divelab/Sys2Bench huggingface dataset:
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Euro 1000 more than D, what is B's share?
Options:
A)Euro 500
B)Euro 1500
C)Euro 2000
D)None of these
E)Cannot be determined
Rationale: Explanation: Let the shares of A, B, C and D be Euro 5x, Euro 2x, Euro 4x and Euro 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Euro 2x = Euro (2 x 1000) = Euro 2000.
Answer: Option C
Answer: C
Question: The total of company C's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)10N
E)20
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 100% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$500 + 1x$500 = $500 + $500 =$1000
This is 10 times the 1992 number, so the correct answer is 10N.
D
Answer: D
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)176 m
B)179 m
C)500 m
D)169 m
E)576 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Answer: C
Question: Eric throws 2 dice,and his score is the sum of the values shown.Sandra throws one dice and her score is the square of the value shown. what is the probabilty that Sandras score will be strictly higher than Erics score??
Options:
A)137/216
B)137/218
C)137/217
D)136/216
E)138/216
Rationale: sandra score can be like 1,4,9,16,25,36
eric score less then 1-->0
eric score less then 4=(1,1),(1,2)(2,1)-->3
eric score less then 9 are (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(4,1)(4,2)(4,3)(4,4)(5,1)(5,2)(5,3)(6,1)(6,2)-->26
eric score will always be less then 16--->36
eric score will always be less then 25--->36
eric score will always be less then 36--->36
total favorable outcomes=3+26+36+36+36=137
total possible outcomes=216(36*6)
probability=137/216
ANSWER:A
Answer: A
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 1536 sq m, the cost of fencing it at 50 ps per meter is?
Options:
A)51
B)1287
C)125
D)988
E)271
Rationale: 3x * 2x = 1536 => x = 16
2(48 + 32) = 102 m
102 * 1/2 = Rs.51
Answer: A
Answer: A
Question: A 270-metre-long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 secs. What is the length of the other train?
Options:
A)240 metres
B)320 metres
C)260 metres
D)230 metres
E)None of these
Rationale: Relative speed = 120 + 80 kmph = 200 × 5⁄18 m/sec
t = Distance/Speed=(270+x)×9/500
or 270 + x = 9×500/9x = 500 – 270 = 230 m
Answer D
Answer: D
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit?
Options:
A)s.2323
B)s.2380
C)s.2329
D)s.2660
E)s.2312
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 7790 * 14/41
= Rs.2660.
Answer: D
Answer: D
Question: There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first?
Options:
A)5.4 km /hr
B)7.2 km /hr
C)8.4 km/hr
D)9.6 km /hr
E)None
Rationale: Solution
Clearly, the cyclist moves both ways at a speed of 12 km/hr.
So, average speed of the cyclist	= 12 km/hr.
Average speed	= (2x14x6/14+6) km/hr
= 42/5 kmph
= 8.4 kmph
Since the average speed of the cyclist is greater, he will return to A first.
Answer C
Answer: C
Question: Find out the wrong number in the series.
6, 12, 48, 104, 384, 768, 3072
Options:
A)768
B)384
C)104
D)488
E)12
Rationale: Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 104.
ANSWER:C
Answer: C
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
Options:
A)Rs.150
B)Rs.132
C)Rs.100
D)Rs.125
E)Rs.225
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2 = Rs.132
ANSWER:B
Answer: B
Question: What is the number of different committees of 6 people that can be selected from a group of 10 people?
Options:
A)a) 20
B)b) 40
C)c) 80
D)d) 120
E)e) 210
Rationale: 10c6 = 210
Answer is E.
Answer: E
Question: Two pipes A and B can separately fill a tank in 12 minutes and 15 minutes respectively. Both the pipes are opened together but 8 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)5min
B)9min
C)7min
D)6min
E)8min
Rationale: 8/12 + x/15 = 1
x = 5
ANSWER:A
Answer: A
Question: A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
Options:
A)A.72
B)B.50
C)C.48
D)D.46
E)E.23
Rationale: At 6:00 it'll chime 6 times. If we assume that the time taken to chime is x, then time between chimes is also x. So you have 6 chimes, which is 6x and 5 time intervals between chimes. This means that 11x = 11 seconds. Thus x = 1 seconds.
By a similar logic, at 12:00, there are 12 chimes and 11 intervals so the total time is (12+11)x = 23x = 23 seconds.
Answer E
Answer: E
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is -.
