divelab/Sys2Bench huggingface dataset:
Question: Mala purchased a cooker and a stove for Rs. 6000 &Rs. 9000 respectively. He sold the cooker at a loss of 4% and the mobile stove at a profit of 8%. Overall how much he make a profit.
Options:
A)480
B)220
C)120
D)596
E)327
Rationale: Let the SP of the cooker and the stove be Rs. r and Rs. m respectively.
r = 6000(1 - 4/100) = 6000 - 240
m = 9000(1 + 8/100) = 9000 + 720
Total SP - Total CP = r + m - (6000 + 9000) = -240 + 720= Rs. 480
As this is positive, an overall profit of Rs. 480 was made.
A
Answer: A
Question: How much time will it take for an amount of Rs. 1400 to yield Rs. 140 as interest at 5% per annum of simple interest?
Options:
A)8 years
B)4 years
C)7 years
D)6 years
E)2 years
Rationale: Explanation:
Time = (100 x 140)/(1400 x 5) years
= 2 years.
Answer: E
Answer: E
Question: An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
Options:
A)1/7
B)3/7
C)4/5
D)5/7
E)6/11
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 10/15
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 9 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 9/14
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 10/15 × 9/14 = 3/7
B)
Answer: B
Question: Alice picked a number of pears, each of which she sold, canned, or poached. She canned 20 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 42 pears, then how many pears did she sell?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Let x be the amount of pears that she sold.
Then she poached 0.5x.
Then she canned 1.2*0.5x=0.6x.
The total amount of pears is x+0.5x+0.6x=2.1x
The fraction of pears that she sold is 1/2.1=10/21.
The number of pears she sold is (10/21)*42=20.
The answer is A.
Answer: A
Question: If the average of 20,21, 23, 24, 25, 28, 28, 29, 31 and x is 26, what is the value of x?
Options:
A)26
B)28
C)30
D)31
E)32
Rationale: Sum of the deviations of the numbers in the set from the mean is always zero
20, 21, 23, 24, 25, 28, 28, 29, 31
mean is 26
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 26 + 5 = 31
D
Answer: D
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
Options:
A)2777
B)1900
C)1887
D)20989
E)2671
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer:B
Answer: B
Question: A tank is filled in TWELVE hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)42 hours
B)28 hours
C)55 hours
D)66 hours
E)47 hours
Rationale: 1/A + 1/B + 1/C = 1/12 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/12
=> (1 + 2 + 4)/2B = 1/12
=> 2B/7 = 12
=> B = 42 hours.
Answer: A
Answer: A
Question: P is a positive integer and 225 and 216 are both divisors of P. If P=(2^x)*(3^y)*(5^z), where x, y and z are positive integers, what is the least possible value of x+ y+ z?
Options:
A)4
B)5
C)6
D)8
E)7
Rationale: Lets make factorization of 225 and 216 ..
225 = 5 X 5 X 3 X 3 X 3
216 = 2 X 2 X 2 X 3 X 3 X 3
P would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2 = 8(D)(answer) ...
Answer: D
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)17
B)27
C)60
D)13
E)12
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: C
Answer: C
Question: What is the least number to be subtracted from 11, 15, 21 and 30 each so that resultant numbers become proportional?
Options:
A)5
B)6
C)3
D)8
E)1
Rationale: Let the least number to be subtracted be x, then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.
<=> (11 - x) : (15 - x) = (21 - x) : (30 - x)
=> (11 - x)(30 - x) = (15 - x)(21 - x)
From the options, when x = 3
=> 8 * 27 = 12 * 18
Answer:C
Answer: C
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options:
A)4
B)8
C)16
D)18
E)None of these
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B
Answer: B
Question: The food in a camp lasts for 25 men for 55 days. If five more men join, how many days will the food last?
Options:
A)80 days
B)30 days
C)46 days
D)16 days
E)15 days
Rationale: one man can consume the same food in 25*55 = 1375 days.
