divelab/Sys2Bench huggingface dataset:
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
Options:
A)35
B)36
C)37
D)43
E)39
Rationale: James worked for 41 hours hence he earned 40*x+5*2x=50x dollars;
We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours.
Answer: D.
Answer: D
Question: 64 + 5 * 12 / (180/3) = ?
Options:
A)22
B)77
C)29
D)65
E)21
Rationale: 64 + 5 * 12 / (180/3) = 64 + 5 * 12 / (60)
= 64 + (5 * 12)/60 = 64 + 1 = 65.Answer:D
Answer: D
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
Options:
A)15 days
B)13 days
C)12 days
D)11 days
E)18 days
Rationale: D
(5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
Question: Of 70 players on a football team, 43 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)54
B)59
C)63
D)61
E)92
Rationale: Total = 70
Thrower = 43
Rest = 70 - 43 = 27
Left Handed = 27/3 = 9
Right handed = 18
If all Thrower are right handed then total right handed is 43 + 18 = 61
so D. 61 is the right answer
Answer: D
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)132 km
B)167 km
C)143 km
D)162 km
E)245 km
Rationale: D
12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: D
Question: The ratio of 2 numbers is 10:20 and their H.C.F. is 100. Their L.C.M. is ?
Options:
A)1100
B)3000
C)2100
D)1000
E)2000
Rationale: Let the numbers be 10x and 20x
Their H.C.F. = 100
so the numbers are 10*100 , 20*100 = 1000, 2000 L.C.M =2000
Answer is E
Answer: E
Question: X is able to do a piece of work in 8 days and Y can do the same work in 12 days. If they can work together for 3 days, what is the fraction of work left?
Options:
A)8/5
B)6/5
C)7/5
D)3/5
E)4/5
Rationale: Explanation :
Amount of work X can do in 1 day = 1/8
Amount of work Y can do in 1 day = 1/12
Amount of work X and Y can do in 1 day = 1/8+ 1/12= 5/24
Amount of work X and Y can together do in 3 days = 3 × (5/24) = 5/8
Fraction of work left = 1 – 5/8= 3/5
Answer : Option D
Answer: D
Question: If 0 < P < Y, P is an odd number and Y is a prime number, which of the following can be the value of P + Y ?
Options:
A)11.
B)13.
C)17.
D)10.
E)7.
Rationale: If P is odd ,implies p(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2p=1 since 0<P<Y therefore P+Y =3. But 3 is not an option
which implies y is odd,
Now P(odd)+Y(odd)=Even
10 is the only option that is even=D
Answer: D
Question: A car during its journey travels 30 minutes at a speed of 60 kmph, another 45 minutes at a speed of 80 kmph, and 1 hours at a speed of 70 kmph.The average speed of the car is
Options:
A)63.07 kmph
B)64 kmph
C)75 kmph
D)80 kmph
E)None of these
Rationale: First car travels 30 min at speed of 60 kmph
distance = 60 x 1/2 = 30 m
Then car travels 45 min at a speed of 80 kmph
distance = 45 min at speed of 80 kmph
distance = 80 x 3/4 = 60 m
at last it travels 1 hours at speed of 70 kmph
distance = 70 x 1 = 70 m
Total distance = 30 + 80 + 70= 180
Total time= 1/2 + 3/4 + 1 = 2.25
Average speed of the car = 180/2.25 = 80
ANSWER:D
Answer: D
Question: What should come in place of the question mark (?) in the following number series?
11 20 31 44 59 ?
Options:
A)75
B)76
C)77
D)78
E)79
Rationale: The numbers increase by 9, 11, 13, 15,...
The next number should be 59+17 = 76
The answer is B.
Answer: B
Question: Given that there are 5 basketball players per team, how many ways can you select 3 basketball players from 4 teams if no more than one player can be selected from each team?
