divelab/Sys2Bench huggingface dataset:
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 80 with him, what was the average amount with the group before his joining the group?
Options:
A)s.12
B)s.10
C)s.15
D)s.29
E)s.19
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 80. So, the amount with remaining 6 people = 140 - 80 = Rs. 60
The average amount with them = 60/6
= Rs.10.
Answer:B
Answer: B
Question: Raman mixed 54 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Options:
A)129
B)287
C)196
D)188
E)112
Rationale: Explanation:
CP per kg of mixture = [54(150) + 36(125)]/(54 + 36) = Rs. 140
SP = CP[(100 + profit%)/100]
= 140 * [(100 + 40)/100] = Rs. 196.
Answer:C
Answer: C
Question: The Guests at a football banquet consumed a total of 325 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
Options:
A)160
B)161
C)162
D)163
E)164
Rationale: To minimize one quantity maximize other.
162*2 (max possible amount of food a guest could consume) = 324 pounds, so there must be more than 162 guests, next integer is 163.
Answer: D.
Answer: D
Question: 1, 1, 3, 9, 11, 121,?
Options:
A)122
B)123
C)124
D)125
E)126
Rationale: 1^2 = 1 ......... 1+2 = 3
3^2 = 9 ....... 9+2 = 11
11^2 = 121 ...... 121+2 = 123
ANSWER:B
Answer: B
Question: A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number K is
Options:
A)74
B)K=75
C)K=175
D)K=680
E)690
Rationale: I solved this question by plugging in numbers from the answer choices.
A.) 74
Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.
B.) 75
I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.
15-7 = 8 so I know the correct answer isB
Answer: B
Question: If a and b are each greater than x and y, which of the following must be true?
I. ab > xy
II. a + b > x + y
III. |a| + |b| > |x| + |y|
Options:
A)I only
B)II only
C)I and II
D)I and III
E)I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: B.
Answer: B
Question: A train leaves Delhi at 9 a.m. at a speed of 35 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
Options:
A)229
B)288
C)600
D)888
E)1400
Rationale: D = 35 * 5 = 175
RS = 40 – 35 = 5
T = 175/5 = 35
D = 40 * 35 = 1400 km
Answer: E
Answer: E
Question: How many zeros does 1000! end with?
Options:
A)20o
B)24o
C)249
D)30o
E)325
Rationale: According to above 1000! has 1000/5+1000/25+1000/125+1000/625=200+40+8+1=249 trailing zeros.
Answer: C
Answer: C
Question: A shopkeeper purchased 77 kg of potatoes for Rs. 539 and sold the whole lot at the rate of Rs. 8.50 per kg. What will be his gain percent?
Options:
A)18 1/9 %
B)28 9/3 %
C)28 1/3 %
D)32 1/3 %
E)21 3/7 %
Rationale: C.P. of 1 kg = 539/77 = Rs. 7S.P. of 1 kg = Rs. 8.50Gain % = 1.50/7 * 100 = 150/7 = 21 3/7 %Answer: E
Answer: E
Question: In a competitive examination in batch A, 8% candidates got selected from the total appeared candidates. batch B had an equal number of candidates appeared and 12% candidates got selected with 50 more candidates got selected than A. What was the number of candidates appeared from each batch?
Options:
A)1200
B)650
C)281
D)587
E)5000
Rationale: Batch A and Batch B had an equal number of candidates appeared.
In Batch A, 8% candidates got selected from the total appeared candidates
In Batch B, 12% candidates got selected from the total appeared candidates
But in Batch B, 50 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 50
=> total appeared candidates in Batch B = 50 x 100 = 5000
=> total appeared candidates in Batch A = total appeared candidates in Batch B = 5000
Answer : E
Answer: E
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 4:5, find his marks in Science?
Options:
A)10.9
B)20.9
C)30.9
D)35
E)45
Rationale: S:E = 1:3
E:M = 4:5
------------
S:E:M = 4:12:15
4/31 * 162 = 20.9
ANSWER:B
Answer: B
Question: A group of 4 doctors and 2 nurses recently frequented the Lolly's Restaurant. The total bill for the meal, including 20% gratuity, came to $1440. On average, how much did the meal of each individual cost before gratuity?
Options:
A)$160
B)$60
C)$200
D)$80
E)$55
Rationale: 4 doctors and 2 nurses - so total 6 people
The bill $1440 includes 20% gratuity... so the actual cost of dinner was $1200
Now, the cost per person will be $1200/6 which is $200
Option C
Answer: C
Question: If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions W represents the final price of the item?