Options:
A)17/25
B)17/27
C)17/18
D)17/22
E)17/09
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer:A
Answer: A
Question: Dividing by 3⁄8 and then multiplying by 5⁄8 is the same as dividing by what number?
Options:
A)31⁄5
B)16⁄5
C)20⁄9
D)9⁄20
E)5⁄3
Rationale: say X/3/8*5/8 = x*8/3*5/8 = x*5/3
E
Answer: E
Question: The average age of a family of four members is 25 years. If the age of the youngest member be 15 years then what was the average age of the family at the time of the birth of the youngest member?
Options:
A)13.5
B)14
C)15
D)13.33
E)16
Rationale: Explanation :
At present the total age of the family = 4 * 25 = 100
The total age of the family at the time of the birth of the youngest member = [100-15-(15*3)]
= 40
Therefore, average age of the family at the time of birth of the youngest member = 40/3
= 13.33
Answer : D
Answer: D
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 100kmph, find the rate at which the train B runs.
Options:
A)40
B)60
C)150
D)80
E)100
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 100 kmph, speed of B must be 100*(3/2) = 150 kmph
Answer C
Answer: C
Question: In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:4:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?
Options:
A) $900
B) $720
C) $675
D) $450
E) $225
Rationale: To solve this question, it will be best to first express the given ratio using variable multipliers. Thus, we have:
Household Expenses : Food : Miscellaneous = 5x : 4x : x
Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:
5x + 4x + x = 1,800
10x = 1,800
x = 180
Thus, the total amount allocated to food is 4 x 180 = $720.
Answer B.
Answer: B
Question: If Rs. 578 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?
Options:
A)s.300
B)s.408
C)s.389
D)s.368
E)s.323
Rationale: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 578 * 2/17 = Rs. 68
B's share = 578 * 3/17 = Rs. 102
C's share = 578 * 12/17 =Rs.408.
Answer:B
Answer: B
Question: Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/4, what is the ratio of rectangle A’s area to rectangle B’s area?
Options:
A)3/4
B)9/16
C)16/3
D)4/3
E)3/16
Rationale: The area of rectangle A is ab.
c=4a/3 and d=4b/3.
The area of rectangle B is cd=16ab/9.
The ratio of rectangle A's area to rectangle B's area is ab / (16ab/9) = 9/16.
The answer is B.
Answer: B
Question: If a sequence of 8 consecutive odd integers with increasing values has 3 as its 7th term, what is the sum of the terms of the sequence?
Options:
A)-16
B)-8
C)-4
D)4
E)8
Rationale: Let x be the first term.
Then x + 12 = 3 and x = -9
The sum is: x + (x+2) +...+ (x+14) =
8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-9) + 56 = -16
The answer is A.
Answer: A
Question: A and B can do a work in 18 day, B and C in 30 days, A and C in 22 (1/2) days. In how many days can A,B and C individually do the work?
Options:
A)30,45,90
B)30,45,60
C)30,45,40
D)30,43,60
E)30,44,60
Rationale: (A+B+C)'s two days work = 1/18 + 1/30 + 2/45
= (5 + 3 + 4)/90 = 2/15
(A+B+C)'s one day work = 2/15 * 1/2 = 1/15
A's one day's work = 1/15 - 1/30 = 1/30
B's one day's work = 1/15 - 2/45 = 1/45
C's one day's work = 1/15 - 1/18= 1/90
So, A,B and C can individually do the work in 30, 45 and 90 days.
Answer:A
Answer: A
Question: If points A and B are (8-3) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: I. The area of a square region with side AB --> side=AB=(8-3) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Answer: A
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
A)1/9
B)1/3
C)1/5
D)1/1
E)1/2
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer:C
Answer: C
Question: The product Z of two prime numbers is between 20 and 60. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 18 but less than 36 then what is Z?
Options:
A)21
B)35
C)39
D)51
E)57
Rationale: The smallest possible product is 57 which is 3*19.
All other products are too big.
The answer is E.
Answer: E
Question: If there are 156 laborers in a crew, and on a certain day, 70 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
Options:
A)45.9%
B)43.9%
C)42.9%
D)41.9%
E)44.9%
Rationale: 70/156*100=44.87
44.9%
correct answer E
Answer: E
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
Options:
A)245
B)255
C)260
D)267
E)278
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: B
Question: The smallest 2 digit prime number is?