Options:
A) 15
B) 30
C) 60
D) 75
E) 100
Rationale: 3 teams can be selected from 3 teams in 4C3 ways = 4 ways
as the condition is that the 3 players should be from different teams
one player can be chosen from 1st team in 5 ways
similarly another player can be chosen from 2nd team in 5 ways
Total number of ways to choose the player = 5 * 5 * 4 = 100 ways
Correct Answer - E
Answer: E
Question: The ratio of 7 seconds to 5 hours
Options:
A)1:80
B)1:3600
C)1:600
D)1:400
E)1:500
Rationale: 1 hour =3600 sec
then 7 hours =7*3600=25200
so ,7:25200=1:3600
ANSWER:B
Answer: B
Question: The average of 6 quantities is 8. The average of 4 of them is 5. What is the avg. of the remaining 2 numbers?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Sum of 8 quantities = Total No of quantities X Average of them
= 6 X 8 = 48
Sum of 4 quantities = 4 X 5 = 20
Sum of 4 Quantities + Sum of 2 Quantities = Sum of 6 Quantities
20 + Sum of 2 Quantities = 48
Sum of 2 Quantities = 28
Average of 2 Quantities = Sum of 2 Quantities / 2
= 28/2 = 14
ANSWER:D
Answer: D
Question: A pair of prime numbers that can be expressed in the form R{p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT
Options:
A) 11
B) 13
C) 17
D) 19
E) 23
Rationale: definetly a sitter.plug in the values for middle term and calculate.We can see clearly that R for 19 , 19+6 gives 25 which is not a prime
therefore correct answer D
Answer: D
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.24000, my total savings for the two-year is
Options:
A)s. 8000
B)s. 7000
C)s. 9900
D)s. 9990
E)s. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (24000 + 35000)
= 66000 - 59000 = Rs. 7000
B
Answer: B
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability W that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
Options:
A)15/64
B)30/64
C)1/2
D)1/4
E)52/64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days W= 15/64
Ans A it is.
Answer: A
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 54, the dividend is:
Options:
A)6324
B)7344
C)8336
D)9356
E)9400
Rationale: Divisor = (5 * 54) = 270
= 10 * Quotient = Divisor
=> Quotient = 270/10 = 27
Dividend = (Divisor * Quotient) + Remainder
Dividend = (270 * 27) + 54 = 7344.
B
Answer: B
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 120 sandwiches were made, how many bologna sandwiches
were made?
Options:
A)15
B)30
C)38
D)42
E)48
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
120 / 20 = 6 sandwiches in one part
For bologna we have 7 parts so:
7 * 6 = 42
Answer is D
Answer: D
Question: Two trains, A and B, started simultaneously from opposite ends of a 200-mile route and traveled toward each other on parallel tracks. Train A, traveling at a constant rate, completed the 200-mile trip in 10 hours; Train B, traveling at a constant rate, completed the 200-mile trip in 6 hours. How many miles had train A traveled when it met train B?
Options:
A) 70
B) 75
C) 87.5
D) 90
E) 92.5
Rationale: As the ratio of the rates of A and B is 6 to 10 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that A would cover 6/(6+10)=6/16 of 200 miles: 200*6/16=75 miles.
Answer: B.
Answer: B
Question: What should come in place of the question-mark (?) in the following number series?
5690, 5121, 4552, 3983, 3414, 2845, ?
Options:
A)278
B)279
C)569
D)127
E)199
Rationale: Sol:
The difference of the numbers in the series is same i.e 569.
5690 – 5121 = 569
5121 – 4552 = 569
4552 – 3983 = 569
3983 – 3414 = 569
3414 – 2845 = 569
So
2845 – 2276 = 569
Answer:C
Answer: C
Question: A thief goes away with a SANTRO car at a speed of 45 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
Options:
A)A)2
B)B)4
C)C)7
D)D)5
E)E)8
Rationale: Explanation:
|-----------20--------------------|
50 45
D = 20
RS = 50 – 45 = 5
T = 20/5 = 4 hours
Answer: Option B
Answer: B
Question: A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 14 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
Options:
A)$2,240
B)$2,120
C)$1,960
D)$1,920
E)$1,400
Rationale: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 14: x+x-2=14 --> x=8: 8 $20 chips were lost and 8-2=6 $100 chips were lost.