5 more men join, the total number of men = 30
The number of days the food will last = 1375/30
= 46 days.
Answer:C
Answer: C
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 522 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
Options:
A)220
B)230
C)210
D)240
E)250
Rationale: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(522-9-90*2)/3=210
Answer : C
Answer: C
Question: What is the remainder when the number W=14^2 * 15^8 is divided by 5?
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: 14^2 has units digit 6
15^8 has units digit 5
Thus W=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train?
Options:
A)150 meter
B)200 meter
C)666 meter
D)155 meter
E)144 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12
= 200 meter
Answer: B
Answer: B
Question: At the foot of a mountain the elevation of its summit is 45 degrees. After ascending one
KM towards the mountain upon an incline of 30 degrees, the elevation changes to 60
degrees. Find the Height of the mountain?
Options:
A)1.333Km
B)1.366Km
C)1.233Km
D)1.266Km
E)None of these
Rationale: At the foot of a mountain the elevation of its summit is 45 degrees. After ascending one KM towards the mountain upon an incline of 30 degrees, the elevation changes to 60 degrees. The Height of the mountain is guven by
[ Height -- sin 30 ] = [ Height -- cos 30 ] tan 60
whence Height = [tan 60 cos 30 -- sin 30 ] / [ tan 60 -- 1 ] km = 1.366 km
ANSWER:B
Answer: B
Question: A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 56 lots are to have 100 feet of frontage each, what is the value of x ?
Options:
A)400
B)3,200
C)6,160
D)4,400
E)4,760
Rationale: Total number of plots,be T
Plots with 80ft is (1/9)th of total plots.
Plots with 100ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 56 T = 63
Total lake frontage = 56X100 + 7X80 = 6160
Answer : C
Answer: C
Question: There are 50 students in a class. If 12% are absent on a particular day, find the number of students present in the class.
Options:
A)43
B)36
C)28
D)129
E)44
Rationale: Number of students absent on a particular day = 12 % of 50
i.e., 12/100 × 50 = 6
Therefore, the number of students present = 50 - 6 = 44 students.
Answer:E
Answer: E
Question: Three machines, each working at the same constant rate, together can complete a certain job in 18 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 9 days?
Options:
A)3
B)5
C)7
D)9
E)8
Rationale: Rate of one machine = 1 job / (18*3) days
let X = number of machines needed to complete the job in 9 days
1/(3*18) * 9 * X = 1 job
X = 6
6-3= 3
ANSWER: A
Answer: A
Question: In a meeting of 3 representatives from each of 7 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
Options:
A)189
B)179
C)159
D)169
E)180
Rationale: In fact, all 21 people will shake hands with 18 others.
So, it SEEMS like the TOTAL number of handshakes = (21)(18)
HOWEVER, we need to keep in mind that we have counted each handshake TWICE.
To account for this DUPLICATION, we must divide (21)(18) by 2.
So, the TOTAL # of handshakes = (21)(18)/2 = 189
Answer : A
Answer: A
Question: What is the unit digit in 12^100?
Options:
A)0
B)1
C)2
D)4
E)6
Rationale: Unit digit in 12^100 = unit digit in [(12^4)^25 ]But unit digit in 12^4=6unit digit 12^100= 6Answer is E
Answer: E
Question: A fellow borrowed a certain sum of money at 3% per annum at simple interest and in 3 years the interest amounted to Rs.1820 less than the sum lent. What was the sum lent?
Options:
A)1050
B)1220
C)1250
D)2000
E)1110
Rationale: P - 1820 = (P*3*3)/100
P = 2000
Answer: D
Answer: D
Question: If R = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in R than the median of the numbers in R?
Options:
A) 1.0
B) 1.5
C) 2.0
D) 2.5
E) 3.0
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (1 + 7 + 18 + 20 + 29 + 33)/6 = 18
Median = (18 + 20)/2 = 19
Difference = 1
Option A
Answer: A
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Options:
A)30%
B)32%
C)40%
D)44%
E)48%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120	x	m	= 6	x	m.
