divelab/Sys2Bench huggingface dataset:
Question: If A speaks the truth 30% of the times, B speaks the truth 40% of the times. What is the probability that at least one will tell the truth
Options:
A)0.58
B)0.9
C)1.9
D)2.2
E)2.3
Rationale: probability of A speaks truth p(A)=3/10;false=7/10
probability of B speaks truth p(B)=4/10;false=6/10.For given qtn
Ans=1-(neither of them tell truth).Because A & B are independent events
=1-[(7/10)*(6/10)]=1-42/100=1-0.42=0.58
ANSWER:A
Answer: A
Question: If x + |x| + y = 7 and x + |y| - y =6 , then x + y =
Options:
A)3
B)4
C)5
D)6
E)9
Rationale: If x + |x| + y = 7 and x + |y| - y =6 , then x + y =
can be done in 2.3 mins :
there are 4 cases to be tested :
1) x is -ve and y is -ve
substituting in the equation , we get x-x+y=7 and x-y-y=6 solve for x and y we get x=20 and y=7 , so x+y=27 REJECT
2)x is +ve and y is +ve
substitute in the equation, we ger x+x+y=7 and x+y-y=6 solve for x and y we get x=6 and y=-5 ,therefore x+y=1 not on list so REJECT
3) x is -ve and y is +ve
substitute , we get x-x=y=7 and x+y-y=6 solve fo x and y we get x=6 and y=7, x+y=13 not on list so REJECT
4) x is +ve and y is -ve
substitute , we get x+x=y=7 and x-y-y=6 solve for x and y , we get x=4 and y= -1 ,x+y=3 , ANSWER CHOICE ANSWER A
Answer: A
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
Options:
A)20
B)200
C)300
D)400
E)140
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 5300
[4L - 40] = 5300 / 26.50 = 200
4L = 240
L = 240/4= 60 meters. Answer: B
Answer: B
Question: A bakery opened yesterday with its daily supply of 60 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
Options:
A) 1
B) 2
C) 3
D) 4
E) 6
Rationale: answer is E ...6 dozens ....
half sold by noon --> 30 dozens (30 *12 =360)
remaining --> 30 dozens i.e 360 eggs...
80% sold --> 80*360/100 =288 eggs
remaining 20 % --> 72 eggs (6 dozens ) --> answer
Answer: E
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 14,720, Deepak's share is:?
Options:
A)s.8467
B)s.8428
C)s.8400
D)s.8960
E)s.8420
Rationale: Ratio of their shares
= 22500 : 35000
= 9:14
Deepak's share
= 14720 * 14/23
= Rs.8960.
Answer:D
Answer: D
Question: Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to fill the tank
Options:
A)17 1/7 mins
B)20 mins
C)8 mins
D)9 mins
E)none of these
Rationale: A = 20
B = 30
C = -40
LCM = 120
=> A = 6,TIMES
B = 4
C = -3
=> A+B-C
= 7
TIME TAKEN TO FILL THE TANK = 120/7 MINS = 17 1/7 MINS
ANSWER:A
Answer: A
Question: A boy has 5 trousers and 13 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)299
B)65
C)68
D)67
E)271
Rationale: The boy can select one trouser in 5 ways.
The boy can select one shirt in 13 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 13
= 65 ways.
Answer: B
Answer: B
Question: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B. Which of the following CANNOT be the difference of A and B ?
Options:
A)72
B)45
C)33
D)27
E)9
Rationale: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B:
A = 10x + y
B = 10y + x
A - B = (10x + y) - (10y + x) = 9(x - y). As you can see the difference must be a multiple of 9. Only option C is not a multiple of 9.
Answer: C.
Answer: C
Question: A shopkeeper wants to make a minimum net profit of 5% on a pair of jeans she is selling, which she bought for $100. If originally, she was selling the pair at 20% gain, what is the largest discount she can allow?
Options:
A)12.5%
B)8%
C)8.3%
D)15%
E)4%
Rationale: A
If she bought the jeans at $100, she is currently selling them at (120/100)*100 = $120.
She wants to make a profit of 5%, which means she needs to sell them at (105/100)*100 = $105
The max discount she can allow is thus ((120-105)/120)*100 = 12.5%
Answer: A
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?