Total worth of chips lost is 8*20+6*100=$760, so the gambler kept $3,000-$760=$2,240.
Answer: A.
Answer: A
Question: A bag contains a total of 93 coins in the form of one rupee and 50 paise coins. If the total value of coins in the bag is Rs.56, find the number of 50 paise coins in the bag?
Options:
A)22
B)11
C)27
D)74
E)28
Rationale: Explanation:
Let the number of one rupee coins in the bag be x.
Number of 50 paise coins in the bag is 93 - x.
Total value of coins
[100x + 50(93 - x)]paise = 5600 paise
=> x = 74
Answer: D
Answer: D
Question: 0.35 represents what percent of 0.07?
Options:
A)0.05%
B)0.5%
C)5%
D)500%
E)5000%
Rationale: One more method
0.35 represents what percent of 0.07?
Adjusting the decimal
35 represents what percent of 7?
Divide by 7
5 represents what percent of 1?
Answer = 5*100 = 500% = D
Answer: D
Question: How must a grocer mix 4 types of peanuts worth 54 c, 72 c, $1.2 and $1.44 per pound so as to obtain a mixture at 96 cents per pound?
Options:
A)8:4:4:7
B)24:12:12:50
C)4:8:7:4
D)16:42:28:10
E)Cannot be uniquely determined
Rationale: As we know Sum of (Respective Quantity x Respective Price) = Total Price = Average price x Total Quantity
Option 1
Ratio of quantity mixed - 8a:4a:4a:7a
Total quantity = 23a parts (8+4+4+7)
(8a.9 + 4a.12 + 4a.20 + 7a.24) = 16.23a
368a = 368a
LHS = RHS
Thus option 1 satisfy the condition
Option 2
Ratio of quantity mixed - 24a:12a:12a:50a or 12a:6a:6a:25a
Total quantity = 49a parts
(12a.9 + 6a.12 + 6a.20 + 25a.24) = 16.49a
900a = 784a
LHS is not equal to RHS
Thus option 2 does not satisfy the condition
Option 3
Ratio of quantity mixed - 4a:8a:7a:4a
Total quantity = 23a parts
(4a.9 + 8a.12 + 7a.20 + 4a.24) = 16.23a
368a = 368a
LHS = RHS
Thus option 3 satisfy the condition
As we are asked a unique case, a problem can't have two solutions. Thus answer is it Cannot be uniquely determined
Answer E
Answer: E
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 2 hours; pumps A and C, operating simultaneously, can fill the tank in 1 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
Options:
A)1/3
B)1/2
C)1/4
D)5/2
E)5/6
Rationale: A+B =2; A+C =1 ,B+C =2 ; ADD THEN 2*(A+B+C) = 5
A+B+C = 5/2 HRS
D
Answer: D
Question: In a class of 87 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
Options:
A)6
B)15
C)24
D)33
E)54
Rationale: Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total
so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 87
54 + NOT = 87
NOT = 87 - 54 = 33
So answer is D
Answer: D
Question: The difference between simple interest and compound interest on Rs.1200 for one year at 10% per annum reckoned half-yearly is :
Options:
A)Rs.2.50
B)Rs.3
C)Rs.3.75
D)Rs.4
E)Rs.5
Rationale: S.I = (1000 *10 *4)/100 = Rs.400
C .I =1200 *1+5/100)2 –1200 = 123.
Difference = Rs.(123-120) = Rs.3
ANSWER:B
Answer: B
Question: You collect balls. Suppose you start out with 105. John gives you another 100 balls. How many balls do you have at the end?
Options:
A)205
B)105
C)100
D)502
E)501
Rationale: Solution
Start with 105 balls.
John gives you 100 balls: 105 + 100 = 205 balls.
So you have 205 balls at the end.
Correct answer: A
Answer: A
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If three minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
Options:
A)12
B)24
C)36
D)60
E)72
Rationale: the difference of the speed is 1m per second so in three minute Sacha will be 180 m ahead of Bruno..
Bruno will cover this in 180/5=36 secs..
