divelab/Sys2Bench huggingface dataset:
Question: If there are 200 questions in a 3 hr examination. Among these questions are 10 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
Options:
A)17.14286 min
B)62 min
C)70.1346 min
D)74 min
E)76.1346 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
190x+10*2x=180
x=180/210
x=0.72
time taken for type A problem=10*2*0.857143=17.14286min
ANSWER:A
Answer: A
Question: Seven cards numbered from 1 to 7 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 9, what is the probability that one of the two cards drawn is numbered 5?
Options:
A)1/2
B)1/3
C)1/5
D)2/5
E)2/7
Rationale: There are 6 ways to get a total sum of 9.
2 of these ways include the number 5.
The probability that one of the cards is a 5 is 2/6 = 1/3
The answer is B.
Answer: B
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)4%
C)6%
D)3%
E)2%
Rationale: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer: B
Answer: B
Question: If n is a natural number, then 6n^2 + 6n is always divisible by?
Options:
A)6 only
B)6 and 12 both
C)12 only
D)18 only
E)20 only
Rationale: 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B
Answer: B
Question: A watch was sold at a loss of 10%. If it was sold for Rs.500 more, there would have been a gain of 10%. What is the cost price?
Options:
A)1000
B)2998
C)2500
D)2788
E)2991
Rationale: 90%
110%
--------
20% ---- 500
100% ---- ? => Rs.2500
Answer:C
Answer: C
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Options:
A)14 years
B)19 years
C)33 years
D)38 years
E)42 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer: Option A
Answer: A
Question: CONVERT 2.5 hectares in ares
Options:
A)130 ares.
B)160 ares.
C)180 ares.
D)230 ares.
E)250 ares.
Rationale: 2.5 hectares in ares
1 hectare = 100 ares
Therefore, 2.5 hectares = 2.5 × 100 ares
= 250 ares.
ANSWER- E
Answer: E
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A)2:5
B)2:7
C)1:6
D)1:4
E)1:3
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (5 - 3)/(10 - 5) = 2/5
So they should be mixed in the ratio 2:5
Answer - A
Answer: A
Question: Given distinct positive integers 1, 12, 3, x, 2, and 9, which of the following could be the median?
Options:
A)1
B)3
C)6
D)8
E)9
Rationale: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
Arrange numbers in ascending order: 1, 2, 3, 9, 11, and x.
Now, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 3).
Next, if x is 3<x<9 then the median will be the average of 3 and x. As all answers for the median are integers, then try odd values for x:
If x=5, then median=(3+5)/2=4 --> not among answer choices;
If x=7, then median=(3+7)/2=5 --> not among answer choices;;
If x is more than 9 so 10 or more then the median will be the average of 3 and 9 so (3+9)/2=6 (the maximum median possible).
Answer: C
Answer: C
Question: Four faces of a fair die are Yellow, three faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
Options:
A)1/36
B)1/18
C)1/32
D)1/37
E)None of these
Rationale: Probability of getting yellow color = P(Y) = 4/6 = 2/3
Probability of getting red color = P(R) = 3/6 = 1/2
Probability of getting blue color = P(B) = 1/6
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 2/3 x 1/2 x 1/6 = 1/18
ANSWER:B
Answer: B
Question: A man buys a cycle for Rs.1400 and sells it at a loss of 20%. What is the selling price of the cycle?
Options:
A)Rs.1090
B)Rs.1160
C)Rs.1120
D)Rs.1202
E)NONE
Rationale: Solution
S.P	= 80% of Rs.1400
= Rs.(80/100×1400)
Rs.1120.
Answer C
Answer: C
Question: How many seconds does Puja take to cover a distance of 500 m, if she runs at a speed of 30 km/hr?
Options:
A)60 sec
B)82 sec
C)95 sec
D)100 sec
E)120 sec
Rationale: Hint:
Time =	Distance / Speed
We see that the distance is given in metres while the speed is given in km/hr and the answer is asked in seconds.
So, convert km/hr into m/s by multiplying	5 /18	m/s to the given value of speed.
30	km / hr	= 30 x	5 /18	=	75 /9 m/sec
i.e. Place these values in the formula:
Time = 500 x	9 / 75= 60 sec
ANSWER IS A
Answer: A
Question: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 5, which of the following best approximates the circumference of circle O?