Options:
A)27 grams
B)28 grams
C)29 grams
D)31 grams
E)32 grams
Rationale: Let original mass be 100
The final mass of that element will be 7
So whatever option we have it will be divisible by 7
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 27 grams
27/7 = 3.857...
B. 28 grams
28/7 = 4
C. 29 grams
29/7 = 4.142.......
D. 31 grams
31/7 = 4.428.....
E. 32 grams
32/7 = 4.571....
Hence our answer will be (B)
Answer: B
Question: A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is
Options:
A)12km
B)16 km
C)20 km
D)24 km
E)None of these
Rationale: Explanation :
Let distance be D
10 = D/4 + D/6
Answer – D
Answer: D
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 182 cms. What was the ratio of men to women?
Options:
A) 5:2
B) 5:1
C) 4:3
D) 4:1
E) 3:1
Rationale: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 182cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 182M)/(W+M) = 180
170W + 182M = 180W + 180M
2M = 10W
M = 5W
M/W = 5/1
The ratio of men to women is 5 to 1.
B
Answer: B
Question: Three distinct single-digit numbers. A,B,C are in GP. If abs(x) for real x is the absolute value of x(x if x is +ve or 0 and -x if x is -ve), then the number of different possible values of abs(A+B+C) is
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: A,B,C may be
(1,2,4) & (4,2,1)
(1,3,9) & (9,3,1)
(2,4,8) & (8,4,2)
(4,6,9) & (9,6,4)
find abs(A+B+C) for these 8 GPs
7,13,15,19
So,we get 4 different values
ANSWER:D
Answer: D
Question: Round off 9824.119 to the nearest thousand, hundred, ten and one.Represent the result with q,r,s,t, respectively.Which of the following statements is correct?
Options:
A)q<s<t<r
B)s<r<t<q
C)r<s<q<t
D)r<q<t<s
E)r<s<t<q
Rationale: 9824.119..
Nearest thousand 10000..q
Nearest hundred 9800..r
Nearest ten 9820..s
Nearest one 9824..t
r<s<t<q
The correct option is E
Answer: E
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)10
B)18
C)63
D)36
E)72
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
ANSWER:D
Answer: D
Question: Evaluate: 30 - 12÷3×2 =
Options:
A)11
B)22
C)33
D)44
E)55
Rationale: According to order of operations, 12÷3×2 (division and multiplication) is done first from left to right
12÷3×2 = 4 × 2 = 8
Hence
30 - 12÷3×2 = 30 - 8 = 22
correct answer is B) 22
Answer: B
Question: A train running at the speed of 72 km/hr crosses a pole in 8 seconds. Find the length of the train.
Options:
A)150 meter
B)145 meter
C)160 meter
D)135 meter
E)None of these
Rationale: Explanation:
Speed = 72*(5/18) m/sec = 20 m/sec
Length of Train(Distance) = Speed * Time
=20*8=160 meter
Option C
Answer: C
Question: Last September the sales total for a certain car dealership was 400% greater than the average monthly sales total for the other 11 months. The sales total for September was approximately what percent of the year´s sales?
Options:
A)15 %
B)27%
C)31%
D)42%
E)75%
Rationale: 11 moth avg = x
11 month total = 11x
sept = 400% of x + x = 5x
sept/total = =5x/(11x+5x) = =31%
ANSWER:C
Answer: C
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 360 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
Options:
A)600
B)620
C)500
D)520
E)720
Rationale: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 360) = 2 + 2(extra)
=> 2x - 720 = x => x = 720.
ANSWER:E
Answer: E
Question: The supplementary of an angle is thrice its complimentary. Find the angle.
Options:
A)60
B)45
C)90
D)180
E)120
Rationale: let angle=x;
by question--
180-x=3(90-x)
x=45
ANSWER:B
Answer: B
Question: The average weight of 25 girls increases by 1 kg when a new girl comes in place of one of them weighing 55 kg. What might be the weight of the new girl?
Options:
A)85 kg
B)90 kg
C)83 kg
D)80 kg
E)82 kg
Rationale: Total weight increased = 25 x 1 kg = 25 kg.
Weight of new person = 55 + 25 kg =80 kg
Answer : D
Answer: D
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age five years back was:
Options:
A)A)14
B)B)17
C)C)56
D)D)89
E)E)34
Rationale: Let the son's present age be x years. Then, (44 - x) = x
2x = 44.
x = 22.