100	5
New breadth = 120	y	m	= 6	y	m.
100	5
New Area = 6	x x	6	y	m2	= 36	xy	m2.
5	5	25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11	xy x	1	x 100	%	= 44%.
25	xy
D
Answer: D
Question: Equal weights of two alloys containing tin, copper and lead in the ratio 3:2:7 and 4:11:3 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
Options:
A)41:81:37
B)33:91:81
C)17:28:27
D)51:86:89
E)None of these
Rationale: Exp. Let the weight of the two alloys be w each
Required ratio =
(3w/12 +4w/18): ( 2w/12 +11w/18 ): (7w/12+3w/18)
= 17w/36 : 28w/36 : 27w/36
= 17:28: 27
Answer: C
Answer: C
Question: The cost of fuming the engine of an army tank is proportional to the square of the speed and Rs 64 per hour for a speed of 16km/hr. Other costs amount to Rs 400 per hour. The tank has to make a journey of 400km at a constant speed.The most economical speed for this journey is :
Options:
A)20 km/hr
B)30 km/hr
C)35 km/hr
D)40 km/hr
E)None of these
Rationale: Explanation :
Cost = k2×speed2[ Where k is constant], And
=>64 = k×16×16
=>k=1/4.
=>cost=speed2 /4.
Total cost=[(speed2/4)+400]×400/speed
using options, putting different values of speed, we find speed = 40km/hr to be most economical.
Answer : D
Answer: D
Question: Two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 125 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)6
B)14
C)16
D)20
E)18
Rationale: Sol.
Speed of the first train = [150 / 10] m/sec = 15 m/sec.
Speed of the second train = [150 / 15] m/sec = 10 m/sec.
Relative speed = (15 + 10) = m/sec = 25 m/sec.
∴ Required time = (125 + 125) / 25 secc = 6 sec.
Answer A
Answer: A
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Options:
A)45
B)37
C)29
D)26
E)12
Rationale: A:B:C = (10×7):(12×5):(15×3)
= 70 :60 :45
= 14 :12 :9
C's rent = Rs.(175×9/35)
=Rs. 45.
Answer: A
Answer: A
Question: A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
Options:
A)1,250 meters / minute
B)1,350 meters / minute
C)1,450 meters / minute
D)1,550 meters / minute
E)1,650 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
75 kilometers per hour = 75 km/hr
= (75 * 1000 meters) / (60 minutes) = 1,250 meters / minute
correct answer A
Answer: A
Question: Antony can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows Antony has in his herd?
Options:
A)155
B)120
C)456
D)180
E)336
Rationale: On first look B,C,E are not divisible either by 5 or 6 - ruled out.
D,B divisible by both 5,6, but 180 is divisible by 9.
Answer : B
Answer: B
Question: What is the product of all the prime factors of 12?
Options:
A)108
B)18
C)9
D)6
E)12
Rationale: 12 , factors are 2,3,4,6,1. Now again prime Numbers are Only Two i.e 2 and 3 , this time we would have 2*2*3=12
Answer : E
Answer: E
Question: If 325/999=0.125, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
Options:
A)3
B)3.5
C)4
D)4.5
E)5
Rationale: 0.[u]325[/u = 0.325325325.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E
Answer: E
Question: Thomas has age that is twice of Matt now, two years from now Thomas's age would be 1.5 times that of Matt. How old is the Matt now?
Options:
A)2
B)6
C)8
D)12
E)4
Rationale: Lets assume the age of Matt be x, so that makes Thomas's age y.
From 2 years from now (y+2)=1.5(x+2)
and y is 2x, so substituting we get (2x+2)=1.5x+3
.5x=1 and it makes x=2.
Matt's current is 2
Answer:A
Answer: A
Question: The difference between a number and its three-fifth is 50. What is the number?