Options:
A)28
B)22
C)20
D)16
E)12
Rationale: Given that (1/a)+a =3
Square both sides of the equation:
We get,
[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)
Diameter D = (1/a)^2 + a^2
= 7 (From (1))
So Radius = D/2 = 7/2
Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
=28
So the answer should be A.
Answer: A
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)170
B)180
C)200
D)210
E)220
Rationale: Option 'D'
7p3 = 7 × 6 × 5 = 210
Answer: D
Question: A certain junior class has 1,200 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?
Options:
A)3/40,000
B)1/3,600
C)9/2,000
D)1/60
E)1/16,000
Rationale: Total number of ways of choosing one student from each group is = 800 * 1200
Number of cases in which a sibling pair will be got is = 60
Thus the probability that the 2 students selected will be a sibling pair is
= 60 /(800 * 1200)
= 1/16,000
E
Answer: E
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 10 and 7 respectively, is:
Options:
A)123
B)1
C)235
D)305
E)505
Rationale: Explanation:
Required number = H.C.F. of (1657 - 10) and (2037 - 7)
= H.C.F. of 1647 and 2030 = 1. Answer: B
Answer: B
Question: Find 6 + 9 + 12 + . . . + 30
Options:
A)162
B)165
C)167
D)169
E)171
Rationale: a = 6
l = 30
d = 9 – 6 = 3
ANSWER IS A
Answer: A
Question: The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
Options:
A)1,159
B)1,333
C)1,860
D)2,160
E)2,272
Rationale: The question states that all these 4,999 locations were measured twice, once on each day.
It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 4999
But, for the second day count, W = 1.20 T
i.e. for Second day count, T + 1.20T = 4999
i.e. 2.20 T = 4999
i.e. T = 2272
E
Answer: E
Question: ind next number in the series
23 21 24 19 26 15 28 11 30 7 36 ?
Options:
A)12
B)20
C)5
D)40
E)34
Rationale: C
5
23-2=21
21+3=24
24-5=19
19+7=26
26-11=15
15+13=28
28-17=11
11+19=30
30-23=7
7+29=36
36-31=5
(2,3,5,7,11,13,17,19,23,29,31,37,41,43... are Prime Numbers)
Answer: C
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Options:
A)2500
B)2700
C)2200
D)2900
E)2400
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Answer is E.
Answer: E
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: Option B
Answer: B
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
A)7 days
B)8 days
C)5 days
D)4 days
E)2 days
Rationale: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: B
Answer: B
Question: In a class 30 students play cricket, 40 students play football and 20 play none of the two games.
If there are 80 students exactly in the class, how many play exactly ONE of the two games?
Options:
A)40
B)50
C)80
D)85
E)90
Rationale: n(C) = 30, n(F) = 40 and n(C' or F') = 20
=> n(C or F) = 80 - 20 = 60
also, n(C or F) = n(C) + n(F) - n(C and F)
=> 60 = 30 + 40 - n(C and F)
i.e. n(C and F) = 10
so, 30 - 10 = 20 students play just football and 40 - 10 = 30 students play just cricket
=> 20 + 30 = 50 students play exactly ONE game
B)
Answer: B
Question: 47% of the students in a class of 40 students has glasses or contacts. How many students in the class have either glasses or contacts?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: a=r⋅b
47%=0.47a
=0.47⋅40
a≈19
Option E is correct.
Answer: E
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 70?
Options:
A)11
B)12
C)13
D)14
E)17
Rationale: four wheeler=17*4=68(max)
2 wheel=1
so no of 4 wheeler=17
ANSWER:E
Answer: E
Question: A problem is given to 3 students A, B and C whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the chance that the problem is solved.
Options:
A)2/3
B)1/2
C)1/4
D)3/4
E)3/7
Rationale: Explanation :
P(A) = 1/2, P(~A) = 1 - (1/2) = 1/2. [ Prob. of not solving A ]
P(B) = 1/3, P(~B) = 1 - (1/3) = 2/3. [ Prob. of not solving B ]
P(C) = 1/4, P(~C) = 1 - (1/4) = 3/4. [ Prob. of not solving C ]
The problem is solved means atleast one of A,B and C will solve the problem.
Whenever 'at least one' is present it is easier to do the problem by using the complement of the event (opposite of the event i.e problem not solved )
P (problem is not solved)
= P(~A~B~C)
= P(~A) x P(~B) x P(~C).
= (1/2) x (2/3) x (3/4).
