divelab/Sys2Bench huggingface dataset:
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Options:
A)1/2
B)1/2
C)8/15
D)9 by 20
E)9/24
Rationale: Explanation :
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20
Answer : D
Answer: D
Question: A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 49/64. How many marbles are in the bag?
Options:
A)24
B)48
C)60
D)96
E)84
Rationale: ok let me see if i can explain what went on in the previous post
lets say i have x marbles in the bag in total --> out of them 12 are red
so the probability of pulling a non-red marble is (x -12) / x
now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x
probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n
so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]
this is given as 49/64
-->(x-12)^2= 49/64
x^2
square rooting u have x-12/x = 7/8 or x = 96
D
Answer: D
Question: What least number must be added to 9599, so that the sum is completely divisible by 100 ?
Options:
A)1
B)2
C)4
D)6
E)8
Rationale: If we divide 9599 by 100 remainder is 99
100-99 =1
Answer : A
Answer: A
Question: A can do a piece of work in 8 days. B can do it in 12 days. With the assistance of C they completed the work in 4 days. Find in how many days can C alone do it?
Options:
A)87 days
B)20 days
C)16 days
D)24 days
E)36 days
Rationale: C = 1/4 - 1/8 - 1/12 = 1/24
=> 24 days
Answer:D
Answer: D
Question: The speed at which a boy can row a boat in still water is 60 kmph. If he rows downstream, where the speed of current is 12 kmph, what time will he take to cover 220 metres?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Speed of the boat downstream = 60 + 12 = 72 kmph
= 72 * 5/18 = 20 m/s
Hence time taken to cover 220 m = 220/20 = 11 seconds. Answer: E
Answer: E
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 50% while buying and by 10% while selling. What is his percentage profit?
Options:
A)10.22%
B)20.22%
C)21.22%
D)50%
E)Can't be calculated
Rationale: The owner buys 100kg but actually gets 150kg;
The owner sells 100kg but actually gives 90kg;
Profit: (150-90)/90*100=50%
Answer: D.
Answer: D
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)65 sec
C)18 sec
D)16 sec
E)17 sec
Rationale: Speed = 45 * 5/18
= 25/2 m/sec
Total distance covered
= 360 + 140
= 500 m
Required time = 500 * 2/25
= 40 sec
Answer:A
Answer: A
Question: Find the fourth proportional to 4, 9, 12
Options:
A)17
B)37
C)47
D)67
E)27
Rationale: Let the fourth proportional to 4, 9, 12 be x.
Then, 4 : 9 : : 12 : x
=4 x x=9x12
=X=(9 x 12)/14=27;
Fourth proportional to 4, 9, 12 is 27.
Answer is E
Answer: E
Question: After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 75%?
M13-03.
Options:
A)N−35
B)N+72
C)2N+78
D)2N+72
E)2N−35
Rationale: Say N=1.
So, after 1 test John has 70 correct answers.
In 2 tests, so in 200 questions he needs to have 0.75*200=150 correct answers, so in the second test he must get 150-70=80 questions correctly.
Now, plug N=1 into the answer choices to see which one yields 80. Only option D fits.
Answer: C.
Answer: C
Question: If X,Y is 15%,30% smaller than Z then how much percentage is Y greater than X?
Options:
A)12 1/2 %
B)13%
C)13 1/2%
D)14%
E)17 11/17%
Rationale: X = 85 %
Y = 70 %
Z = 100 %
X-Y/X × 100 = 5/85× 100 = 17 11/17 % greater than X
E
Answer: E
Question: What is the greatest power that 3 can be raised to so that the resulting number is a factor of 9!?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: the number of 3s in 9!= 9/3=3..
ans B
Answer: B
Question: In the faculty of Reverse-Engineering, 350 second year students study numeric methods, 250 second year students study automatic control of airborne vehicles and 100 second year students study them both. How many students are there in the faculty if the second year students are approximately 25% of the total?
Options:
A)1800
B)1900
C)2100
D)2000
E)2200
Rationale: Total number of students studying both are 350 + 250 - 100 = 500 (Subtracting the 100 since they were included in the both the other numbers already).