Options:
A)75
B)100
C)125
D)150
E)175
Rationale: Let the number be x. Then,
x - 3/5 x = 50 => 2/5 x = 50
x = (50 * 5)/2 = 125.
ANSWER:C
Answer: C
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is?
Options:
A)5/18
B)5/12
C)5/17
D)5/11
E)5/10
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: B
Question: If after 100 grams of water were added to the 20%-solution of alcohol, the strength of the solution decreased by one-fourth, how much of the 20%-solution was used?
Options:
A)300
B)250
C)150
D)200
E)210
Rationale: The 20% alcohol solution decreases by 1/4 once the 100 grams of water is added so 100/.05 =2000*.15% (3/4 of 20%) is 300 grams.
answer is A
Answer: A
Question: Cindy paddles her kayak upstream at b kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?
Options:
A)bnp
B)bn/p
C)(b + n)/p
D)bnp/(b + n)
E)pm/n- pn/m
Rationale: let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/b
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/b)+(d/n)
=d(b+n)/bn
d=pbn/(b+n)=D
Answer: D
Question: Which of the following points is symmetric with y=x at (-3,-4)?
Options:
A)(-2,-1)
B)(-4,-3)
C)(2,1)
D)(-1,-2)
E)(-1,2)
Rationale: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.
(-3,-4) would become (-4,-3).
Answer (B).
Answer: B
Question: Narendra started a business, investing 40000. Six months later, Chandan joined him with 20000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra?
Options:
A)A)Rs.7000
B)B)Rs.8000
C)C)Rs.8500
D)D)Rs.8600
E)E)Rs.8700
Rationale: The ratio of their investments = 40000 × 12 : 20000 × 6 = 4 : 1.
:. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000.
B)
Answer: B
Question: If the average cost of a house was $40,000 in 1965 and was x in 2005, what was the average increase in home prices per year over this period?
Options:
A)A)(x+50,000)/40
B)B)(x-40,000)/40
C)C)(50,000/40)+x
D)D)(50,000-x)/40
E)E)x/40
Rationale: Average house price in 2005: x
Average house price in 1965: 40,000
2005-1965=40
Average increase per year: (x-40,000)/40
Answer is B
Answer: B
Question: In a right isosceles triangle, the lengths of the two nonhypotenuse sides are designated a. What is the area of the triangle in terms of a?
Options:
A)1/3*a^2
B)√2/3∗a^2
C)1/2*a^2
D)√3/2∗a^2
E)√2^a2
Rationale: Since it is right angled isosceles triangle then other two sides will be equal let's say a and a and third side be c
Area of triangle is 1/2*b*h = 1/2*a*a .
option C is correct answer.
Answer: C
Question: If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 9 people to do 9 times of that particular work?
Options:
A)1
B)2
C)3
D)9
E)12
Rationale: 3 people can do the work one time in one day.
1 person can do 1/3 of the work in one day.
9 people can do 9/3 of the work in one day.
9 people can do 9 times the work in 3 days.
The answer is C.
Answer: C
Question: If cost of sugar increases by 50%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
Options:
A)33%
B)50%
C)20%
D)90%
E)60%
Rationale: 100
150
-----
150 ----- 50
100 ------ ? => 33%
Answer: A
Answer: A
Question: The set X = {7,8,9,10}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?
Options:
A)7/16
B)5/16
C)3/16
D)7/8
E)5/8
Rationale: The total number of x and y pairs is 4*4=16.
There are five pairs such that x / y is an integer.
The probability that x / y is an integer is 5/16.
The answer is B.
Answer: B
Question: When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.15
II.18.16
III. 17.18
Options:
A) I only
B) II only
C) III only
D) I and III only
E) I and II only
Rationale: Problem statement was difficult to parse. but some how I managed to understand what we can do.
