divelab/Sys2Bench huggingface dataset:
Question: David covered a distance of 50 miles on his first trip. On a later trip he traveled 50 miles while going three times as fast. His new time compared with the old time was:
Options:
A)twice as much
B)three times as much
C)the same
D)half as much
E)a third as much
Rationale: Let t be the time of the first trip.
On the later trip, David can travel 150 miles in time t.
The trip of 50 miles takes t/3.
The answer is E.
Answer: E
Question: A room is 25 meters long, 20 meters wide 10 meters in height. The longest possible rod which can be placed in the room is
Options:
A)30.54 meters
B)32.54 meters
C)34.54 meters
D)33.54 meters
E)35.54 meters
Rationale: Square root of 25^2+20^2+10^2...(Diognal) which is square root of 1125 that lies 33<√1125<34. Hence the answer should be D
Answer: D
Question: 6 people meet for a meeting. Each person shakes hands once with each other person present. How many handshakes take place?
Options:
A)30
B)21
C)18
D)15
E)10
Rationale: Let's look at the logic.
Every person shakes hand with other '5'. So, 6 people shake hands with 6X5= 30 people
But in this 30 we have counted two times the total handshakes (e shakes hand with f and f shakes hand with e)
So just divide 30/2= 15 total handshakes
Answer is D
Answer: D
Question: A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)276 m
B)279 m
C)210 m
D)207 m
E)202 m
Rationale: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 34 = 15
x + 300 = 510
x =210 m.
Answer: C
Answer: C
Question: Sam invested Rs. 12000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
Options:
A)13230.0
B)12300.02
C)16537.5
D)15000.0
E)16537.11
Rationale: P = Rs. 12000 ; R = 10% p.a. = 5% per half-year; T = 1 year
= 2 half-year
Amount = [12000 * (1 + 5/100)2]
= (12000 * 21/20 * 21/20)
= Rs.13230.00
Answer:A
Answer: A
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 6, how many people got on at the first stop?
Options:
A)128
B)64
C)32
D)16
E)8
Rationale: 7 - > 1
6 - > 2
5 - > 4
4 - > 8
3 - > 16
2 - > 32
1 - > 64
because people get off after the first stop
=> the formula will be : 2^(n-1) where n is the stop number
in this case n =6
=> 2^(6-1) = 2^5 = 32
=> answer is C
Answer: C
Question: Raman mixed 48 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Options:
A)129
B)287
C)195
D)188
E)112
Rationale: Explanation:
CP per kg of mixture = [48(150) + 36(125)]/(48 + 36) = Rs. 139.28
SP = CP[(100 + profit%)/100]
= 139.28 * [(100 + 40)/100] = Rs. 195
Answer:C
Answer: C
Question: The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?
Options:
A)715
B)469
C)400
D)750
E)850
Rationale: Explanation:
Let C.P be Rs. x
900 - x = 2(x - 450)
=> x = Rs.600
C.P = 600 gain required is 25%
S.P = [(100 + 25) × 600]/100
= Rs.750
Answer: D
Answer: D
Question: 0.0203 x 2.92/0.0073 x 14.5 x 0.7 = ?
Options:
A)0.4
B)0.6
C)0.8
D)0.5
E)0.3
Rationale: = 0.0203 x 2.92/0.0073 x 14.5 x 0.7
= 203 x 292/73 x 145 x 7
= 4/5
= 0.8
Answer is C.
Answer: C
Question: 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
Options:
A)4 days
B)6 days
C)8 days
D)2 days
E)10 days
Rationale: Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
Option A
Answer: A
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
3 ~ 2 ~ 7 ~ 4 = ____
Options:
A)1412
B)2910
C)2940
D)3749
E)4470
Rationale: A
1412
1412
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
3 ~ 2 ~ 7 ~ 4 = [first digit of (3 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (3 * 4)]
= 1412
Thus 1412 is the missing number.
Answer: A
Question: 0.2 x 0.7 = ?
Options:
A)0.0001
B)0.001
C)0.01
D)0.14
E)NONE OF THESE
Rationale: Explanation:
2 x 7 = 14.
Sum of decimal places = 2
0.2 x 0.7 = 0.14
Answer- D
Answer: D
Question: During a certain season, a team won 65 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?
Options:
A)80
B)75
C)56
D)50
E)105
Rationale: We are first given that a team won 65 percent of its first 100 games. This means the team won 0.65 x 100 = 65 games out of its first 100 games.
We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:
0.5(T – 100) = number of wins for remaining games
0.5T – 50 = number of wins for remaining games
Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:
Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season
65 + 0.5T – 50 = 0.7T
15 = 0.2T
150 = 2T
75 = T
Answer is B.