Options:
A)A)11
B)B)13
C)C)19
D)D)113
E)E)None
Rationale: The smallest 3-digit number is 10, which is divisible by 2.
10 is not a prime number.
11 is a prime number.
Hence 11 is the smallest 2-digit prime number.
A)
Answer: A
Question: A can do a piece of work in 90 days & Y can do it in 80 days. They began working together but A leaves after some days and then B completed the remaining work in 46 days. The number of days after which A left the work was?
Options:
A)12 days
B)18 days
C)16 days
D)19 days
E)21 days
Rationale: A and B did the work for some days.
After that , B completed the remaining work in 46 days .
In 46 days, word done by B =
1
80
x 46 =
23
45
Remaining work = 1 – 23/45
= 17/45
Remaining work is done by both A and B together =
17/45x 90 x 80/90 + 80
= 16 days
C
Answer: C
Question: If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 11 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Options:
A)25 pounds
B)46 pounds
C)92 pounds
D)110 pounds
E)146 pounds
Rationale: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*11 --> x = 110.
Answer: D.
Answer: D
Question: A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 50% more recliners. What is the percentage increase of the gross?
Options:
A)10%
B)15%
C)20%
D)25%
E)50%
Rationale: Say a recliner is actually worth $100
If she sells 100 recliners then she earns $10000
After the discount of 20%, she will earn $80 per recliner and she sells 50% more ie.,150 recliners
Hence her sales yields 150*80=$12000
Increase in sales=12000-10000=$2000
So% increase = 2000*100/10000 =20%
C is the answer
Answer: C
Question: Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 5 grades are D's. What is the number of students in the course?
Options:
A) 80
B) 110
C) 160
D) 100
E) 400
Rationale: We start by creating a variable for the total number of students in the math course. We can say:
T = Total number of students in the math course
Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 5 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:
#A’s + #B’s + #C’s + #D’s = Total number of students in the class
1/5(T) + ¼(T) + ½(T) + 5 = T
We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:
4T + 5T + 10T + 100 = 20T
19T + 100 = 20T
100 = T
There are a total of 100 students in the math class.
Answer is D.
Answer: D
Question: After decreasing 15% in the price of an article costs Rs.915. Find the actual cost of an article?
Options:
A)915
B)1000
C)1076
D)1067
E)1760
Rationale: CP* (85/100) = 915
CP= 10.76 * 100 => CP
= 1076
Answer:C
Answer: C
Question: In a recent election, James received 1.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election?
Options:
A)901
B)989
C)990
D)971
E)1,001
Rationale: James = (1.5/100)*2000 = 30
Votes to win = (50/100)*Total Votes +1 = (50/100)*2000 +1 = 1001
Remaining Voted needed to win election = 1001 - 30 = 971
Answer: option D
Answer: D
Question: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long R would it take Victor to complete 10 jobs without any supervision?
Options:
A)34
B)52
C)60
D)70
E)92
Rationale: Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).
For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.
Victor to complete 10 jobs without any supervision will need R 10(t + 3) = 60 days.
Answer: C.
Answer: C
Question: If Tim had lunch at $50.50 and he gave 10% tip, how much did he spend?
Options:
A)$30.60
B)$60.60
C)$70.60
D)$55.55
E)$50.60
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 50.50 = (10/100)*50.50 = $5.05
Total spent
50.50 + 5.05 = $55.55
correct answer D
Answer: D
Question: If two integers x, y (x>y) are selected from -10 to 10 (inclusive), how many possible cases are there?
Options:
A)150
B)180
C)190
D)210
E)240
Rationale: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?
A. 150
B. 180
C. 190
D. 210
E. 240
--> 21C2=21*20/2=210. Therefore, the answer is D
Answer: D
Question: When all the students in a school are made to stand in rows of 60, 35 such rows are formed. If the students are made to stand in rows of 25, how many such rows will be formed ?
Options:
A)31
B)84
C)78
D)19
E)21
Rationale: Explanation:
Total number of students = 60 x 35
When arranged in rows of 25, number of rows formed are,
= 84.
Answer: B
Answer: B
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
Options:
A)38 sec
B)35 sec
C)44 sec
D)40 sec
E)48 sec
Rationale: train length= 360m
platform length = 140m
time= ?
length = speed * time
total length =360+140 = 500m
speed = 45 km/hr =45 * (5/18) (m/sec) =12.5 m/sec
time = length/speed = 500/12.5 = 40sec
ANSWER:D
Answer: D
Question: A can finish a work in 21 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Options:
A)6
B)5
C)5.5
D)7
E)8
Rationale: B's 10 day's work = ( 1 x 10 ) = 2 .