= 1/4.
P (problem is solved i.e atleast one solves)
= 1 - P(~A~B~C).
= 1 - (1/4).
= 3/4.
Answer : D
Answer: D
Question: In one hour a boat goes 6 km/hr along the stream and 14 km/hr against the stream. The speed of the boat in still water(in km/hr) is?
Options:
A)20 km/hr
B)10 km/hr
C)15 km/hr
D)30 km/hr
E)40 km/hr
Rationale: Explanation:
Speed of boat in still water = 1/2 (Speed downstream + speed up stream)
= 1/2 (6 + 14) = 1/2 x 20
= 10 km/hr
Answer: Option B
Answer: B
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be ?
Options:
A)8 days
B)10 days
C)12 days
D)14 days
E)16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
A)
Answer: A
Question: Average age of A and B is 24 years and average age of B, C and D is 22 years. The sum of the ages of
A, B, C and D is
Options:
A)90
B)98
C)120
D)Data is not adequate
E)None of these
Rationale: Answer: Option D
Answer: D
Question: If a man can cover 10 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)135 km
B)125 km
C)115 km
D)105 km
E)235 km
Rationale: 10 m/s = 10 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 10 * 18/5 * 15/4 km = 135 km.
ANSWER:A
Answer: A
Question: In a group of ducks and cows, the total number of legs are 30 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)11
B)12
C)14
D)15
E)18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 30
=> 2x = 30 => x = 15
D
Answer: D
Question: There are 10 points on a circle. A hexagon can be formed by linking 6 of the 10 points. How many such hexagons are possible?
Options:
A)60
B)120
C)200
D)210
E)600
Rationale: 6 points can be selected out of 10 points in 10C6 ways
=10 !/6!*4!=210
Ans D
Answer: D
Question: One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time?
Options:
A)70 min
B)94 min
C)110 min
D)112 min
E)120 min
Rationale: First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
And now we have 4 robots
So Total = (1) + (2) = 70 minutes
Answer - A
Answer: A
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 73%?
M13-03.
Options:
A)N−35
B)N+72
C)2N+70
D)2N+74
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 0.73*200=146 correct answers, so in the second test he must get 146-70=76 questions correctly.
Now, plug N=1 into the answer choices to see which one yields 76. Only option D fits.
Answer: D.
Answer: D
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5760. What is the average monthly balance maintained by John in his
account during the year?
Options:
A) 2840
B) 28800
C) 6840
D) 7540
E) 28400
Rationale: bank balance is doubled with accumulation of interest tp 5760..
this means INTEREST is 5760/2=2880 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 28800..
B
Answer: B
Question: A Cuban cigar would cost 4 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
Options:
A)11.8$.
B)23$.
C)13.7$.
D)35$.
E)37.4$.
Rationale: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options A,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.
Therefore C is the answer.
Answer: C
Question: Set Q consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set Q, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: A = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of Q = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C
Answer: C
Question: A car traveled from San Diego to San Francisco at an average speed of 66 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options:
A)24.
B)32.
C)36.
D)42.
E)44.
Rationale: Let the time taken be = x
One way distance = 66x
Total distance traveled = 2 * 66x = 132x
Total time taken = x + 2x = 3x
Average speed = 132x/3x = 44
Answer: E
Answer: E
Question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours Q will it take if Jim types the report and Mary edits it immediately after he is done?
Options:
A)41.4
B)34.1
C)13.4
D)12.4
E)10.8
Rationale: Break down the problem into two pieces: typing and editing.
Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);
Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23 in theory below)--> x=150/7;
Jim needs 12 hours to edit the report--> Jim's editing rate = 1/12;
Mary and Jim can edit a report in 7.5and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;
How many Q hours will it take if Jim types the report and Mary edits it immediately after he is done--> x+y=150/7+20=~41.4
Answer: A.
Answer: A
Question: 10(150) ÷ 10(146) = ?
Options:
A)10(6)
B)100000
C)1000
D)10000
E)None of these
Rationale: 10(150) ÷ 10(146) = ?
or ? = 10(150)/10(146)=10(150−146)
i.e, [m(x)/m(y)=m(x−y)]
= 10(4) = 10000
Answer D
Answer: D
Question: P, Q and R have Rs.6000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options:
A)2388
B)3722
C)2400
D)2872
E)1231
Rationale: Explanation:
Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(6000 - r) => 3r = 12000 - 2r
=> 5r = 12000 => r = 2400.