Answer: B
Question: CMM, EOO, GQQ, _____, KUU
Options:
A)MSQ
B)IPS
C)IIS
D)ISS
E)POL
Rationale: The first letters are in alphabetical order with a letter skipped in between each segment: C, E, G, I, K. The second and third letters are repeated; they are also in order with a skipped letter: M, O, Q, S, U.
ANSWER:D
Answer: D
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.50. What is the price of 2 doughnuts?
Options:
A)$ 0.55
B)$ 1.00
C)$ 1.10
D)$ 1.30
E)$ 1.50
Rationale: 3D + C = 2.25......(1)
2D + C = 1.5........(2)
(1) - (2) --> D = 0.75 --> 2D = 1.5
Answer: E
Answer: E
Question: Six children — A, B, C, D, E and F — are going to sit in six chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
Options:
A)240
B)720
C)1440
D)4320
E)4800
Rationale: for such questions , we can treat both as one then total person=5..
these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =5!*2=240
ans A
Answer: A
Question: The value of x + x(x*x*(in x)) when x = 2 is:
Options:
A)10
B)16
C)18
D)36
E)64
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Correct Answer:A)10
Answer: A
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
Options:
A)720
B)740
C)760
D)800
E)810
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
A)
Answer: A
Question: A cylinder of height h is 7/8 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
Options:
A)25%
B)50%
C)69%
D)80%
E)100%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 7/8
New cylinder 3/5
So 3/5/7/8 = 3/5*8/7 = 0.69 or 69%.
Answer C
Answer: C
Question: If the LCM and HCF of 4 and another number is 36 and 2 respectively. Find the other number ?
Options:
A)18
B)16
C)14
D)13
E)15
Rationale: HCF x LCM = Product of Numbers
2 x 36 = 4 x the other number
other number = (2 x 36) / 4
other number = 18
ANSWER : A
Answer: A
Question: How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman?
Options:
A)6
B)8
C)10
D)12
E)16
Rationale: 2 Women and 4 Men. Three people needed
It is always better to subtract the total from none in case of at least one problems.
Total ways = 6C3 = 20
Total ways without any women = 4C3 = 4
Hence ways in which at least one women will be present = 20 - 4 = 16
Correct option: E
Answer: E
Question: The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area R of that hemisphere?
Options:
A) 6/π
B) 9/π
C) 6
D) 9
E) 12
Rationale: Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4 *PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !!
Answer: D
Question: If 6log(4*5^2) = x, find x
Options:
A)10
B)11
C)7
D)12
E)9
Rationale: 6(log2^2*5^2)=x
6log(5*2)^2=x
6*2log(5*2)=x
12log10=x
log10 base 10=1
so
12*1=x
x=12
ANSWER:D
Answer: D
Question: The edges of a cuboid are 2 cm, 5 cm and 3 cm. Find the volume of the cuboid?
Options:
A)20
B)60
C)80
D)30
E)45
Rationale: 2*5*3
= 30
Answer: D
Answer: D
Question: In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his history paper, his average per paper would have been 65. How many papers were there in the examination?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: x(total marks)/y( no . of subjects)= 63;
x+20+2/y= 65;x+22/y=65
on solving :
y=11
ANSWER:D
Answer: D
Question: In what ratio must water be mixed with milk costing Rs.12 per litre to obtain a mixture worth of Rs.8 per litre?
Options:
A)1 : 2
B)2 : 1
C)4 : 3
D)5 : 3
E)None
Rationale: Ratio of water to milk = 4 : 8 = 1 : 2
Answer A
Answer: A
Question: Two numbers are less than third number by 60% and 74% respectively. How much percent is the second number less than by the first ?
Options:
A)18%
B)29%
C)35%
D)41%
E)None of these
Rationale: Explanation :
Let the third number is x.
then first number = (100-60)% of x
= 40% of x = 4x/10
Second number is (26x/100)
Difference = 4x/10 - 26x/100 = 14x/10
So required percentage is, difference is what percent of first number
=> (14x/100 * 10/4x * 100 )% = 35%
Answer : C
Answer: C
Question: In how many ways the letters of the word LOOC be arranged?
Options:
A)8
B)9
C)12
D)14
E)17
Rationale: In this four letters means 4! = 24 ways
But 'O' is repeated two times.
And thus we divide the final ways by 2. I.e. there are only 24/2 = 12 ways of arranging the letters of this word.