C
Answer: C
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.7 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
Options:
A)24 years
B)44 years
C)34 years
D)64 years
E)84 years
Rationale: If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 7 = 11
4A + 7 = 9
9(5A + 7)=11(4A + 7)
A = 14
Thomasâ€™s current age = 4A
= 64 years.
D
Answer: D
Question: Which of the following fractions can be written as the difference of reciprocals of two consecutive integers
Options:
A)1/24
B)7/30
C)1/30
D)13/56
E)1/73
Rationale: Difference of reciprocals means 1 has to be in the numerator;
So option BD can be ignored
For option A, BE, we require to search two consecutive numbers whose product is the denominator
24 = 4 * 6 ......... Ignore
30 = 5 * 6 ........ Answer
73 = 7 * 9 ................ Ignore
Answer = C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 36 seconds. Find the length of the train?
Options:
A)150 meter
B)600 meter
C)167 meter
D)719 meter
E)169 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 36
= 600 meter
Answer: B
Answer: B
Question: A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 150 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
Options:
A)1.5
B)2.5
C)3.5
D)4.5
E)5.5
Rationale: The distance between the nest and the ditch is 150 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 150 = 4500.
D = ST
4500/1.5 = T , I think we can take 4500 meters as 4.5 km, then only we get T = 4.5.( 1000 meters = 1 km)
D)
Answer: D
Question: Pipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)2.5
C)3
D)3.5
E)4
Rationale: The part filled by A + B + C in 1 hour is 1/6 + 1/8 + 1/24 = 1/3
All the three pipes together will fill the tank in 3 hours.
The answer is C.
Answer: C
Question: To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 9 hours a day?
Options:
A)34
B)36
C)32
D)40
E)44
Rationale: Man-hours required to asphalt 1 km road=30*12*8=2880
Man-hours required to asphalt 2 km road=2880*2=5760
Man-hours available per day=20*9=180
Therefore number of days=5760/180=32 days
Ans=C
Answer: C
Question: A single discount equal to a discount series of 10% and 20% is
Options:
A)25%
B)28%
C)30%
D)35%
E)None of these
Rationale: Equivalent discount = 10 + 20 - 10×20/100
= 30 – 2 = 28%
Answer B
Answer: B
Question: At the college entrance exam, a candidate is admitted according to whether he has passed or failed the test. Of the candidates who are really capable, 80 % pass the test and of the incapable, 25 % pass the test.Given that 40 % of the candidates are really capable, then the proportion of the really capable students who can pass the test to the total students who can pass is about?
Options:
A)30/47
B)32/47
C)34/47
D)36/47
E)38/47
Rationale: If there are total 100 candidates, 40 candidates are really capable and 60 candidates are incapable.Of the candidates who are really capable, 32 pass the test and of the incapable, 15 pass the test.
Total candidates who passed the test = 32+15=47
the proportion of the really capable students who can pass the test to the total students who can pass = 32/47
ANSWER:B
Answer: B
Question: 14! is equal to which of the following?
Options:
A)87,178,291,200
B)88,180,293,207
C)89,181,294,209
D)90,000,000,003
E)91,114,114,114
Rationale: after 4!, every factorial last digit ends in 0.
5!=120
6!=720.
so only option A last digit ends with 0.
So option A is correct.
Answer: A
Question: The bus fare for the first mile is $1,5 and then fare for each additional mile costs 35 cents. What is the maximum distance that you can travel by bus if you paid $5 ?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: b is the number of miles at a price of $0,35/mile
1,5 + 0,35b = 5
35b = 500 - 150
b=10
The maximum distance to be traveled --> 1 +10 = 11 miles
ANSWER: B
Answer: B
Question: A man walking at a rate of 10km/hr crosses a bridge in 18 minutes. The length of the bridge is?
Options:
A)1521
B)3000
C)1667
D)1254
E)1112
Rationale: Speed = 10*5/18 = 50/18 m/sec
Distance covered in 10minutes = 50/18 *18 *60 = 3000 m
Answer is B
Answer: B
Question: A coin is tossed 7 times. What is the probability of getting exactly 6 heads?