So 25% of total is 500, so 100% is 2000
Answer is D
Answer: D
Question: The bus fare for two persons for travelling between Agra and Aligarh id four-thirds the train fare between the same places for one person. The total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is Rs.1512. Find the train fare between the two places for one person?
Options:
A)Rs.126
B)Rs.132
C)Rs.120
D)Rs.114
E)None of these
Rationale: Let the train fare between the two places for one person be Rs.t
Bus fare between the two places for two persons Rs.4/3 t
=> 6/2 (4/3 t) + 8(t) = 1512
=> 12t = 1512 => t = 126.
ANSWER:A
Answer: A
Question: 66% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 53% of respondents did not use M. 47% used N. What percent of respondents used only N?
Options:
A)19.5%
B)21.5%
C)20%
D)18.5%
E)17%
Rationale: From the question, we can summarize the information as follows:
N Not N
M X
Not M Ans y 53
47 100
Then we can set a system of 3 equations 3 unknowns described below:
X + Y = 66
X + Ans = 47
Y + Ans = 53
Sum up all three equations to get 2X + 2Y + 2Ans = 166
Divide both sides by 2 to get X + Y + Ans = 83
Replace X + Y with 66 to get 66 + Ans = 83
Substract 66 from both sides to get Ans = 83 - 66 = 17
The answer must be E.
Answer: E
Question: A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.600 more. What was the Sum?
Options:
A)1200
B)2877
C)2779
D)1770
E)1887
Rationale: Explanation:
At 5% more rate, the increase in S.I for 10 years = Rs.600 (given)
So, at 5% more rate, the increase in SI for 1 year = 600/10 = Rs.60/-
i.e. Rs.60 is 5% of the invested sum
So, 1% of the invested sum = 60/5
Therefore, the invested sum = 60 × 100/5 = Rs.1200
Answer: A) Rs.1200
Answer: A
Question: A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work?
Options:
A)14
B)8
C)20
D)10
E)7
Rationale: Option D
Explanation:
Let A worked for x days.
x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18
A worked for 18 days. So, A can complete the remaining work in 18 - 4 = 14 days.
Answer: A
Question: If a and b are the two values of t that satisfy
the equation t^2 â€“ 7t + 10 = 0, with a > b, what is the value of a â€“ b?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Factor the left side of the equation:
t^2 â€“ 7t + 10 = 0
(t â€“ 2)(t â€“ 5) = 0
t = 2, t = 5
Thus, a = 5 and b = 2. So a â€“ b = 5 â€“ 2 = 3.
The answer is B.
Answer: B
Question: If 6 Men or 7 Women take 6 days to complete some work, how many days will 10 Men and 6 Women working together take to complete the work?
Can anyone explain please?
Options:
A)1. 3/2 days
B)2. 2 Days
C)3. 9/4 days
D)4.5/2 days
E)5.126/53 days
Rationale: 6 men or 7 women takes 6 days to complete the work
So 6M = 7W
W = 6/7M
1 man in 1 day does 1 unit of work
so 6 M in 6 M = 36 units of work
now 10 M and 6 W = 10 M + 6(6/7)M
= 10M + 36M/7
= 106M/7
Since both set do the same work
106M/7 in n Days = 36 units of work
n = 36 *7/106 = 126/53 days.
E
Answer: E
Question: A train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)328
B)279
C)270
D)288
E)231
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 38 = 15
x + 300 = 570
x = 270 m. Answer:C
Answer: C
Question: Raman mixed 24 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)228
B)2767
C)189
D)266
E)211
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer: C
Answer: C
Question: In how many Q ways can 5 people from a group of 6 people be seated around a circular table
Options:
A)56
B)80
C)100
D)120
E)144
Rationale: Q=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner)
= 6 * 4!
= 6 * 24
= 144
Answer - E
Answer: E
Question: At the end of the month, a certain ocean desalination plant’s reservoir contained 40 million gallons of water. This amount is one fifth of the normal level. If this amount represents 80% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: the Q talks of total capacity, normal level, present level, shortage etc..
so it is all about not going wrong in these terms
40 MG= 80% of Total..
total = 40/.8=50MG..
Normal level= 1/5 of 50=10MG..
shortage of normal level=50-10=40MG..
C
Answer: C
Question: Find a sum for first 5 prime number'ss?
