divelab/Sys2Bench huggingface dataset:
Question: 5/6 of the lights bulbs on a string of all red christmas lights will light up. Then Fred replaced 1/2 of the dead bulbs with green bulbs. What fraction of the lights that light up are green?
Options:
A)1/11
B)1/6
C)2/11
D)1/12
E)1/8
Rationale: If there are 12 bulbs on the string of lights, that would mean 10 of the lights lit red and 2 of the bulbs were dead. If Fred replaced half of the dead light bulbs with green light bulbs, he would have replaced 1 dead light bulb with a green light bulb. This light bulb would be 1 of 11 functioning light bulbs or 1/11. (Answer: A)
Answer: A
Question: If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 6:4, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?
Options:
A)1/25
B)2/25
C)3/25
D)4/25
E)21/25
Rationale: 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 6:4
So, 10x=30 ---> x=3
Red marbles = 2*x = 2*3 = 6
Blue marbles = 3*x = 3*3 = 9
Prob to select a red marble = 6/30 = 1/5
Prob to select 2 red marbles with replacement = 1/5*2*5 = 2/25
Hence, answer will be B.
Answer: B
Question: The purchase price of an article is $48. In order to include 10% of cost for overhead and to provide $12 of net profit, the markup should be
Options:
A)15%
B)25%
C)35%
D)40%
E)45%
Rationale: Cost price of article = 48$
% of overhead cost = 10
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 10 = 35%
Answer C
Answer: C
Question: A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)3:5
B)3:8
C)3:2
D)9:9
E)3:1
Rationale: (4*6 + 8*6): (4*12)
72:48 =>
3:2
Answer:C
Answer: C
Question: When 1/10 percent of 7,000 is subtracted from 1/10 of 7,000, the difference is
Options:
A) 0
B) 50
C) 450
D) 693
E) 500
Rationale: We can break this problem into two parts:
1) What is 1/10 percent of 7,000?
2) What is 1/10 of 7,000?
To calculate 1/10 percent of 7,000 we must first remember to DIVIDE 1/10 BY 100.
So we have: (1/10)/(100)
To divide a number by 100 means to multiply it by 1/100, so we have:
1/10 x 1/100 = 1/1,000
Thus, 1/10 percent of 7,000 = 1/1,000 x 7,000 = 7.
Now let's concentrate on part 2. We need to calculate 1/10 of 7,000. To do this we simply multiply 1/10 by 7,000.
1/10 x 7,000 = 700
The answer to part 1 is 7, and the answer to part 2 is 700. Their difference is 700 – 7 = 693.
Answer D.
Answer: D
Question: In a triangle if the length of sides are as given below which one will not form triangle?
Options:
A)(5,5,5)
B)(5,4,5)
C)(4,4,9)
D)(3,4,5)
E)(3,4,8)
Rationale: using property :"sum of two side of a triangle is greater than its third side (4+4) is not greater than 9,so ans c
ANSWER:C
Answer: C
Question: The tax on a commodity is diminished by 24% but its consumption is increased by 12%. Find the decrease percent in the revenue derived from it?
Options:
A)20%
B)18%
C)15%
D)12%
E)14%
Rationale: 100 * 100 = 10000
76 * 112 = 8512
10000------- 1488
100 ------- ? = 15%
ANSWER:C
Answer: C
Question: If the average (arithmetic mean) of (2a+16) and (3a-8) is 79, what is the value of a?
Options:
A)25
B)30
C)28
D)36
E)42
Rationale: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 79
a= 30
The answer is B.
Answer: B
Question: At an election 2 candidates are participated and a candidate got 20% of votes and defeated by 500. and 10 votes are invalid. Find the total polled votes?
Options:
A)843
B)1023
C)965
D)413
E)1245
Rationale: Winner votes = 100-20 = 80
polled votes = [(100*500)/2*80-100]+10 = 843 (approximately)
Answer is A
Answer: A
Question: If a certain sample of data has a mean of 24.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)13.5
C)17.0
D)23.5
E)26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 24-7.5=16.5or more than 24+7.5=31.5.
Answer: C.
Answer: C
Question: The H.C.F of two numbers is 17 and their L.C.M is 5134. If one of the numbers is 289, then the other is?
Options:
A)302
B)304
C)306
D)308
E)310
Rationale: Other number = (17 * 5134)/289
= 302.
Answer: A
Answer: A
Question: The speed at which a girl can row a boat in still water is 75 kmph. If he rows downstream, where the speed of current is 15 kmph, what time will he take to cover 300 metres?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: Speed of the boat downstream = 75 + 15 = 90 kmph
= 90 * 5/18 = 25 m/s
Hence time taken to cover 400 m = 400/25 = 16 seconds. Answer: A
Answer: A
Question: A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?
