divelab/Sys2Bench huggingface dataset:
Question: The speed of light is approximately 1,86 * 10^4 miles per second. This approximate speed is how many miles per hour?
Options:
A) 1,11 * 10^7
B) 6,70 * 10^7
C) 1,11 * 10^8
D) 1,86 * 10^8
E) 6,70 * 10^8
Rationale: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(1.86*10^4)*3600 = (1.86*10^4)*(3.6*10^3) = some number*10^7...
The key is realizing that thesome numberhas to be bigger thatn 1.86 (because 1.86*3.6), and the only answer that fits that is B
Answer: B
Question: A train 280 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 200 m long?
Options:
A)32 sec
B)42 sec
C)45 sec
D)18 sec
E)49 sec
Rationale: total length= 280+200=480
speed=54km/h=(54*5)/18= 15/1m/s
time=(480*1)/15=32 sec.
ANSWER:A
Answer: A
Question: If 4/(a - 5) = 5/(a + 5), then a = ?
Options:
A)40
B)45
C)35
D)55
E)50
Rationale: Multiply all terms of the given equation by (a - 5)(a + 5), simplify and solve
(a - 5)(a + 5)[ 4/(a - 5) ] = (a - 5)(a + 5) [5/(a + 5) ]
4 (a + 5) = 5 (a - 5)
a =45
correct answer B
Answer: B
Question: In August,a cricket team that played 120 matches won 26% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
Options:
A)40
B)52
C)65
D)80
E)98
Rationale: let the no of matches played more=x
so,
(120+x)*52/100=31.2+x
by solving we get x=65
ANSWER:C
Answer: C
Question: A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 72 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?
Options:
A)20
B)30
C)48
D)56
E)72
Rationale: Total distance = 72
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2
d1 + d2 = 72
s1t1 + s2t2 = 72
8*t1 + 16*t2 = 72
t1 + 2*t2 = 9 ----- (1)
Given: t1 + t2 = 8 ----- (2)
(1) - (2) --> t2 = 1 and t1 = 8 - 1 = 7
Walking distance = s1*t1 = 8*7 = 56
Answer: D
Answer: D
Question: If it is possible to from a word with the first, fourth, seventh and eleventh letters in the word 'SPHERVLVODS' write the second letter of thet word. Otherwise, X is the answer.?
Options:
A)D
B)E
C)S
D)P
E)Q
Rationale: The first, fourth, seventh and eleventh letters of the word 'SPHERVLVODS'
The word formed is LESS
The second letter is E.
ANSWER B
Answer: B
Question: What is the units' digit of the following expression (11)^5*(1)^3*(21)^5?
Options:
A)0
B)1
C)3
D)5
E)9
Rationale: We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 11,1,21 - are ODD and since the PRODUCT contains 1, the units digit of the product will remain 1
B
Answer: B
Question: By selling 28 metres of clothes, a shopkeeper gains the price of 3 metres of clothes. His gain per cent is
Options:
A)16%
B)15%
C)14%
D)13%
E)12%
Rationale: Suppose S.P of 28 meters of cloth = Rs 28
Therefore, Gain = Rs 3 => C.P = Rs 25
Gain % = 3/25 x 100 = 12%
Gain = 12%
ANSWER:E
Answer: E
Question: The sum of three consecutive odd natural numbers, each divisible by 3 is 87. What is the largest among them?
Options:
A)21
B)24
C)27
D)32
E)45
Rationale: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 =87
3X = 78
X = 26
The numbers are 26, 29, 32
Therefore the largest number is 32
Answer D.
Answer: D
Question: The current ofa stream runs at the rate of 2 km/hour. A motor boat goes 10 km upstream & back again to the starting point in 55 min. Find the speed of the motor boat in still water?
Options:
A)20 km/hr
B)22 km/hr
C)28 km/hr
D)30 km/hr
E)34 km/hr
Rationale: Let the speed of the boat in still water =x km/hr
Speed of the current = 2 km/hr
Then, speed downstream =(x+2) km/hr
speed upstream =(x−2) km/hr
Total time taken to travel 10 km upstream and back = 55 minutes =5560 hour = 1112 hour
⇒10x−2+10x+2=1112 120(x+2)+120(x−2)=11(x2−4) 240x=11x2−44 11x2−240x−44=0 11x2−242x+2x−44=0 11x(x−22)+2(x−22)=0 (x−22)(11x+2)=0 x=22 or −211
Since x cannot be negative, x = 22
i.e., speed of the boat in still water = 22 km/hr
B
Answer: B
Question: Which of the following is the median number of goals scored per student?