Son's age 5 years back (22 - 5) = 17 years.
Answer:B
Answer: B
Question: L = {3, 4, 5, 5, 6, 7}
M = {2, 2, 2, 8, 8, 8}
N = {15, 15, 15, 15, 15, 15}
Rank those three sets from least standard deviation to greatest standard deviation.
Options:
A)L, M, N
B)M, L, N
C)M, N, L
D)RANKING=N, L, M
E)N, M,
Rationale: Square of Standard deviation is sum of squares of deviation from the mean divided by the number of terms.
If deviation from the mean is higher for the same number of elements, standard deviation will be higher.
L = {3, 4, 5, 5, 6, 7}
Mean is 5 and deviation of 2 elements from mean is 0, of 2 elements is 1 and of 2 elements is 2.
M = {2, 2, 2, 8, 8, 8}
Mean is 5 and deviation of all elements from the mean is 3. So SD here will be higher than SD of L.
N = {15, 15, 15, 15, 15, 15}
Mean is 15 here and all elements have 0 deviation from mean so SD = 0 here. This is the minimum possible SD.
Answer N, L, M
Answer (D)
Answer: D
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Options:
A)4years
B)8years
C)10years
D)12years
E)None of these
Rationale: Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
Answer: A
Answer: A
Question: The difference between a two-digit number and the number obtained by interchanging the digit 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: Explanation:
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 the ten's and unit's digits be 2x and x respectively.
Then, (10 * 2x + x) - (10x + 2x) = 36
9x = 36
x = 4
Required difference = (2x + x) - (2x - x) = 2x = 8.
ANSWER IS B
Answer: B
Question: Find the area of a parallelogram with base 20 cm and height 10 cm?
Options:
A)287 cm2
B)887 cm2
C)200 cm2
D)250 cm2
E)668 cm2
Rationale: Area of a parallelogram = base * height
= 20 * 10
= 200 cm2
Answer: C
Answer: C
Question: The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:
Options:
A)30º
B)45º
C)60º
D)90º
E)80º
Rationale: shadow of the tree is √3 times the height of the tree.
shadow of a tree will be = √3x.
tan θ = AB/AC = x/√3x.
tan θ =1/√3.
tan θ = tan 1/√3.
tan θ = tan30°.
θ = 30° ANSWER : A
Answer: A
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
Options:
A)2.2 m
B)2.4 m
C)3 m
D)3.4 m
E)3.6 m
Rationale: Area of the park = (60 x 40) m2= 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2= 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
ANSWER : C
Answer: C
Question: One night 10 percent of the female officers on a police force were on duty. If 200 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
Options:
A)90
B)180
C)270
D)500
E)1,000
Rationale: Let total number of female officers in the police force = F
Total number of officers on duty on that night = 200
Number of female officers on duty on that night = 200/2 = 100
(10/100)*F =100
=>F = 1000
Answer E
Answer: E
Question: If a refrigerator contains 12 cans such that there are 7 blue cans and 5 red cans. In how many ways can we remove 8 cans so that at least 1 blue can and 1 red can remains in the refrigerator.
Options:
A)452
B)453
C)454
D)455
E)456
Rationale: The possible cases of (b,r) draws are (6,2) (5,3) (4,4)
6 2---->7c6*5c2--->7*10=70
5 3---->7c5*5c3--->21*10=210
4 4---->7c4*5c4--->35*5=175
70+210+175=455
ANSWER:D
Answer: D
Question: The sum an integer N and its reciprocal is equal to 78/15. What is the value of N?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Write equation in N as follows
N + 1/N = 78/15
Multiply all terms by N, obtain a quadratic equation and solve to obtain N = 5.
correct answer is E) 5
Answer: E
Question: 60% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
Options:
A)70
B)97
C)80
D)90
E)76
Rationale: Given, 60% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 60% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/60 = 40
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (40 + 120)/2 = 80.
Answer:C
Answer: C
Question: A standard Veggiematik machine can chop 25 carrots in 5 minutes. How many carrots can 5 standard Veggiematik machines chop in 5 minutes?