Options:
A)7 days
B)6 days
C)5 days
D)4 days
E)None of these
Rationale: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(1/3−1/6)=(6−3)/18=1/6
So son will do whole work in 6 days
Answer: B
Answer: B
Question: 6/7 of a certain number is 96. Find quarter of that number.
Options:
A)112
B)32
C)56
D)28
E)30
Rationale: Explanation:
6/7x = 96
x = 112
y = x/4 = 112/4 = 28
ANSWER D
Answer: D
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)10 sec
B)17 sec
C)99 sec
D)90 sec
E)12 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer:A
Answer: A
Question: Using all the letters of the word "HEAD", how many words can be formed, which begin with H and end with D?
Options:
A)8
B)4
C)2
D)7
E)9
Rationale: There are five letters in the given word.
Consider 4 blanks ....
The first blank and last blank must be filled with H and D all the remaining three blanks can be filled with the remaining 2 letters in 2! ways.
The number of words = 2! = 2.
Answer:C
Answer: C
Question: One side of a rectangular field is 13 m and one of its diagonal is 17 m. Find the area of the field.
Options:
A)100
B)141.7
C)150
D)180
E)None
Rationale: Solution
Other side = √(17)2 - (13)2
= √289 - 169
= √120
= 10.9 m.
∴ Area = (13 x 10.9)m2 = 141.7 m2.
Answer B
Answer: B
Question: How many positive integers of three different digits, each less than 400 can be formed from the digits 1, 2, 3, 4, 5 and 6?
Options:
A)30
B)60
C)90
D)120
E)150
Rationale: For the # to be < 400 the 100s digit shud be < 4 => one out of 3 choices 1/2/3
if the 100s digit is 1 then 10s digit can be selected in 5C1 and the units digit can be selected in 4C1 ways ==> 5C1*4C1=20
the same is the case with 2 and 3 too.
hence answer is 20+20+20 = 60
ANSWER:B
Answer: B
Question: rahul played weel in this season.his current batting averagge is 51.if he score 69 runs in today match.his batting average will become 54.how many matches had he played in this season.
Options:
A)8
B)10
C)9
D)6
E)5
Rationale: 51x+69=54(x+1)
=>3x=15
=>x=5
ANSWER:E
Answer: E
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 240 m long?
Options:
A)40
B)99
C)48
D)77
E)21
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 240 = 600 m
Required time = 600 * 2/25 = 48 sec
Answer:C
Answer: C
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)29
B)27
C)27
D)80
E)26
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Answer: D
Question: Elena purchased Brand X pens for $5.00 apiece and brand Y for $2.80 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=6 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).
Answer: C.
Answer: C
Question: A reduction of 40% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)80
B)72
C)64
D)56
E)48
Rationale: 800*(40/100) = 320 ---- 5
? ---- 1 => Rs.64
Answer: C
Answer: C
Question: How many figures are required to number the pages the pages of a book containing 365 pages?
Options:
A)987
B)656
C)286
D)126
E)181
Rationale: Explanation:
1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 365 = 266 * 3 = 798
-----------
987
Answer: A
Answer: A
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 126 kmph. In how much time will the trains cross each other?
Options:
A)87/7 sec
B)80/7 sec
C)80/9 sec
D)80/5 sec
E)20/3 sec
Rationale: Relative speed = (90 + 126)* 5/18 = 12 * 5 = 60 mps.
The time required = d/s = (100 + 100 + 200)/60
= 400/60 = 20/3 sec.
Answer: E
Answer: E
Question: The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 72 on the exam is in what percentile of the school?
Choices
Options:
A)63rd percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile
Rationale: (78-65)/6.5 = 2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2 = 68th percentile
B
Answer: B
Question: Two trains 140 m and 170 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9 sec
B)10.1 sec
C)10.6 sec
D)10.8 sec
E)11.16 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 170 = 310 m.
Required time = 310 * 9/250=11.16 sec.
Answer:E
Answer: E
Question: Question: What is the remainder when T=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
Options:
A) 0
B) 25
C) 49
D) 81
E) 100
Rationale: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when T=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Answer: D
Question: Billy lives in a town in which 75% of pets are dogs. Of the non-dog pets, 50% are cats. If there are 50 pets in town that are not cats or dogs, how many pets are there in town?
Options:
A)250
B)350
C)400
D)450
E)500
Rationale: Let x be the number of pets in town.Then N is the number of non-dog pets given byN = x - 75%xAnd P is the number of pets that aren't cats or dogs, given byP = N - 50%Nfor P = 50, solve for x50 = (x - 75%x) - 50%(x - 75%x)x = 400, correct answer C
Answer: C
Question: What is the dividend? The divisor is 800, the Quotient is 594, and the Remainder is -968.