LOOK, LOKO, LKOO, KOOL, KOLO, KLOO, OOLK, OOKL, OLOK, OKOL, OLKO, OKLO = 12 Ways
C
Answer: C
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
Options:
A)338
B)286
C)266
D)500
E)128
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
Answer: D
Answer: D
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)2888
B)1640
C)2782
D)833
E)2772
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640.Answer: B
Answer: B
Question: What will be the cost of building to decorate which area equal to 225 sq ft, if the price per foot of building is Rs. 5?
Options:
A)300
B)150
C)600
D)1200
E)800
Rationale: Let the side of the square plot be a ft.
a2 = 225 => a = 15
Length of the fence = Perimeter of the plot = 4a = 60 ft.
Cost of building the fence = 60 * 5
= Rs.300.
Answer: A
Answer: A
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)50 km/hr
B)24 km/hr
C)8 km/hr
D)5 km/hr
E)16 km/hr
Rationale: Explanation:
Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: A
Answer: A
Question: Look at this series: 375000,75000,25000, ... What number should come next?
Options:
A)17
B)10
C)15
D)5000
E)8
Rationale: 5000
This is a simple division series. Each number is divided by 5.
ANSWER D
Answer: D
Question: $378 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share?
Options:
A)$200
B)$208
C)$216
D)$224
E)$232
Rationale: Let the shares for A, B, and C be x, 2x, and 4x respectively.
7x = 378
x = 54
4x = 216
The answer is C.
Answer: C
Question: If on an item a company gives 25% discount and 25% profit it makes. if they now gives 10% discount then the profit %age made by the company will be...
Options:
A)40
B)55
C)35
D)30
E)50
Rationale: Let the Marked Price of the item is x and the Cost Price be y.
For 25% discount the Selling price is 0.75x.
(0.75x-y)/y=0.25 which gives y=0.6x
next if the SP is 0.9x then
gain%=(0.9x-y)/y * 100 = (0.9x-0.6x)/0.6x * 100=50%
hence,profit% = 50%.
ANSWER:E
Answer: E
Question: An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes :
Options:
A)10%
B)10.25%
C)10.5%
D)None of these
E)Cannot be determined
Rationale: Let the sum be Rs 100. Then,
S.I. for first 6 months = (100×10×1/100×2) = 5
S.I. for last 6 months = (105×10×1/100×2) = 5.25
So, amount at the end of 1 year = (100 + 5 + 5.25) = 110.25.
∴ Effective rate = (110.25 – 100) = 10.25%.
Answer B
Answer: B
Question: A number is mistakenly divided by 5 instead of being multiplied by 5. Find the percentage change in the result due t this mistake.
Options:
A)96%
B)95%
C)2400%
D)200%
E)400%
Rationale: lets take a number 20
20/5 = 4
20*5 = 100
diff = 100 - 4 = 96 %
ANSWER:A
Answer: A
Question: Q is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in Q?
I. 9
II. 15
III. 27
Options:
A)I only
B)II only
C)I and II only
D)I and III only
E)I, II, and III
Rationale: Ans: C
Q->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Answer: C
Question: In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?
Options:
A)24
B)36
C)72
D)84
E)96
Rationale: The prompt gives us the specific restriction that a boy can't sit next to another boy and a girl can't sit next to another girl. Since there are chairs on one side of the table and stools on the other side of the table, we have to account for 2 possible seating arrangements:
BGB
GBG
and
GBG
BGB
From here, we can use a simple permutation to get to the answer:
Moving from left-to-right....
For the firstspot, there are 3 different boys to choose from
For the secondspot, there are 3 different girls to choose from
For the thirdspot, there then 2 different boys to choose from
For the fourthspot, there are then 2 different girls to choose form
For the fifth and sixthspots, we have the 1 boy and 1 girl that are left
(3)(3)(2)(2)(1)(1) = 36 possible seating arrangements for each of the two options.
(36)(2) = 72
C
Answer: C
Question: The average height of 35 boys in a class was calculated as 181cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
Options:
A)187.89 cm
B)179.29 cm
C)123.98 cm
D)149.98 cm
E)146.89 cm
Rationale: Calculated average height of 35 boys = 181 cm.
Wrong total height of 35 boys = 181 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 181 cm - (166 cm - 106 cm)/35
= 181 cm - (166 cm - 106 cm)/35 = 181 cm - 60 /35 cm
= 181 cm - 1.71 cm = 179.29 cm.
Answer: B
Answer: B
Question: If selling price is doubled, the profit triples. Find the profit percent:
Options:
A)200%
B)500%
C)100%
D)450%
E)800%
Rationale: C
C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
Answer: C
Question: Ayesha's father was 34 years of age when she was born while her mother was 28 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)16
B)14
C)15
D)10
E)12
Rationale: Mother's age when Ayesha's brother was born = 28 years.
