 65, what is the least possible difference between n and m.
Options:
A)a.1
B)b.3
C)c.5
D)d.6
E)e.9
Rationale: 2n+5m=65
try with n=5 and m=11 the equation will be satisfied
2(5)+5(11)=65
so difference between M and N is 6,
Answer D
Answer: D
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 25 terms of set X?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: 25*4 + 24*40 + 23*400 = 100 + 960 + 9200 = 10260
The hundreds digit is 2.
The answer is B.
Answer: B
Question: Set X is composed of nine numbers, labeled X1 through X9. Set Y is also composed of nine numbers, labeled Y1 through Y9. Set Y is defined as follows: Y1 = 1 + X1; Y2 = 2 + X2; and so on, including Y9 = 9 + X9. How much larger is the sum of set Y's mean and range than the sum of set X's mean and range?
Options:
A)cannot be determined
B)4
C)9
D)5
E)12
Rationale: Yes, the correct answer is A
Answer: A
Question: Rohit spends 40 % of his salary on food, 20% on house rent,10% on entertainment and 10% on conveyance. If his savings at the end of the month are Rs. 1500, Then his monthly salary is:
Options:
A)Rs.6000
B)Rs. 7500
C)Rs. 8000
D)Rs. 9,000
E)Rs. 10,000
Rationale: Saving = [100 – (40 + 20 +10 + 10)] %
= 20 %
Let the monthly salary be Rs. X
Then,
20% of X = 1500 ¡ê 20X / 100 = 1500
X = 1500 x 5 = 7500
X = 7500
answer : C
Answer: C
Question: The largest number among st the following that will perfectly divide 101^100 – 1 is:
Options:
A)9,000
B)9900
C)10,000
D)11,000
E)12000
Rationale: The easiest way to solve such problems for objective exam purposes is trial and error or by back
substituting answers in the choices given.
1012 = 10,201
1012 − 1 = 10,200.
This is divisible by 100.
Similarly try for 1013 − 1 = 1,030,301−1 = 1,030,300.
So you can safely conclude that (1011 − 1) to (1019 − 1) will be divisible by 100.
(10110 − 1) to (10199 − 1) will be divisible by 1000.
Therefore, (101100 − 1) will be divisible by 10,000.
C
Answer: C
Question: If x : y = 2 : 9, find the value of (2x + 2y) : (5x – y)
Options:
A)22:1
B)22:3
C)7:1
D)5:3
E)8:1
Rationale: Explanation:
Given: x/y = 2/9
(2x + 2y) : (5x – y)
= (2*2 + 2*9) : (5*2 – 9)
= 22:1
ANSWER: A
Answer: A
Question: If x is 13 percent greater than 80, then x =
Options:
A)88.8
B)90.4
C)88.0
D)70.9
E)71.2
Rationale: 13% of 80 = (80*0.13) = 10.4
11% greater than 80 = 80 + 10.4 = 90.4
Answer is clearly B.
Answer: B
Question: The average age of a family of 6 members is 22 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?
Options:
A)15
B)18
C)21
D)12
E)19
Rationale: Present age of total members = 6 X 22 = 132
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 132 - 42 = 90
Therefore, avg age at the birth of youngest member = 90/6 = 15.
ANSWER:A
Answer: A
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Options:
A)23.56
B)23.58
C)23.56
D)23.51
E)23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer:E
Answer: E
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)8
B)7
C)5
D)2
E)1
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
ANSWER A
Answer: A
Question: If y > 0, (4y)/20 + (3y)/10 is what percent of y?
Options:
A)40%
B)50%
C)60%
D)70%
E)80%
Rationale: can be reduced to 2y/10+3y/10 =y/2=50%
Answer B
Answer: B
Question: If the sum of two numbers is 18 and the sum of their squares is 220, then the product of the numbers is
Options:
A)40
B)44
C)52
D)88
E)90
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 18 and x2 + y2 = 220.
Now, 2xy = (x+y)2 - (x2 + y2)
= (18)2 - 220= 324 - 220= 104
xy = 52.
Answer C
Answer: C
Question: Eight years ago, the ratio of ages of P and Q was 5:2. Six years from now, the ratio of their ages will be 4:3. What is P's age at present?
Options:
A)16
B)18
C)20
D)22
E)24
Rationale: 2(P-8)/5 = (Q-8). Then Q = 2(P-8)/5 + 8
3(P+6)/4 = Q+6
3(P+6)/4 = 2(P-8)/5 +14
15P+90 = 8P + 216
7P = 126
P = 18
The answer is B.
Answer: B
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)2888
B)2669
C)2500
D)2762
E)8227
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
Answer:C
Answer: C
Question: A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 5 students hold membership in both organizations, how many different committee are possible?