Answer: C
Answer: C
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)2/7
B)1/7
C)6/8
D)1/4
E)2/9
Rationale: Explanation:
Original share of 1 person =1/8
New share of 1 person =1/7
Increase =(1/7-1/8)=1/56
Required fraction =(1/56)/(1/8)=(1/56*8/1)=1/7
Answer:B
Answer: B
Question: A 180 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train?
Options:
A)54 kmph
B)108 kmph
C)176 kmph
D)134 kmph
E)161 kmph
Rationale: S = 180/12 * 18/5
= 54 kmph
Answer: A
Answer: A
Question: A number is doubled and 8 is added. If the resultant is trebled, it becomes 84. What is that number?
Options:
A)10
B)6
C)8
D)None of these
E)Cannot be determined
Rationale: Solution
Let the number be x.
Then, 3(2x + 8)	‹=› 84
‹=› 2x+8 = 28
‹=› 2x= 20
x= 10.
Answer A
Answer: A
Question: If the height of a cone is increased by 100% then its volume is increased by?
Options:
A)100
B)777
C)998
D)729
E)2879
Rationale: 100%
Answer:A
Answer: A
Question: How many positive integers less than 120 are there such that they are multiples of 13 or multiples of 12 but not both?
Options:
A)13
B)19
C)15
D)16
E)17
Rationale: for 13: 13...117=13*9 = 117
for 12: 12...120=12*10 =120
but there is one integer 13*12. so
N=(9)+(10)=19
B
Answer: B
Question: A survey was sent to 75 customers, 7 of whom responded. Then the survey was redesigned and sent to another 60 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
Options:
A)2%
B)5%
C)14%
D)60%
E)73%
Rationale: Rate of first survey = 7/75
Rate of second survey = 9/60
% Response rate increase (9/60-7/75)/(7/75) = 60%
Answer is D = 60%
Answer: D
Question: A committee is composed of w women and m men. If 3 women and 3 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by
Options:
A)w/m
B)w/(w+m)
C)(w+3)/(m+3)
D)(w+3)/(w+m+3)
E)(w+3)/(w+m+6)
Rationale: The number of women is w+3.
The total number of people is w+m+6.
P(a woman is selected) = (w+3) / (w+m+6)
The answer is E.
Answer: E
Question: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 20 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
A)1/125
B)1/59
C)1/56
D)1/54
E)1/53
Rationale: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 20/100 = 1/5
Three are independent;probability of rich and fair complexioned girl is:
(1/4) Ã—(1/5) Ã— (1/5) = 1/125
Answer: A
Answer: A
Question: If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number?
Options:
A)601
B)238
C)293
D)298
E)272
Rationale: If the word started with the letter A then the remaining 5 positions can be filled in 5! Ways.
If it started with c then the remaining 5 positions can be filled in 5! Ways.Similarly if it started with H,I,N the remaining 5 positions can be filled in 5! Ways.
If it started with S then the remaining position can be filled with A,C,H,I,N in alphabetical order as on dictionary.
The required word SACHIN can be obtained after the 5X5!=600 Ways i.e. SACHIN is the 601th letter.
Answer: A
Answer: A
Question: In a certain parking lot, 5% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
Options:
A)20%
B)25%
C)30%
D)35%
E)40%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
5%*x = 20%*y
y/x = 1/4 = 25%
The answer is B.
Answer: B
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
Options:
A)4!*3!
B)3!*8!*4!*4!
C)3!*8!
D)5!*3!
E)8!*4!
Rationale: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
Ans: B
Answer: B
Question: How many even number in the range between 10 to 150 inclusive are not divisible by 3
Options:
A)15
B)30
C)31
D)33
E)47
Rationale: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
10,12,14...150
using AP formula, we can say 150 = 10 + (n-1) *2
or n=71.
For 6,
12,18,...96
using AP formula, we can say 150 = 12 + (n-1) *6
or n=24.
Hence, only divisible by 2 but not 3 = 71-24 = 47. hence, Answer E
Answer: E
Question: How many cases do you need if you have to pack 112 pairs of shoes into cases that each hold 28 shoes?
Options:
A)6
B)9
C)8
D)12
E)10
Rationale: C
8
112 pairs of shoes = 224 shoes.
= 224 ÷ 28
= 8.
Answer: C