Options:
A)7/32
B)3/64
C)5/64
D)3/128
E)7/128
Rationale: The number of possible outcomes is 2^7 = 128
There are 7 ways to get exactly 6 heads.
P(exactly 6 heads) = 7/128
The answer is E.
Answer: E
Question: In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction E of all babies born who were NOT part of a set of twins or triplets?
Options:
A)z - 2x - 3y
B)(2x+3y)/z
C)(x+y)/z
D)1 - (2x+3y)/z
E)1 - (x+y)/z
Rationale: X set of twins implies 2x babies of twin category.
Y set of triplets means 3y babies of triplet category.
Let K be the babies other than twin or triplet category.
Total babies = z = 2x+3y+k.
or K=Z-(2x+3y)
=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.
E= 1- (2x+3y)/Z. Hence answer is D.
Answer: D
Question: In a recent head-to-head run-off election, 10,000 absentee ballets were cast. 2/3 of the absentee ballets were thrown out and 2/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?
Options:
A)2,000
B)3,000
C)6,000
D)8,000
E)9,000
Rationale: 1/3 * 3/5 (total absentee votes) = 1/5 (total votes)=1/5*10000=2000
Answer is A
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)388
B)2769
C)177
D)150
E)821
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer: D
Answer: D
Question: If a and n are integers, and a^2 = 24n, then n must be divisible by which of the following?
Options:
A)2
B)4
C)12
D)18
E)24
Rationale: a^2=24n
a^2=2^2∗6n
Least value of n to make "a" a perfect square is 6
Answer = A = 2
Answer: A
Question: If 5 persons can do 5 times of a particular work in 5 days, then, 7 persons can do 7 times of that work in
?
Options:
A)3 days
B)7 days
C)5 days
D)11 days
E)15 days
Rationale: That is, 1 person can do one time of the work in 5 days.
Therefore, 7 persons can do 7 times work in the same 5 days itself.
Option 'C'
Answer: C
Question: Ratio of the ages of Mahesh and Nilesh is 5:x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
Options:
A)14.5
B)14.1
C)14.2
D)14.8
E)14.5
Rationale: Let the present ages of Mahesh, Nilesh and Ramesh be M, N and R respectively.
M/N = 5/x --- (1)
M = R - 18 --- (2)
R + 9 = 47 --- (3)
M - N = R --- (4)
(3) => R = 47 - 9 = 38 years
(2) => M = 38 - 18 = 20 years
(1) => 20/N = 5/x => N = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5
Answer:E
Answer: E
Question: Look at this series: 15, 15, 27, 27, 39, 39, 51, 51, 63, 63, ? ... What number should fill the blank?
Options:
A)51
B)39
C)75
D)15
E)None
Rationale: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option C
Answer: C
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder Q when N is divided by 30?
Options:
A)(a) 4
B)(b) 7
C)(c) 11
D)(d) 13
E)(e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder Q when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: C
Question: In the list 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?
Options:
A)2/9
B)1/8
C)2/5
D)2/3
E)7/9
Rationale: Mode: The mode of any set is the term which has the highest frequency (Occurrence)
Highest frequent term in the set is 5 (with frequency 4) hence
Mode = 5
ONE term (4) out of a total of 8 terms are less than mode of the set.
Fraction of set that are less than Mode of set = 1/8
Answer: Option B
Answer: B
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Options:
A)3 1/89%
B)3 7/3%
C)3 1/3%
D)2 1/3%
E)3 5/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Options:
A)6/63
B)2/63
C)125/126
D)1/126
E)1/63
Rationale: Required probability = 1 - 1/126 = 125/126
ANSWER:C
Answer: C
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 14 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
Options:
A)6
B)16
C)20
D)30
E)174
Rationale: The number of integers that belong to set X ONLY is 14-6=8;
The number of integers that belong to set Y ONLY is 18-6=12;
The number of integers that belong to set X or set Y, but not both is 8+12=20.
Answer: C.
Answer: C