Options:
A)0
B)1
C)2
D)3
E)None of the above
Rationale: Total number of students = 8+2+5= 15
so median must be the middle term out of the 15 terms i.e., 8th term when arranged in ascending order
arranging in ascending order we have {1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3}
median number of goals scored per student = 1
ANSWER:B
Answer: B
Question: A bag contains 25p coins, 50p coins and 1 rupee coins whose values are in the ratio of 8:4:2. The total values of coins are 840. Then find the total number of coins
Options:
A)220
B)240
C)260
D)280
E)340
Rationale: Value is given in the ratio 8:4:2.
(8x/0.25) + (4x/0.5) + (2x/1) = 840.
X = 20. Total amount = 14*20 = 280
Answer:D
Answer: D
Question: In his pocket, a boy has 3 red marbles, 4 blue marbles, and 5 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The worst case scenario would be that he has taken 4 blue and 5 green, a total of 9 marbles, and still doesn't have 3 distinct colors. But the next draw will surely be red as only the red marbles are left in his pocket.
The answer is D.
Answer: D
Question: A man invests a certain sum of money at 6% per annum simple interest and another sum at 7% per annum simple interest. His income from interest after 2 years was Rs. 354. One-forth of the first sum is equal to one-fifth of the second sum. The total sum invested was :
Options:
A)Rs.3100
B)Rs.2700
C)Rs.2200
D)Rs.1800
E)Rs.2100
Rationale: Explanation :
Let the man invests Rs.x at 6% and Rs.y at 7%
Simple Interest on Rs.x at 6% for 2 years + Simple Interest on Rs.y at 7% for 2 years = Rs.354
x × 6 ×2 /100+y×7×2/100=354
x × 6 × 2+y×7×2=354×100
x × 6+y × 7=177×100
6x+7y=17700⋯(1)
One-forth of the first sum is equal to one-fifth of the second sum
=>x/4=y/5
=>x=4y/5⋯(2)
Solving (1) and (2),
6x+7y=17700
6(4y/5)+7y=17700
24y+35y=17700×5
59y=17700×
y=300×5=1500
x=4y/5
=4×1500/5
=4×300
=1200
total sum invested = x + y = 1500 + 1200 = 2700
Answer : Option B
Answer: B
Question: If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x?
Options:
A)-1
B)2
C)1
D)-2
E)0
Rationale: If we solve the question, we get x=-2.
Option: D
Answer: D
Question: A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed Q of the train.
Options:
A)a) 45
B)b) 33
C)c) 48
D)d) 55
E)e) 61
Rationale: Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1
Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late
so, (y-24)/(3x/4) - (y-24)/x = 25/60
4(y-24)/3x - (y-24)/x = 5/12
(y-24)/x (4/3-1) = 5/12
(y-24)/x *1/3 = 5/12
(y-24)*12 = 3x*5
(y-24)*4 = 5x
4y-5x = 96 ....... 2
eq2 - eq1
2x=96
x=48=Q
Ans = C
Answer: C
Question: If a survey shows that 40 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
Options:
A)56%
B)64%
C)80%
D)82%
E)86%
Rationale: Those who support = 40.
% of those who don't support it is (200-40)/ 200 = 80%
Answer C
Answer: C
Question: Evaluate: 2344 - 12*3*2 =?
Options:
A)2337
B)1227
C)3327
D)5457
E)7677
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
2344 - 12*3*2 = 2344 - 8 = 2337
correct answer A
Answer: A
Question: Total of the ages of A, B ahd C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at present
Options:
A)25
B)30
C)45
D)60
E)65
Rationale: Explanation:
Let their ages 10 years ago is x, 2x and 3x years.
10 + 2x + 10 + 3x + 10 = 90 hence x= 10
B’s present age = (2x + 10) =30 years
Option B
Answer: B
Question: A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time W it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
Options:
A) 0.8(80 – y)
B) 0.8 + 0.0025y
C) 80/y – 1.25
D) 80/1.25y
E) 80 – 0.25y
Rationale: This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks.
Which means finishing all houses at normal rate W=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks.
7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9.
Answer: B
Question: Set M contains number that satisfy the condition that, if integer x is in the set then x + 2 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M?
I) -6
II) -2
III) 2
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II and III
Rationale: Since -4 is in the set, then the set must also include -2, 0, 2, 4, etc...
Depending on whether -4 is the starting element in the set or not, we can have -6...or not.
The answer is D.