Options:
A)215
B)275
C)325
D)385
E)495
Rationale: student government + the student advisory board consists of 9 + 8 = 17 members.
5 students hold membership in both, so they were counted twice.
The total number of people to choose from is 17 - 5 = 12
The number of ways to choose 8 members from 12 is 12C8 = 495
The answer is E.
Answer: E
Question: Which of the following is an integer?
I. 9! / 6!
II. 9! / 8!
III. 9! / 7!5!
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: 9!/6! = 9*8*7 which is an integer.
9!/8! = 9 which is an integer.
9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer.
The answer is D.
Answer: D
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $18, what was the price before the first discount?
Options:
A)$32
B)$34.31
C)$28.44
D)$67.54
E)$65.23
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 18
(x - 25%x) - 25%(x - 25%x) = 18
Solve for x
x = $32
correct answer A
Answer: A
Question: Having scored 96 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?
Options:
A)28
B)27
C)26
D)22
E)24
Rationale: Explanation :
Let the average score of the first 18 innings be n
18n + 96 = 19(n+4)=> n = 20
So, Average score after 19th innings = x+4 =24.
Answer : E
Answer: E
Question: Two pipes A and B can fill a tank in 10 hours and 20 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Options:
A)10/3
B)20/3
C)15/7
D)11/17
E)1/4
Rationale: Part filled by A in 1 hour = 1/10
Part filled by B in 1 hour = 1/20
Part filled by (A+B) in 1 hour = 1/10 + 1/20 = 3/20
Both the pipes together fill the tank in 20/3 hours
Answer is B
Answer: B
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 450-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
Options:
A)1,108
B)3,700
C)2,108
D)2,124
E)2,256
Rationale: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.
Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 450 for $22.95.
For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 450x8 = 3600 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 3700 hot dogs.
2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 3700 (ANSWER B)
Answer: B
Question: 4, 6, 12, 14, 28, 30, ?
Options:
A)20
B)40
C)60
D)80
E)100
Rationale: C
60
The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
Answer: C
Question: In a sample of books, 10 percent are 100-200 pages long, and 60 percent have more than 100 pages. What percentage of the books are more than 200 pages?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: 60 percent are more than 100 pages --> This means 60 percent of books are either 100-200 pages or more than 200 pages
Already, we know % of 100-200 pages= 10 %
So, % of 200+ page books = 60 % - 10 % = 50 % .. => (B).. Is it correct ?
Answer: B
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
Options:
A)Rs.208
B)Rs.279
C)Rs.228
D)Rs.205
E)Rs.225
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer:D
Answer: D
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
Options:
A)456 kms
B)482 kms
C)552 kms
D)556 kms
E)None of these
Rationale: Explanation:
Total distance travelled in 12 hours =(35 + 37 + 39 + .....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n = 12 , d = 2.
Required distance = 12/2[2 × 35 + {12 - 1) × 2] =6(70 + 23)
= 552 kms.
Answer: C
Answer: C
Question: A tank can be filled by a tap in 20 minutes and by another tap in 60 minutes. Both the taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will be completely filled in what time ?
Options:
A)10 mins
B)15 mins
C)20 mins
D)25 mins
E)30 mins
Rationale: Explanation:
How we can solve this question ?
First we will calculate the work done for 10 mins, then we will get the remaining work, then we will find answer with one tap work, As
Part filled by Tap A in 1 min = 1/20
Part filled by Tap B in 1 min = 1/60
(A+B)'s 10 mins work =
10∗(1/20+1/60)
=10∗4/60=2/3
Remaining work = 1−2/3=1/3
METHOD 1
=>1/60:1/3=1:X
=>X=20
METHOD 2
1/60 part filled by B in=1min1/3 part will be filled in=1/3/1/60=60/3=20
Option C
Answer: C
Question: If x and y are integers and xy = 330, x or y must be divisible by which of the following?
Options:
A)3
B)4
C)6
D)20
E)30
Rationale: xy = 330 = 2 * 3 * 5 * 11
One of x or y must be divisible by 3.
The answer is A.
Answer: A
Question: What will be remainder when (67^67 + 67) is divided by 68 ?
Options:
A)65
B)66
C)67
D)71
E)72
Rationale: (xn + 1) will be divisible by (x + 1) only when n is odd.
(67^67 + 1) will be divisible by (67 + 1)
(67^67 + 1) + 66, when divided by 68 will give 66 as remainder.
B)
Answer: B
Question: If A : B= 3 : 5 and B : C = 7 : 9, then A : B : C is:
Options:
A)2:4:8
B)21:35:45
C)5:10:15
D)12:24:36
E)36:42:8
Rationale: A:B=3:5, B:C=7:9, A:B:C=3Ã—7:7Ã—5:5Ã—9
â‡’ 21:35:45
Answer: B.
Answer: B