Options:
A)W=(10,000z + 100z(x – y) – xyz)/10,000
B)W=(10,000z + 100z(y – x) – xyz)/10,000
C)W=(100z(x – y) – xyz)/10000
D)(100z(y – x) – xyz)/10000
E)10000 /(x – y)
Rationale: -A-
z=Original Price
x=MU
y= MD
New price with MU:
z(x/100+1)
New price with MD:
z[(x/100+1)(-y/100+1)]
Solvingâ€¦
=z[((x+100)/100)((-y+100)/100)]
=z(x100-xy+10000-100y)/10000
=(zx100-xyz+10000z-100yz)/10000 --> similar to A
Answer: A
Question: A scale 10 ft. 5 inches long is divided into 5 equal parts. Find the length of each part.
Options:
A)25 inches
B)77 inches
C)66 inches
D)97 inches
E)66 inches
Rationale: Explanation:
Total length of scale in inches = (10*12) + 5 = 125 inches
Length of each of the 5 parts = 125/5 = 25 inches
ANSWER:A
Answer: A
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 6600 ?
Options:
A)11
B)13
C)14
D)18
E)10
Rationale: Required difference = [3 ½ % of Rs.6600] – [3 1/3 % of Rs.6600]
= [(7/20-(10/3)]% of Rs.6600 =1/6 % of Rs.6600
= Rs. [(1/6)8(1/100)*6600] = Rs. 11.
Answer is A.
Answer: A
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
Options:
A)1/7 m
B)1/3 m
C)1/4 m
D)1/5 m
E)1/6 m
Rationale: After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7.
Answer: A.
Answer: A
Question: A room contains 150 people, 12 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Say group of x people left the room.
# of women in the room was 0.12*150=18;
# of women in the group that left 0.15x;
# of women in the room after the group left it is 0.1(150-x);
So, 18-0.15x= 0.1(150-x) --> x=60.
Answer: C.
Answer: C
Question: Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
Options:
A)66
B)70
C)72
D)75
E)78
Rationale: Let the distance one way be x
Time from home to work = x/75
Time from work to home = x/105
Total time = 2 hrs
(x/75) + (x/105)= 2
Solving for x, we get x = 175/2
Time from home to work in minutes= (175/2)*60/75 = 70 minutes
Ans= B
Answer: B
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
Options:
A)50 kmph
B)520 kmph
C)56 kmph
D)59 kmph
E)53 kmph
Rationale: A
50 kmph
Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
Answer: A
Question: A 15 by 20 rectangle is inscribed in circle. What is the circumference of the circle?
Options:
A)5π
B)10π
C)15π
D)20π
E)25π
Rationale: The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: E
Answer: E
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Options:
A)20088
B)20000
C)67892
D)28826
E)25781
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Answer: B
Question: 5358 x 54 = ?
Options:
A)272258
B)272358
C)289332
D)274258
E)274358
Rationale: 5358 x 51	= 5358 x (50 + 4)
= 5358 x 50 + 5358 x 4
= 267900 + 21432
= 289332.
C)
Answer: C
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
Options:
A)65°
B)67.8°
C)67.5°
D)69.5°
E)67.2°
Rationale: Hence the angle
=30(5-15/5)+15/2
=30(5-3)+7.5
=30 X 2 + 7.5+=67.5 °
Answer C
Answer: C
Question: There are some goats in James farm. If they don't die for any reason James can make new farm in 6 years with baby goat and older goats. But goats die for many reason, if no baby goats are born the farm will be empty in 12 years. If new babies are born and older die in same time , how many time needed for make a new farm?
Options:
A)10
B)15
C)5
D)12
E)20
Rationale: Goats die in every year = 1/12
Goats born in every year = 1/6
Total growth in every year = 1/6 - 1/12 = 1/12
So James can make a new farm in = 12 years
ANSWER:D
Answer: D
Question: The population of a town increases 10% and 20% respectively in two consecutive years. After the growth the present population of the town is 1320. Then what is the population of the town 2 years ago?
Options:
A)1100
B)1001
C)1010
D)1000
E)1002
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
1320 * 100/110 * 100/120 = 1000
Answer: Option D
Answer: D
Question: The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 80 minutes after it was poured was how many degrees Fahrenheit?
Options:
A)45
B)56
C)60.4
D)85
E)90
Rationale: Answer: B
The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 80 minutes after it was poured is:
F = 120 ( 2 ^ -80/10) + 60
F = 120 * 1/ 256 + 60
F = 15/32 + 60
F = 1935/32=60.4
C
Answer: C
Question: If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much % should he reduce the quantity of gasoline that he buys?