Answer: D
Question: What is the HCF of 2/3, 4/12 and 6/5
Options:
A)7/45
B)2/45
C)4/15
D)1/30
E)9/45
Rationale: Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 12, 5) = 2/60 = 1/30
Answer: Option D
Answer: D
Question: n a Festival season Director informed his 20 staffs with their family to go for a one day tour. Package for one day is 750/- Some staffs are married and some are unmarried and some having their Kids. Director & 8 staffs are married with 2 kid each. What is the total package:
Options:
A)30000
B)38000
C)45000
D)33000
E)36000
Rationale: Total staffs = 20
Married staffs including Director = 9 *4= 36
Unmarried Staff = 20-8 = 12
Total persons = 48
Total package = 48 * 750 = 36000
Answer is E
Answer: E
Question: From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 3, what is the probability that the 2 numbers included the number 1?
Options:
A)1/5
B)2/5
C)1
D)3/5
E)1/4
Rationale: We know that the sum of two numbers picked was 3. So, there could be the following cases:
(1, 2);
(2, 1);
Total of 2 cases out of which 2 have 1, thus the probability is 2/2=1.
Ans C
Answer: C
Question: Each family in a locality has atmost two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls and more girls than families. Then the minimum possible number of families in the locality is
Options:
A)4
B)5
C)2
D)3
E)1
Rationale: Explanation :
As per the question, we need to satisfy three
conditions namely:
1. Adults (A) > Boys (B)
2. Boys (B) > Girls (G)
3. Girls (G) > Families (F)
Clearly, if the number of families is 2, maximum number of adults can only be 4. Now, for the second condition to be satisfied, every family should have atleast two boys and one girl each.
This will result in non-compliance with the first condition because adults will be equal to boys. If we consider the same conditions for 3 families, then all three conditions will be satisfied.
Answer : D
Answer: D
Question: A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time?
Options:
A)75 m.
B)80 m.
C)150 m.
D)100 m.
E)None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 50m is 50/1=50m
so the total time taken by a and b to reach =2*50=100m
ANSWER:D
Answer: D
Question: An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres
Options:
A)1300
B)1400
C)2400
D)2500
E)2600
Rationale: It means that 0.08% of x = 2
(8100×100 ×x)=2
x=2×100×1008
x=2500
ANSWER :D
Answer: D
Question: At 3:00 pm, a car has driven 10 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?
Options:
A)a) 10
B)b) 11
C)c) 12
D)d) 20
E)e) 14
Rationale: 0.8 minutes --> 1 mile
1 minute --> 1/0.8 = 10/8 = 1.25 miles/minute
Distance covered in 40 minutes = 1.25 * 40 = 12.5 * 4 = 50 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
10 + x = 50 - x
2x = 40
x = 20
Answer: D
Answer: D
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 60/kg. how much did a kg of coffee cost in june ?
Options:
A)50
B)60
C)80
D)100
E)120
Rationale: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (600gm) of tea and 1/2 kg (600gm) of coffee (equal quantities) = 60
1.2x(1/2) + 0.8x(1/2) = 60
=> x =60
Thus proved...option B.
Answer: B
Question: A women buys an article and sells it at a profit of 20%. If she had bought it at 20% less and sold it for $75 less, she could have gained 25%. What is the cost price?
Options:
A)392
B)424
C)375
D)273
E)429
Rationale: C
375
CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: C
Question: If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio W of the resistors’ sum of A and C to the resistors’ sum of A and B?
Options:
A)2(R1+R2):(R1+2R2)
B)(R1+R2):(R1+2R2)
C)(2R1+R2):(R1+2R2)
D)2(R1+R2):(2R1+R2)
E)2(R1-R2):(R1+2R2)
Rationale: two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio W of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
=2(r1+r2)/2r2+r1.A
Answer: A
Question: A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 50 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?
Options:
A)1 hour
B)1 hour 20 minutes
C)2 hours 30 minutes
D)1 hour 40 minutes
E)2 hours 10 minutes
Rationale: v1 and V2 are speeds.
v1.t /50 = v2
v2.t/40 = v1
v1/v2 = 5/4
which train A would 50. 4/5 mins to cover the same distance
40 + 40 = 80 mins (ANS B)
Answer: B
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
A)5 mins
B)3 mins
C)7 mins
D)9 mins
E)2 mins
Rationale: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins
Answer: B
Answer: B
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 4 per metre approximately
Options:
A)4457
B)4567
C)5943
D)4547
E)4675
Rationale: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 4) = Rs. 5943.