Father's age when Ayesha's brother was born = (34 + 4) years = 38 years.
Required difference = (38 - 28) years = 10 years.
Answer:D
Answer: D
Question: Shane is playing a board game. For his first turn he moved ahead 3 spaces, for the second, 5
spaces and for the third, 1 space. For his next turn he had to go back 6 spaces. After that he got
a card that said he could move two times the biggest forward move he had done so far. Now how
many spaces from the beginning is Shane’s game piece?
Options:
A)3
B)13
C)23
D)33
E)43
Rationale: You may want to draw this one.
biggest move is 5, so two times
biggest move is 10.
3 + 5 + 1 = 9
9 - 6 = 3
3 + 10 = 13, so he is 13 spaces
from the beginning.
correct answer B
Answer: B
Question: Find the greatest number which leaves the same remainder when it divides 25, 62 and 105.
Options:
A)1
B)8
C)12
D)16
E)None of these
Rationale: 105 - 62 = 43
62 - 25 = 37
105 - 25 = 80
The H.C.F of 37, 43 and 80 is 1.
ANSWER:A
Answer: A
Question: Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 9 meters. What is value of the radius in meters?
Options:
A)1/2
B)1/3
C)1.5
D)3
E)6
Rationale: 10*0.31 = 3.1 = pi*R^2*h
R^2 = 3.1 / (pi*9) which is about 1/9
R = 1/3
The answer is B.
Answer: B
Question: The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 5 months. At this time, the construction was behind schedule by how many projects?
Options:
A)34
B)62
C)198
D)204
E)504
Rationale: Project/month : 612/18 = 34
Project in 6 month to be completed = 34*5 =170
Lag :170-108 = 62
B is the answer
Answer: B
Question: The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b?
Options:
A)2
B)3
C)4
D)5
E)Cannot be determined from the information given.
Rationale: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2.
Answer: A.
Answer: A
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)21.1
D)21.7
E)23
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
Option 'B'
Answer: B
Question: A circle in the coordinate plane passes through points (-3, -2) and (2, 4). What is the smallest possible area of that circle?
Options:
A)13π
B)15.25π
C)262√π
D)52π
E)64π
Rationale: The distance between the two points is sqrt(61).
radius = sqrt(61)/2
Area= pi*(sqrt(61)/2)^2
B. 15.25π
Answer: B
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 15,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.31,570. Suganya's share is
Options:
A)Rs.9471
B)Rs.12,628
C)Rs.18,040
D)Rs.7015.56
E)None
Rationale: Solution
Ratio of their shares	=(15000Ã—8):(42000Ã—10)
= 2 : 7.
Suganya's share	= Rs.(31570 Ã—2/9)
= Rs.7015.56
Answer D
Answer: D
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 73°, what fraction of the wheel’s area is represented by the smallest sector?
Options:
A)7/60
B)9/80
C)11/120
D)13/240
E)17/360
Rationale: The largest angle is 73.
Let d be the difference between any two angles in the progression.
The sum of all the angles will be:
73 + (73-d) + (73-2d) + ... + (73-7d) = 584 - 28d
The sum of all the central angles in a circle = 360
584 - 28d = 360
d = 224/28 = 8
The smallest sector is (73-7d) = 73-7*8 = 17
The fraction of the area covered is 17/360.
The answer is E.
Answer: E
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
Options:
A)39
B)42
C)45
D)47
E)48
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: B
Question: A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 9 hours. What is the maximum distance he
can cover?
Options:
A)20km
B)40km
C)60km
D)80km
E)90km
Rationale: t=d/s, so
9=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)
9=x(18/80)
x=40km
ANSWER:B
Answer: B
Question: If y is not equal to zero, and y+1/y = 2, then what is the value of y^4 + (1/y)^4?
Options:
A)2
B)4
C)5
D)8
E)0
Rationale: y + 1/y=2
we square both sides so we have y^2 + 1/y^2 +2 = 4
or y^2 + 1/y^2= 2
squaring again we have y^4 + 1/y^4 + 2 = 4
or y^4 + 1/y^4 = 2
answer =2 (A)
Answer: A
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 10 years?
Options:
A)3 : 2
B)1 : 3
C)2 : 3
D)1 : 5
E)2 : 1
Rationale: Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 2 years/Simple Interest for 10 years
=T1/T2
=2/10
=1/5
=1:5
Answer : Option D
Answer: D