15 3
Remaining work = ( 1 - 2 ) = 1 .
3 3
Now, 1 work is done by A in 1 day.
21
Therefore 1 work is done by A in ( 21 x 1 ) = 7 days.
D
Answer: D
Question: A double decked bus can accomodate 120 passengers,50 in the upper deck and 70 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck?
Options:
A)1. 95!/40!55!
B)2. 85!/40!45!
C)3. 110!/50!60!
D)4. 110!50!60!/40!45!
E)5. 110!/40!45!
Rationale: 120 passengers,50 in the upper deck and 70 in the lower deck.
25 passengers have issues as 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck
So those 15 will be put in lower deck and 10 will be in upper deck
So from the rest 95 passengers(120-25), we need to find 40 people to put into upper deck and the rest go to lower deck
So the ways are: C(95,40) = 95!/40!55! . Answer A
Answer: A
Question: A student has 8 trousers and 11 shirts. In how many different ways can the student select a trouser and a shirt?
Options:
A)76
B)88
C)100
D)112
E)124
Rationale: The student can select one trouser in 8 ways.
The student can select one shirt in 11 ways.
The number of ways to select one trouser and one shirt is 8 * 11 = 88 ways
The answer is B.
Answer: B
Question: At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?
Options:
A)24min
B)12min
C)13min
D)14min
E)15min
Rationale: n this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5 Answer: A
Answer: A
Question: A, B, C hired a car for Rs. 720 and used it for 9, 10 and 13 hours respectively. Hire charges paid by B are:
Options:
A)Rs 220
B)Rs.225
C)Rs.230
D)Rs.235
E)Rs.255
Rationale: A : B : C = 9 : 10 : 13.
Hire charges paid by B = Rs. 720 * 10/32
= Rs. 225.
ANSWER:B
Answer: B
Question: 10 machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
Options:
A)2
B)3
C)4
D)5
E)8
Rationale: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
So 3/2* 10 = 15
So we need 15-10 = 5 more machines.
Answer : D
Answer: D
Question: A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: A
5 cartons for large boxes = 5 * 6 = 30 boxes
4 cartons for small boxes = 4 * 9 = 36 boxes
He will need 9 cartons to place 66 boxes.
Answer: A
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of
Options:
A)33
B)40
C)99
D)28
E)72
Rationale: Explanation:
Let the original price of the cycle be 100. After the first reduction the price will be 75.
This new price is then reduced by 20% = 0.8 x 75 = 60
60 represents a reduction of 40 percent on the original.
Answer: B) 40%
Answer: B
Question: The sum of three consecutive even numbers is 63. Find the middle number of the three?
Options:
A)14
B)23
C)25
D)29
E)21
Rationale: Middle no=63/3
=21
Ans E
Answer: E
Question: A "digital word" is defined as a four-letter combination of the digits 1 and 0 only. How many "digital words" are there?
Options:
A)2
B)4
C)6
D)8
E)16
Rationale: only digits allowed are 1 and 0 so for a 4 digit number the possibilities are
1111-> 4!/4! ->1
0000-> 4!/3! ->1
1000-> 4!/3! ->4
1100->4!/2!2! ->6
1110->4!/3! ->4
Total 1+1+4+6+4 = 16 is possible..
E is the answer
Answer: E
Question: If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Let's find a number which when divided by 5 leaves remainder 2 = 5+2 = 7
i.e. one possible value of m = 7
value of 3m = 3*7 = 21
when em is divided by 5 then remainder = Rem (21/5) = 1
Answer: option B
Answer: B
Question: How many positive integers less than 254 are multiple of 4 but NOT multiples of 6?
Options:
A)20
B)31
C)42
D)43
E)64
Rationale: 252/4=63
Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0
240/12=20
63-20=43
Answer: D
Answer: D
Question: In how many ways can you sit 8 people on a bench if 5 of them must sit together?
Options:
A)720
B)2,160
C)2,880
D)4,320
E)40,320
Rationale: In such questions, always tie the person that have to sit together. So we have effectively 3+1= 4 persons to arrange.
They can be arranged in 4! ways.
Now the 5 persons can themselves be arranged in 5! ways.
Total ways: 4!*5! = 2880.
C is the answer.
Answer: C