Options:
A)10%
B)12.5%
C)8%
D)12%
E)6.66%
Rationale: Explanatory Answer
Let the price of 1 litre of gasoline be $x and let Ron initially buy 'y' litres of gasoline.
Therefore, he would have spent $xy on gasoline.
When the price of gasoline increases by 25%, the new price per litre of gasoline is 1.25x.
Ron intends to increase the amount he spends on gasoline by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy
Let the new quantity of gasoline that he can get be 'q'.
Then, 1.25x * q = 1.15xy
Or q = 1.15xy/1.25x = 0.92y.
As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.
Or a reduction of 8%.
The correct choice is (C)
Answer: C
Question: A certain number of men can do a work in 54days. If there were 6 men more it could be finished in 6 days less. How many men were there in the beginning?
Options:
A)50
B)48
C)70
D)40
E)50
Rationale: Explanation:
m(54) = (m+6)(48)
9m-8m=48
M=48
Answer: Option B
Answer: B
Question: A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price q of the machine?
Options:
A)	81
B)	100
C)	120
D)	135
E)	160
Rationale: Since the wholesale price was $90 and the profit was 20% of the wholesale price ([.2][90] = $18), the retail price would have to be above $108, but not that much greater than that.
Let's start by TESTing Answer C: $120....
If.....
Retail Price q= $120
10% discount off = $120 - (.1)(120) = 120 - 12 = 108
20% profit on wholesale price = 90 + (.2)(90) = 90 + 18 = 108
These two numbers MATCH, so this MUST be the answer!
Final Answer:
[Reveal]Spoiler:
C
Answer: C
Question: In 40 litres of a mixture the ratio of milk to water is 7:1. In order to make the ratio of milk to water as
3:1, the quantity of water that should be added to the mixture will be
Options:
A)523 litre
B)413 litre
C)623 litre
D)6 litre
E)None of these
Rationale: Explanation :
By the rule of alligation, we have
Concentration of water
in pure water : 1 Concentration of water
in mixture : 1/8
Concentration of water in the final mixture
1/4
1/4 - 1/8 = 1/8 1 - 1/4 = 3/4
Quantity of water : Quantity of mixture = 1/8 : 3/4 = 1 : 6
Given that quantity of mixture = 40 litre
=>Quantity of water : 40 = 1 : 6
⇒Quantity of water = 40×16=623 litre
Answer : Option C
Answer: C
Question: A computer program generates a sequence of numbers a1, a2, a3, ... such that a1=1, a2=2, and ak=a(k-1)*5 - 3 for 2 < k < n. If n = 10, find a5.
Options:
A)115
B)137
C)141
D)151
E)157
Rationale: a1=1
a2=2
a3=2*5-3=7
a4=7*5-3=35-3=32
a5=32*5-3=160-3=157
157
Answer: E
Question: Of the 8 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Given:
Total number of wires = 5
Number of cable wires = 2
Number of telephone wires = 3
To find:
Number of combination which has at least one cable wires
Solution:
No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2
Since it is a combination of wires, the arrangement is not important
Approach 1:
Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)
Selection 1
Number of ways of selecting one cable wire = 2C1 = 2
Number of ways of selecting 2 telephone wires = 3C2 = 3
Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 2
Number of ways of selecting one cable wire = 2C2 = 1
Number of ways of selecting 2 telephone wires = 3C1 = 3
Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire
Approach 2
Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)
Total number of ways of selecting 3 wires out of 5 = 5C2 = 10
Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1
Selection X - Selection Y = 8
Answer is Option C
Answer: C
Question: 16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
Options:
A)5
B)2
C)8
D)4
E)16
Rationale: 1. We need to find out the time taken by 7 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 16*8 = 128 days
4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job.
5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days.
6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days.
The answer is choice E
Answer: E
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (8/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
Options:
A) 3/8
B) 1/2
C) 11/16
D) 5/7
E) 3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 8/8*c:
(b+c)/2 = (8/8)*c
b = (1)*c
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (1*c)/2 = (1/2)*c
Median = (a + c)/2 = (1/2*c + c)/2 = (3/2)*c/2 = (3/4)*c (ANSWER E)
Answer: E
Question: The present population of a town is 200. Population increase rate is 10% p.a. Find the population of town after 1 years?
Options:
A)100
B)120
C)200
D)220
E)250
Rationale: P = 200
R = 10%
Required population of town = P*(1 + R/100)^T
= 200*(1 + 10/100)
= 200*(11/10)
= 220(approximately)
Answer is D
Answer: D
Question: In an examination, a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 120 questions and secures 180 marks, the number of questions he attempts correctly, is:
Options:
A)45
B)90
C)80
D)75
E)70
Rationale: Let the number of correct answers be x.