Options:
A)45
B)75
C)110
D)125
E)150
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 25 Carrots - 5 minutes,
1 standard Veggiematik machine - 5 Carrots - 1 minute,
Now
5 standard Veggiematik machine - ? Carrots - 5 minutes,
Hence = 5X5X5 =125 Carrots
Answer D
Answer: D
Question: amir has 3 desert every sunday...he stocked up 10 different chocolates and 12 diff icecreams,given that he never has same combination and doesn't 3 chocolates nor 3 icecreams,how many sundays it requires for his stock to be over?
Options:
A)1045
B)1200
C)2400
D)7200
E)3600
Rationale: he either can have 2 chocolates and 1 icecream or 1 chocolate and 2 icecream.
so the solution would be.
10C2*12C1 + 10C1*12C2 = 1200
ANSWER:B
Answer: B
Question: In the next Worldcup of cricket there will be 12 teams, divided equally in 2groups. Teams of eachgroup will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. 4top teams of this round will qualify for the semifinal round, where they play the best of 3matches. The Minimum number of matches in the next World cup will be
Options:
A)25
B)36
C)53
D)55
E)60
Rationale: The number of matches in first round,
= 6C2 +6C2;
Number of matches in next round,
= 6C2;
Number of matches in semifinals,
= 4C2;
Total number of matches,
= 6C2 +6C2+6C2+4C2+2.
= 53.
C
Answer: C
Question: Find the average of first 27 natural numbers.
Options:
A)14
B)14.2
C)15.2
D)15.8
E)28
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 27 natural numbers = (27 x 28)/2 = 378
Therefore, required average of = 378/27 = 14
ANSWER: A
Answer: A
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is
Options:
A)5780 litres
B)5770 litres
C)5760 litres
D)5750 litres
E)5740 litres
Rationale: Explanation:
Work done by the inlet in 1 hour =
1/6−1/8=1/24
Work done by inlet in 1 min=1/24∗1/60=1/1440
=>Volume of 1/1440 part = 4 liters
Volume of whole = (1440 * 4) litres = 5760 litres.
Option C
Answer: C
Question: Find the term next in series ....
1, 1/2,3/2,2,5,1/3,16/3,15,12,1/4,25/4,?
Options:
A)next number is 48
B)58
C)40
D)43
E)44
Rationale: [1,1/2,3/2,2], [5,1/3/16/3,15] ,[12,1/4,25/4,x]
1+1/2=3/2......1/1/2= 2
5+1/3=16/3.....5/1/3= 15
12+1/4=25/4....12/1/4=48
ANSWER:A
Answer: A
Question: If the product of two numbers is 17820 and their H.C.F. is 12, find their L.C.M.
Options:
A)2574
B)2500
C)1485
D)1574
E)None of these
Rationale: Explanation:
HCF * LCM = 17820, because we know
Product of two numbers = Product of HCF and LCM
LCM = 17820/12 = 1485
Option C
Answer: C
Question: Two trains 140 m and 160 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)9
B)9.6
C)10
D)8
E)12
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
ANSWER:D
Answer: D
Question: The length of a rectangle is increased by 20% and its breadth is decreased by 20%. What is the effect on its area?
Options:
A)1288
B)9600
C)1000
D)10000
E)2887
Rationale: 100 * 100 = 10000
120 * 80 = 9600
Answer: B
Answer: B
Question: The sum of two numbers is 16. The difference is 0. What are the two numbers?
Options:
A)10-6
B)8-8
C)9-7
D)11-5
E)13-3
Rationale: 8+8 = 16
8 - 8 = 0
The Answer is B
Answer: B
Question: How many tiems do the hands of a clock coincide in day?
Options:
A)11
B)12
C)22
D)24
E)None
Rationale: Sol.
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e. at 12 o’clock).
∴ The hands coincide 22 times in a day.
Answer C
Answer: C
Question: Which of the following is closer to √0.8+√0.05?
Options:
A)0.5
B)0.7
C)0.9
D)1.1
E)1.2
Rationale: √0.8+√0.05=approximately √0.81+√0.04=0.9+0.2=1.1. Hence, the correct answer is D.