Options:
A)25
B)28
C)30
D)35
E)36
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Answer: B
Question: A motor pool has 300 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 30 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
Options:
A)165%
B)90%
C)65%
D)55%
E)60%
Rationale: Trucks = 30% of 300 = 90
Other Vehicles (Excluding Trucks) = 300-90 = 210
Diesel Vehicle = 20% of 300 = 60 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 60-30 = 30
Trucks that are NOT diesel = 90 - 30 = 60
Other Vehicles that are NOT diesel Vehicles = 210-30 = 180
Required % = (180/300)*100 = 60%
Answer: option E
Answer: E
Question: A man is 29 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options:
A)14 years
B)18 years
C)20 years
D)27 years
E)16 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 29) + 2 = 2(x + 2)
x + 31 = 2x + 4
x = 27.
answer :D
Answer: D
Question: A can fill tank in 9 minutes, B can empty the tank in 18 minutes.. In what time the tank be filled, if both pipes work simultaneously?
Options:
A)14 minutes
B)15 minutes
C)16 minutes
D)17 minutes
E)18 minutes
Rationale: Bigger no=18, Ratio=9:18=1:2
Time taken to fill the tank = 18/(2 - 1)
= 18 minutes
ANSWER:E
Answer: E
Question: If (a-3)(b-2) =0, which of the following must be true ?
I. a=3 and b=2
II. if a is not = 3, then b=2
III. if a=3, then b is not=2
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: (a-3)(b-2)=0
So either a=3 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.
The answer is B.
Answer: B
Question: A man's speed with the current is 20 kmph and speed of the current is 1 kmph. The Man's speed
against the current will be
Options:
A)11 kmph
B)12 kmph
C)18 kmph
D)17 kmph
E)None of these
Rationale: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 1 = 19
Now speed against the current will be
speed of the man - speed of the current
= 19 - 1 = 18 kmph
Answer: C
Answer: C
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 69. What is that number
Options:
A)7
B)10
C)12
D)14
E)15
Rationale: Explanation:
=> 3(2x+9) = 69
=> 2x+9 = 23
=> x = 7
Answer: Option A
Answer: A
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)187 sec
B)190 sec
C)278 sec
D)268 sec
E)987 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50
= 200 sec.
Time taken by A = 200 - 10
=190 sec.
Answer: B
Answer: B
Question: If A and B are two events such that P (A) = 2/4, P (B) = 1/2 and P (A n B) = 3/8,
find P (not A and not B).
Options:
A)A)2/8
B)B)3/8
C)C)4/8
D)D)5/13
E)E)6/8
Rationale: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (2/4 + 1/2 - 3/8)
P(not A and not B) = 1 - (5/8)
P(not A and not B) = 3/8.
B
Answer: B
Question: What is the probability of getting a sum 9 from two throws of a dice?
Options:
A)1/6
B)1/8
C)1/9
D)1/12
E)1/5
Rationale: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =	n(E)/n(S)	=	4/36	=	1/9	.
Answer :C
Answer: C
Question: M is 25% of N. M is also 75% of D. D is 95% of L. How are N and L related?
Options:
A)180%
B)200%
C)300%
D)285%
E)231%
Rationale: If...
M=.25N
M=.75D
D=.95L
Then...
.25N=.75D
Divide both sides by .75
.33N=D
.33N=.95L
Divide both sides by .33
N=2.85L
N is 285% of L
The answer is D
Answer: D
Question: If 4 women can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in?
Options:
A)day
B)day
C)days
D)days
E)days
Rationale: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.
B)
Answer: B
Question: In how many ways can the letters of the word REPORT be arranged?