1) x/y = 15 + 0.15
2) x/y = 18 + 0.16
3) x/y = 17 + 0.18
w.k.t x = yn (i.e Q) + yk=60 (i.e remainder)
therefore :
1) y*0.15=60 -- we can get y an integer.
2) y*0.16=60 -- we can get y an integer.
3) y*0.18=60 -- we can't get y an integer.
Therefore 1 and 2 are possible answers.
Ans E
Answer: E
Question: It takes one machine to paint 1000 sq.m. surface in 24 minutes.Another machine does the same job in 40 seconds.How much time will it take if both machines are put on the same work?
Options:
A)10.0 seconds
B)20.0 seconds
C)38.9 seconds
D)40.0 seconds
E)52.0 seconds
Rationale: By guess it is clear that the time taken will be less than 40 seconds and very near to it. Therefore, answer 38.9 seconds will be correct. Answer-C
Answer: C
Question: Over a three-week period, the price of an ounce of gold increased by 10% in the first week, decreased by 20% in the following week, and increased by 30% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
Options:
A)1.124G
B)1.144G
C)1.164G
D)1.184G
E)1.204G
Rationale: After 3 weeks, the price was 1.3*0.8*1.1*G=1.144G
The answer is B.
Answer: B
Question: If x=kc and y=kt,then 2y-x =?
Options:
A)k(t-c)
B)k(c-t)
C)c(k-t)
D)t(k-c)
E)k(2t-c)
Rationale: Just put in the given values of y and x
2y - x = 2kt - kc
Now take k common
2y - x = k(2t - c)
You get (E) as your answer.
Answer: E
Question: The pilot of a small aircraft with a 60-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 10 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
Options:
A)5
B)12
C)2
D)4
E)6
Rationale: Actual miles/gallon is = 480/60 = 8 miles/gallon.
Current engine miles/gallon is 10 miles/gallon.
Additional 2 miles/gallon is required to match the actual mileage.
ANSWER:C
Answer: C
Question: a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find a+b+c=?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: a^2*b^2+a^2+b^2+1= (a^2+1)(b^2+1)
by using above one we can write
a^2*b^2+a^2+b^2+1=260..(1)
b^2*c^2+b^2+c^2+1=1300..(2)
c^2*a^2+c^2+a^2+1=500..(3)
by doing (1)/(2) we will get a^2+1/c^2+1 = 1/5..(4)
by doing (4)*(3) we will get (a^2+1)^2=10,
by solving a=3, b=5,c=7
so a+b+c=15
ANSWER:C
Answer: C
Question: There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairy tales, novels and plays.
Options:
A)17200
B)17250
C)17280
D)17300
E)17400
Rationale: There are 4 books on fairy tales and they have to be put together.
They can be arranged in 4! ways.
Similarly, there are 5 novels.
They can be arranged in 5! ways.
And there are 3 plays.
They can be arranged in 3! ways.
So, by the counting principle all of them together can be arranged in 4!×5!×3!=4!×5!×3!= 17280 ways
Option is C
Answer: C
Question: One side of a rectangular field is 15 m and one of its diagonal is 17 m. Find the area of the field.
Options:
A)100
B)120
C)150
D)180
E)None
Rationale: Solution
Other side = √(17)2 - (15)2
= √289 - 225
= √64
= 8 m.
∴ Area = (15 x 8)m2 = 120 m2.
Answer B
Answer: B
Question: A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm .If the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted?
Options:
A)408
B)418
C)428
D)438
E)448
Rationale: first the number of cubes....
the hollow cube size 5 cm.thickness 1c.m. so the total no. of unit cubes neede to build one face is 16 cubes..so total no. of cubes (5*16+9*2)=98
the total no. of faces unpainted(98*6 - 25*6)=438
ANSWER:D
Answer: D
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
Options:
A)5/11
B)4/11
C)3/11
D)6/45
E)7/44
Rationale: The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
Answer: C
Answer: C
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)3377
B)2899
C)2500
D)2778
E)1991
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