Answer: D
Question: If Henry were to add 9 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
Options:
A)25
B)40
C)64
D)72
E)96
Rationale: 7/8x-3/4x=9galls
1/8*x=9gallons
x=72 gallons
Answer D
Answer: D
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)445 km
B)415 km
C)420 km
D)480 km
E)490 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420
ANSWER:C
Answer: C
Question: If the ratio of the ages of two friends A and B is in the ratio 3 : 5 and that of B and C is 3 : 5 and the sum of their ages is 147, then how old is B?
Options:
A)27 Years
B)75 Years
C)45 Years
D)49 Years
E)59 Years
Rationale: Explanation:
The ratio of the ages of A and B is 3 : 5.
The ratio of the ages of B and C is 3 : 5.
B's age is the common link to both these ratio. Therefore, if we make the numerical value of the ratio of B's age in both the ratios same, then we can compare the ages of all 3 in a single ratio.
The can be done by getting the value of B in both ratios to be the LCM of 3 and 5 i.e., 15.
The first ratio between A and B will therefore be 9 : 15 and
the second ratio between B and C will be 15 : 25.
Now combining the two ratios, we get A : B : C = 9 : 15 : 25.
Let their ages be 9x, 15x and 25x.
Then, the sum of their ages will be 9x + 15x + 25x = 49x
The question states that the sum of their ages is 147.
i.e., 49x = 147 or x = 3.
Therefore, B's age = 15x = 15 × 3 = 45
Answer: C
Answer: C
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)11 sec
B)36 sec
C)77 sec
D)14 sec
E)12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 600 * 3/50
= 36 sec.
Answer: B
Answer: B
Question: Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took P.E. as an elective, 1/3 of the students took Theatre as an elective, and all of the other students took Music. In this year, 1/3 of the students who took P.E. and 1/4 of the students who took Theatre left school, other students did not leave, and no fresh student come in. What fraction of all students took P.E. or Music?
Options:
A)2/3
B)1/4
C)7/9
D)1/5
E)8/11
Rationale: Lets pick smart numbers. Total number of students: 12
P.E. (1/2): 6
Theatre (1/3): 4
Music (1/6): 2
After leaving school
P.E.: 4
Theatre: 3
Music: 2
New Total number of students: 9
P.E. and Music: 6
Answer 2/3 or A
Answer: A
Question: The events A and B are independent. The probability that event A occurs is a and the probability that event B occurs is b. Which of the following is equal to the probability that exactly one of the events A and B occurs?
Options:
A)a − 2ab
B)b − ab
C)a + b − 2ab
D)a + b −ab
E)a + b
Rationale: Probability of A occuring = a , Probability of A NOT occuring = 1-a
Probability of B occuring = b , Probability of B not occurring = 1-b
Probability of atleast of one of A and B occuring = 1-(1-a)(1-b) =a+b -ab
D
Answer: D
Question: If 7/10 of a pencil is green, 4/5 of the remaining is gold and the remaining 1/2 is white, what is the total length of the pencil?
Options:
A)5
B)3
C)1
D)4
E)2
Rationale: Green is 7/10 Gold is 4/5 which can also be written as 8/10White is 1/2 which can also be written as 5/107/10 + 8/10 + 5/10= 2Answer is E) 2
Answer: E
Question: Vikram borrowed rupees 6450 at 5% simple interest repayable in 4 equal installments. what will be the annual installment payable by him?
Options:
A)1710
B)1810
C)1910
D)1860
E)1850
Rationale: Let the annual instalment be Rs. P.
Amount of ₹ 100 after 4 yr = 100 + (100 x 5 x 4)/100 = ₹ 120
∴ Present Value (PV) of ₹ 120 due after 4 yr = ₹ 100
Present Value (PV) of ₹ due after 4 yr = 100P/120 = 5P/6
Similary, PV of ₹ P due after 3 yr = 20P/23
PV of ₹ P due after 2 yr = 10P/11
PV of ₹ P due after 1 yr = 20P/21
∴ 5P/6 + 20P/23 + 10P/11 + 20P/11 = 6450
⇒ P = ₹ 1810
ANSWER:B
Answer: B
Question: Which is odd one
10, 25, 45, 54, 60, 75, 80
Options:
A)10
B)45
C)54
D)60
E)75
Rationale: All numbers except 54 is multiple of 5.
answer :C
Answer: C
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Options:
A)388
B)375
C)288
D)266
E)269
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer:B
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/29
B)2/28
C)2/21
D)2/22
E)2/26
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: C