Options:
A)1206
B)360
C)2520
D)3000
E)3478
Rationale: REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways
B
Answer: B
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
Options:
A)12 1/2 days
B)12 1/8 days
C)12 1/2 days
D)22 1/2 days
E)12 6/2 days
Rationale: 15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer:A
Answer: A
Question: x = y - (5/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
Options:
A)decrease
B)stay the same
C)increase four fold
D)doubles
E)triples
Rationale: Alternate approach
Plug in some values of y > 0
Let y = 10
So, x = y - (5/y)
Or, x = 10 - (5/10) =9.5
Let y = 20
So, x = y - (5/y)
Or, x = 20 - (5/20) =19.75
So, x increases from 9.5 to 19.75
Hence the number increases 2 times, thus the correct answer will be (D)
Answer: D
Question: Which expression is the greatest
Options:
A)3252/3257
B)3456/3461
C)3591/3596
D)3846/3951
E)3453/3458
Rationale: Options can be re-written as (x-5)x => 1-(5/x)
A) 1- (5/3257)
B) 1- (5/3461)
C) 1- (5/3596)
D) 1- (5/3951)
E) 1- (5/3458)
To get the largest among these second half should be the least and so denominator to be largest. Hence 'D'.
Answer: D
Question: A student needs 60% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 100 marks, find the maximum marks set for the test.
Options:
A)250
B)300
C)350
D)400
E)450
Rationale: 60% = 180 marks
1% = 3 marks
100% = 300 marks
The answer is B.
Answer: B
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
Options:
A)1 hour
B)2 hours
C)3 hours
D)4 hours
E)5 hours
Rationale: Let the duration of the flight be x hours
600/x - 600 (x+1/2)= 200
600/x - 1200/(2x+1) = 200
x(2x + 1) = 3
2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x can't be negative hence x=1
x = 1 hr.
Duration =1 hr
ANSWER:A
Answer: A
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 78000, then the share of B is?
Options:
A)33888
B)24000
C)27778
D)27772
E)36000
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 78000
Share of B = 6/13 (78000) = Rs. 36000
Answer: E
Answer: E
Question: Working together, Jose and Jane can complete an assigned task in 10 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 25 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose
Options:
A)25 days
B)30 days
C)60 days
D)65 days
E)36 days
Rationale: Assume:
Jose does 1 job in x days, so Jose does 1/x job in a day
Jane does 1 job in y days, so Jane does 1/y job in a day
Together, they does (x+y)/xy job in a day. This is equals to 1/20. So
(x+y)/xy = 1/10
10(x+y) = xy
Next, we're told 1 job takes 25 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.
x/2 + y/2 = 25
x+y = 50
So
xy = 500
The answer choices are:
25 days
30 days
60 days
65 days
36 days
From the answer choices, So I'll go for 25 days for Jose and 20 days for Jane.
Answer : A
Answer: A
Question: Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point?
Options:
A)5km north east
B)4km north east
C)5km north west
D)6km north east
E)6km north west
Rationale: she is currently at 5km north east from the starting point
ANSWER:A
Answer: A
Question: A train speeds past a pole in 15 sec and a platform 150 m long in 25 sec, its length is?
Options:
A)50 m
B)150 m
C)225 m
D)300 m
E)None of these
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 150)/25 = x/15 => x = 225 m.
ANSWER:C
Answer: C
Question: Carol spends 1/4 of her savings on a stereo and 1/5 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?
Options:
A)1/4
B)2/7
C)5/12
D)9/20
E)7/12
Rationale: Total Savings = S
Amount spent on stereo = (1/4)S
Amount spent on television = (1-1/5)(1/4)S = (4/5)*(1/4)*S = (1/5)S
(Stereo + TV)/Total Savings = S(1/4 + 1/5)/S = 9/20
Answer: D
Answer: D
Question: there are 35 student in a school. 20 if them speek hindi 19 of them speak eng 9 of them speak both , then how many student neithe speak eng nor speak hindi
Options:
A)28
B)30
C)32
D)35
E)None of these
Rationale: Total Number of Students = 35
No of Hindi Speaking Students (H) = 20
No of English Speaking Students (E) = 19
H intersection E = 9
thus H union E = 20 + 19 - 9 = 30
thus Number of student neithe speak eng nor speak hindi = 35 - 30 = 5
ANSWER:E
Answer: E
Question: A and B can finish a work in 7 days and 8 days respectively.if both do work one day and leave one day.and A start the work then in how much days work will finish?