Options:
A)6623
B)43036
C)51515
D)474232
E)2025
Rationale: Dividend=?
?=D * Q + R
?= 800 * 594 + -968
?= 475,200 + -968
?= 474,232
Answer: D
Question: A reduction of 24% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Options:
A)s.2.8
B)s.2.4
C)s.2.5
D)s.2.2
E)s.3.16
Rationale: 100*(24/100) = 24 --- 10
? --- 1 => Rs.2.4
100 --- 76
? --- 2.4 => Rs.3.16
Answer:E
Answer: E
Question: A certain sum of money at simple interest amounted Rs.800 in 12 years at 3% per annum, find the sum?
Options:
A)337
B)268
C)198
D)588
E)168
Rationale: 800 = P [1 + (12*3)/100]
P = 588'
Answer:D
Answer: D
Question: Priya takes a trip and drives 5 hours from Town X to Town Z at a rate of 50 miles per hour. On her way back, Priya drives 60 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y?
Options:
A)3.0
B)2.25
C)2.08
D)1.75
E)2.0
Rationale: distance from X to Z =5 hr* 50 mph= 250 miles
hence distance from Y to Z= 1/2*250=125
time=125/60=2.08 hrs
IMO: C
Answer: C
Question: Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 7, when a # b = 100?
Options:
A)5
B)8
C)10
D)12
E)17
Rationale: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 7 = 10/2 + 7 =12.
The correct answer is D.
Answer: D
Question: A number when divided by a divisor leaves a remainder of 27. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)12
B)13
C)35
D)40
E)59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+27
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 40
as D is also integer and 40 is a prime number, the D should be 40 to satisfy the above equation.
Hence answer is 'D'
Answer: D
Question: Find the L.C.M of 6, 15, 24 and 20.
Options:
A)140
B)160
C)120
D)150
E)250
Rationale: Explanation:
2 x 3 x 5 x 2 x 2 = 120
Answer: Option C
Answer: C
Question: Solve the equation for time, "t" : 9(t + m) + 1 = 9(-t + m) + 19
Options:
A)1
B)-1
C)2
D)-2
E)3
Rationale: A
1
9(t + m) + 1 = 9(-t + m) + 19
9t + 9m +1 = -9t + 9m + 19
18t = 18
t = 1
Answer: A
Question: Of the 4 numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is?
Options:
A)36
B)40
C)48
D)52
E)56
Rationale: Let the first number be x
sum of the 4 numbers = x+4x = 5x
5x/4 = 60
x = 60*4/5 = 48
Answer is C
Answer: C
Question: Set X consists of 10 integers and has median of 30 and a range of 30. What is the value of the greatest possible integer that can be present in the set?
Options:
A)32
B)37
C)C.40
D)43
E)50
Rationale: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20, 20, 20, 20, 20, 40, 50
This is possible. Hence it is the greatest such number.
Answer (E)
Answer: E
Question: If 0 < x ≤ 5, then which one of the following is the maximum value of (x – 1)^2 + x ?
Options:
A)–2
B)–1
C)0
D)1
E)21
Rationale: the maximum value of (x – 1)^2 + x for 0 < x ≤ 5 is when x=5 --> (x – 1)^2 + x = 21
Answer E
Answer: E
Question: A train covers a distance of 16 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)m
B)m
C)m
D)m
E)m
Rationale: Speed = (16/10 * 60) km/hr
= (96 * 5/18) m/sec = 80/3 m/sec.
Length of the train = 80/3 * 6
= 160 m.
Answer:C
Answer: C
Question: The simple interest on a sum of money will be Rs.600 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)1267
B)1201
C)1200
D)1209
E)1216
Rationale: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer: C
Answer: C
Question: The salaries of A and B together amount to $3000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?
Options:
A)$1000
B)$1250
C)$2500
D)$2250
E)$1200
Rationale: Let A's salary is x
B's salary = 3000-x
(100-95)% of x = (100-85)% of (3000-x)
x = $2250
Answer is D
Answer: D
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)48 Kmph
B)50 Kmph
C)52 Kmph
D)56 Kmph
E)60 Kmph
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
E
Answer: E
Question: If an object travels at 9 feet per second, how many feet does it travel in one hour?
Options:
A)32400
B)30000
C)32000
D)1800
E)22000
Rationale: If an object travels at 5 feet per second it covers 9x60 feet in one minute, and 9x60x60 feet in one hour.
Answer = 32400 Answer:A
Answer: A
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 90kmph, find the rate at which the train B runs.
Options:
A)40
B)60
C)120
D)80
E)135
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 90 kmph, speed of B must be 90*(3/2) = 135 kmph
Answer E
Answer: E
Question: A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 140 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $300, how many of the books sold were paperbacks?