Answer: Option C
Answer: C
Question: If n is a natural number, then (6n2 + 6n) is always divisible by:
Options:
A)Both 6 and 12
B)6 only
C)12 only
D)None of these
E)Cannot be determined
Rationale: Explanation :
6n2 + 6n = 6n(n + 1)
Hence 6n2 + 6n is always divisible by 6 and 12 (∵ remember that n(n + 1) is always even) Answer : Option A
Answer: A
Question: A train 150 m long is running at a speed of 62 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Options:
A)5 sec
B)10 sec
C)12 sec
D)18 sec
E)15 sec
Rationale: Answer : B.
Speed of the train relative to man = (62 - 8) kmph
= (54* 5/18) m/sec = 15m/sec
Time taken by the train to cross the man
= Time taken by It to cover 150 m at 15 m / sec = 150 *1/ 15 sec = 10sec
Answer: B
Question: There are how many hours between x minutes past 12 noon and 8:10 p.m. of the same day, where x < 60?
Options:
A) (490-x)/60
B) (480-x)/60
C) (470-x)/60
D) 60 (60 – x + 7)
E) 60 (60 – x + 17)
Rationale: Let's just say that X is equal to 10 so we will have that the number of hours will be 8, this is our target value. Now plug 10 in the answer choices to see which gives 8.
A is correct here.
Answer: A
Question: P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
Options:
A)16
B)88
C)29
D)14
E)12
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days. Answer: A
Answer: A
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 60 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
Options:
A) 100
B) 120
C) 140
D) 150
E) 160
Rationale: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+60)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=120
Ans B
Answer: B
Question: A BISCUIT manufacturer produces 300 units of a certain model each month at a cost to the manufacturer of £30 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £30,000?
Options:
A)110
B)330
C)220
D)440
E)550
Rationale: 300(x-30)≥30,000
x-30≥300
x≥330
Answer: Option B
Answer: B
Question: 210 college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
Options:
A)25
B)40
C)50
D)60
E)75
Rationale: 120 = 60(Mac) + x(Window) + 20(both) => x=40
ANSWER:B
Answer: B
Question: Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, if Magnabulk charges m dollars for each crate?
Options:
A)100bd/m
B)100m/(bd)
C)bd/(100m)
D)m/(bd)
E)bd/m
Rationale: crate has = bd magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = m / bd
Ans; D
Answer: D
Question: The overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X?
Options:
A)11
B)15
C)12
D)17
E)19
Rationale: C
12
(X + Y) – (Y + Z) = 12
X – Z = 12
Answer: C
Question: In the formula V = (4r)^2, if r is halved, then V is multiplied by
Options:
A)64
B)8
C)1/4
D)1/8
E)1/64
Rationale: Say r=2 => V1 = 16
when r=1; V2 = 4
V2 = 1/4*V1.
Answer : C
Answer: C
Question: Find √? /11= 4 ?
Options:
A)76
B)1936
C)1304
D)1296
E)None
Rationale: Answer
Let √N/11= 4
Then √N = 11 x 4 = 44
∴ N = 44 x 44= 1936.
Correct Option: B
Answer: B
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
Options:
A)0.6976
B)0.7013
C)0.789
D)0.8356
E)0.8666
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Answer: A
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
A)3/140
B)1/280
C)27/280
D)3/35
E)7/56
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280.
Answer: C
Answer: C
Question: From a group of 3 MEN and 3 WOMEN, 4 ADULTS are to be randomly selected. What is the probability that equal numbers of men and women will be selected?
Options:
A)1/5
B)2/5
C)3/5
D)4/5
E)1
Rationale: Using the first example, here is the probability of THAT EXACT sequence occurring:
MMWW = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
MWMW = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.
6(1/10) = 6/10 = 3/5
Final Answer:
C
Answer: C
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get ?
Options:
A)57%
B)60%
C)65%
D)90%
E)None of these
Rationale: Solution
Total number of votes polled= (1136 + 7636 + 11628) = 20400.
∴ Required percentage= ( 11628/20400x 100)%= 57%
Answer A
Answer: A
Question: (160)^2 - (161)^2 =
Options:
A)1
B)100
C)229
D)323
E)349
Rationale: Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 161*2 + 1
= 322+1 = 323 = Answer = D
Answer: D
Question: Find the area of a parallelogram with base 28 cm and height 32 cm.
Options:
A)200
B)384
C)345
D)244
E)896
Rationale: Area of a parallelogram = base * height = 28 * 32 = 896 cm2
Answer: Option E
Answer: E