Number of incorrect answers = (120 â€“ x).
3x â€“ (120 â€“ x) = 180 or 4x = 300 or x = 75
ANSWER:D
Answer: D
Question: The average of five numbers is 45. If one number is excluded, the average becomes 38. The excluded number is?
Options:
A)8
B)73
C)58
D)35
E)96
Rationale: Excluded number
= (45 * 5) - (38 * 4)
= 225 - 152 = 73
Answer:B
Answer: B
Question: Average of 11 results is 59. If the average of first five results is 55 and average of last five results is 60 Then find the sixth result?
Options:
A)71
B)85
C)86
D)74
E)69
Rationale: Option 'D'
Answer: D
Question: 1/2 divived by 1/2 of 1/2 whole divided by 1/2 +1/2 of 1/2
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 1/2 divided by 1/2 of 1/2 :
1/2 of 1/2 = 1/2*1/2 = 0.25
1/2 divided by .25 = 2
1/2+1/2 of 1/2:
1/2+1/2 = 1
1 of 1/2 = 0.5
1/2 divived by 1/2 of 1/2 ) whole divided by 1/2 +1/2 of 1/2
2/0.5 = 4
ANSWER:B
Answer: B
Question: If S is the sum of reciprocals of a list of consecutive integers from 44 to 55, inclusive, S is approximately equal to
Options:
A)0.1
B)0.2
C)0.3
D)0.4
E)0.5
Rationale: We need to find the approximate value of 1/44 + 1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53. Now, the sum of these 10 terms will be very close to 10 times 1/50, which is 0.02*10=0.2.
Answer: B.
Answer: B
Question: Calculate the total gain or loss of a shop owner who sold two items for Rs. 1200 each, if he made a profit of 15% from the first item and a loss of 15% from the second item.
Options:
A)24.5
B)14.5
C)2.25
D)5.5
E)2.5
Rationale: (15*15)/100 = 2.25%
Answer: C
Answer: C
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.900, what is the reduced price for kg?
Options:
A)s.40
B)s.46
C)s.49
D)s.45
E)s.42
Rationale: 900*(25/100) = 225 ---- 5
? ---- 1
=> Rs.45
Answer: D
Answer: D
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options:
A)21.0 sec
B)12.1 sec
C)13.9 sec
D)43.9 sec
E)37.9 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: B
Question: An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
Options:
A)3
B)4
C)6
D)9
E)12
Rationale: Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+34.1)/100 => x*4/3
now we need to find n for x * (4/3)^n = 3x ;or in other words n = 4
ANSWER:B
Answer: B
Question: Average of first five multiples of 8 is
Options:
A)9
B)11
C)24
D)15
E)16
Rationale: Explanation:
Average=8(1+2+3+4+5)/5=24
Answer: Option C
Answer: C
Question: Three balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
Options:
A)60
B)90
C)120
D)150
E)180
Rationale: Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box.
For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.
Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.
For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.
For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.
Total of 40 + 20 = 60 possibilities.
Answer A.
Answer: A
Question: An anti- aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?
Options:
A)0.6872
B)0.4379
C)0.6976
D)0.1274
E)None of these
Rationale: Solution:
Required probability:
=(0.4Ã—0.7Ã—0.8Ã—0.9)+(0.6Ã—0.3Ã—0.8Ã—0.9)+(0.6Ã—0.7Ã—0.2Ã—0.9)+(0.6Ã—0.7Ã—0.8Ã—0.1)+(0.4Ã—0.3Ã—0.8Ã—0.9)+(0.4Ã—0.7Ã—0.2Ã—0.9)+(0.4Ã—0.7Ã—0.8Ã—0.1)+(0.6Ã—0.3Ã—0.2Ã—0.9)+(0.6Ã—0.3Ã—0.8Ã—0.1)+(0.6Ã—0.7Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.2Ã—0.9)+(0.6Ã—0.3Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.8Ã—0.1)+(0.4Ã—0.7Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.2Ã—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
=0.6976
ANSWER IS C
Answer: C
Question: A company recently conducted a survey and found that 30,000 of its customers live in rural areas. If the number of customers who live in urban areas is 130 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?
Options:
A)65,000
B)67,000
C)69,000
D)71,000
E)73,000
Rationale: The number of customers in urban areas is 30,000+1.3*30,000=69,000.
The answer is C.
Answer: C