Options:
A)100
B)110
C)120
D)130
E)140
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 140 books were paperbacks, the dealer would earn a profit of $280.
Since the actual profit was $300, the dealer must have sold 20 hardbacks.
Then the number of paperbacks sold was 140-20 = 120.
The answer is C.
Answer: C
Question: A certain taxi company charges $3.00 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
Options:
A)15.6
B)16.0
C)17.5
D)18.6
E)19.1
Rationale: A certain taxi company charges $3.00 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $3.00 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $3.0 + $15.6 = $18.6.
Answer: D.
Answer: D
Question: Ten persons in an organization including A and B were to be divided in two groups of 5 members each. The total number of groups containing both A and B is what fraction of the total number of groups which can be formed?
Options:
A)1/4
B)1/189
C)3/14
D)1/10
E)28/189
Rationale: The fraction is nothing but the probability..
Number to choose 5 out of 10= 10C5
Number to choose A and B and 2 from remaining 8=8C2..
prob of A and B choosen=8C2/10C5=28/189
Answer :E
Answer: E
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 11 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
Options:
A)2/1
B)4/1
C)2/3
D)9/5
E)3/2
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+11) = 36/20 = 9/5.
Answer: D.
Answer: D
Question: The ratio 5:20 expressed as percent equals to
Options:
A)50 %
B)125 %
C)25 %
D)75 %
E)None of above
Rationale: Explanation:
Actually it means 5 is what percent of 20, which can be calculated as,
(5/20)*100 = 5 * 5 = 25
Answer: Option C
Answer: C
Question: Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability E that Kate has more than $10 but less than $15?
Options:
A)5/16
B)1/2
C)12/30
D)E=15/32
E)E=3/8
Rationale: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities are 3 or 4 heads.
I made an educated guess and it worked fine.
Ans- 'D'
MGMAT's anagram helped here as well.
HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10
Total acceptable cases = 15
Total cases = 32
P = 15/32=D
Answer: D
Question: A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can be make out of this cloth?
Options:
A)300
B)360
C)400
D)None of these
E)cannot be determined
Rationale: Solution
Length of each pieces	= (1 / 8) m
= 0.125 m
Required number of pieces(37.5/0.125)	= (375×100 / 125)
= 300.
Answer A
Answer: A
Question: Find 96 ×× 97
Options:
A)91/198
B)91/12
C)91/13
D)91/10
E)91/11
Rationale: Here both numbers are less than 100. So they are deficient of - 4 and - 3 compared with 100. So
Answer:	B
Answer: B
Question: The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 40, what is the greatest possible value that one of the other 2 integers can have?
Options:
A)55
B)65
C)119
D)109
E)115
Rationale: a + b + c + d = 200
a + b = 80
c + d = 120
Greatest possible = 119 (Just less than 1)
Answer = C
Answer: C
Question: If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab?
Options:
A)10
B)25
C)36
D)61
E)87
Rationale: Explanation:
a2 + b2 + ab = a2 + b2 + 2ab - ab
i.e., (a + b)2 - ab
from x2 - 9x + 20 = 0, we have
a + b = 9 and ab = 20. Hence the value of required expression (9)2 - 20 = 61.
Answer D
Answer: D
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)29
B)27
C)25
D)11
E)65
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75)
= 25 points to C.
Answer:C
Answer: C
Question: The ratio of the age of a man and his women is 4:3. At the time of first meet theratio was 5:3 and After 4 years this ratio will become 9:7. How many yrs ago were they met?
Options:
A)10
B)12
C)15
D)16
E)20
Rationale: Let the present age of the man and his wife be 4x and 3x respectively.
After 4 years this ratio will become 9:7
⇒(4x+4):(3x+4)=9:7⇒7(4x+4)=9(3x+4)⇒28x+28=27x+36⇒x=8
Present age of the man =4x=4×8=32
Present age of his wife =3x=3×8=24
Assume that they got married before t years. Then,
(32−t):(24−t)=5:3⇒3(32−t)=5(24−t)⇒96−3t=120−5t⇒2t=24⇒t=242=12
B
Answer: B
Question: When a 80 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ?
Options:
A)52
B)68
C)25
D)67
E)69
Rationale: Answer
No. of pieces = Total length / Length of each piece
= 80/3.2
= 25
Option: C
Answer: C
Question: Find the average of first 30 natural numbers.
Options:
A)15.5
B)15.9
C)15.2
D)15.8
E)65.2
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 30 natural numbers = (30 x 31)/2 = 465
Therefore, required average of = 465/30 = 15.5
ANSWER: A
Answer: A
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
Options:
A)12
B)61
C)15
D)72
E)30
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways.
Answer:E
Answer: E