Options:
A)52/7
B)8
C)14/2
D)6
E)43/6
Rationale: (A+B) work in 2 days=[1/7+1/8]=15/56
(A+B) work in 6 days=45/56
now,the turn of A,work of A in 1 day=1/7.
till now completed work=[45/56+1/7]=53/56, remaining work=[1-53/56]=3/56
now,turn of B,1/8 work B do in 1 day
so,3/56 part of work B do=[8*3/56]=3/7 days
total time taken=6+1+3/7=52/7 days
answer A
Answer: A
Question: If a man travels f miles an hour for t hours and r miles an hour for k hours, what is his average rate in miles per hour for the entire distance traveled?
Options:
A)ft + rk
B)(ft + rk)/2
C)t/f + k/r
D)(ft + rk)/(t + k)
E)(ft + rk)/(t - k)
Rationale: Average Speed = Total Distance /Total Time Taken
Total Distance travelled in t hours = ft
Total Distance travelled in s hours = rk
Total Time taken = t+k
Therefore , Average Speed = (ft+tk)/(t+k)
Answer D
Answer: D
Question: The jogging track in a sports complex is 561 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
Options:
A)5.29 min
B)5.28 min
C)4.08 min
D)9.28 min
E)5.988 min
Rationale: Clearly, the two will meet when they are 561 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 561 m apart, they take (100/825 * 561/1000) hrs = (561/8250 * 60) min = 4.08 min.
Answer: C
Answer: C
Question: I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation T in which of the following?
Options:
A) I, III, II
B) II, I, III
C) II, III, I
D) III, I, II
E) III, II, I
Rationale: Range of 1st Set = (p-j)
Range of 2nd Set = P+15 - j +10 = (p-j) +25
Range of 3rd Set = P -2 - j - 2 = (p-j) - 4
R2 > R1 > R3 ==> SD2 > SD1 > SD3
Since,T= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B
Answer: B
Question: If 6!/3^x is an integer, what is the greatest possible value of x?
Options:
A)2
B)4
C)5
D)6
E)7
Rationale: 6 - 2*3
3 - 1*3
Hence max of 3^2 is allowed. IMO A.
Answer: A
Question: A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 4 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)42
B)70
C)175
D)165
E)315
Rationale: 5C1*7C4 = 5*35 = 175
the answer is (C)
Answer: C
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.25 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 30 worth of diesel fuel?
Options:
A)20 seconds
B)1 minute
C)1 minute 20 seconds
D)20 minutes
E)1 hour 20 minutes
Rationale: 2 gal / 5 sec
$1.25 / gal
$30/$1.25 = 24 gal
2 gal / 5 sec with 24 gal = 60 sec
B. 1 minute
Answer: B
Question: In how many ways can the letters of the word LITTER be arranged in a row so that the vowels appear in alphabetic order?
Options:
A)390
B)400
C)440
D)360
E)460
Rationale: TWO letters can be arranged in 2! ways.
only one combination EI is required.
6 letters can be arranged in 6! ways.
thus 6!/ 2! * 1 = 360
D
Answer: D
Question: what is the remainder when 9614241 is divided by 99
Options:
A)50
B)65
C)45
D)54
E)60
Rationale: 9614241 / 99
9614241 / 9*11
1068249 / 11 => rem = 6
we have cancelled it by 9
reqd remainder = 9*6 = 54
ANSWER:D
Answer: D
Question: Alfred buys an old scooter for $4700 and spends $800 on its repairs. If he sells the scooter for $6400, his gain percent is?
Options:
A)5.45%
B)16.36%
C)7%
D)8.12%
E)10%
Rationale: C.P. = 4700+800 = $5500
S.P. = $6400
Gain = 6400-5500 = $900
Gain% = 900/5500 * 100 = 16.36%
Answer is B
Answer: B
Question: n a series of numbers , the next number is formed by adding 1 to the sum of the previous numbers, and the 10th number is 1280. Then what is the first number in the series? (series will be like this x , x+1, (x+(x+1))+1,....... )
Options:
A)2
B)4
C)5
D)7
E)9
Rationale: Answer: Option B
Sol.
The given series is x, x + 1, 2x + 2, 4x + 4 ......
If you observe the pattern here, the coefficient of x + 1 is in the powers of 2. So 4th term has a power of 2, 5th term has a power of 3... 10th term has a power of 8. So tenth term would be 2828(x + 1)
= 256(x+1).
Given 256(x+1) = 1280
x = 4.
Answer:B
Answer: B