divelab/Sys2Bench huggingface dataset:
Question: 19 men and 12 boys finish a job in 3 days, 7 men and 7 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
Options:
A)03
B)05
C)12
D)17
E)12
Rationale: 19 M + 12 B ----- 03 days
13 M + 13 B ------- 10 days
18 M + 18 B -------?
247 M +156 B = 234 M +234 B
78 B = 13 M => 1 M = 6 B
114 B + 12 B = 126 B ---- 03 days
108 B + 18 B = 126 B -----? => 03 days
Answer: A
Answer: A
Question: The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is:
Options:
A)12
B)24
C)84
D)48
E)42
Rationale: Let the numbers be x and 4x. Then, x * 4x = 84 * 21 x2 = (84 * 21)/4 = x = 21.
Hence, larger number = 4x = 84.
ANSWER:C
Answer: C
Question: If an integer w is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that w(w + 1)(w + 2) will be divisible by 8?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: for w Total numbers 8*12
There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))
and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))
The answer 5/8 -> D
Answer: D
Question: Rs.12320 were divided among W, X & Y in such a way that W had Rs.640 more than X and Y had Rs 480 more than X . How much was Xâ€™s share?
Options:
A)Rs.4590
B)Rs.4610
C)Rs.4620
D)Rs.4630
E)Rs.4640
Rationale: Let X gets Rs x. Then We can say W gets Rs (x + 640 ) and Y gets Rs ( x + 560) .
x + 640 + x + x + 1120 = 12320
3x = 10560
x = 3520 .
Câ€™s share = Rs ( 3520+1120 ) = Rs.4640
E
Answer: E
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Options:
A)50
B)56
C)70
D)60
E)80
Rationale: Let the actual distance travelled be x km.
Then,x/10=(x + 20)/14
14x = 10x + 200
4x = 200
x = 50 km.
Answer:A
Answer: A
Question: n how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Options:
A)25401600
B)25401800
C)254016200
D)26401600
E)27401600
Rationale: There are 12 words in letter PERMUTATIONS. Out of which T is repeated twice.
Now first we need to see how many ways we can make word with 4 letter between P and S.
Except P and S there are total of 10 letters, so number of way of selecting them = 10C4 = 210
Also note that question is asking to place exactly 4 words between P and S, but does not tells you if P has to be the first letter of S has to be the first letter. So In all the above combinations, we can rotate the position of P and S.
So total way = 210*2 = 420
The selected 4 letters can be rotated between P and S in = 4! ways
So total ways = 420 * 4!
Consider this 6 letter chunk (P, S, and 4 letter between them) as 1 letter.
Remaining letters are 6. So in total we have 7 letters, which can be arranged in 7! ways.
So total number of ways = 7! * 420 * 4!
Now since letter T was repeated twice, we should divide the above result by 2!.
So Total number of ways = 7! * 420 * 4! / 2! = 25401600 A
Answer: A
Question: There are 50 people and 3 clubs M, S, and Z in a company. 14 people joined M, 16 people joined S and 9 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not
join any club?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Answer E.
key is 'atmost' here.
so 14 people joined M.
16 people joined S and 9 people joined Z. to get maximum people who did not join any club, 9 people who joined Z are among 14 people who joined S.
so 16+14 = 30
50-30 = 20
Answer: E
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 22.55%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)60%
B)29%
C)39%
D)56%
E)73%
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 122.55
Let marked price be Rs. x. Then, 95/100 x = 122.55
x = 12255/95 = Rs. 129
Now, S.P. = Rs. 129, C.P. = Rs. 100
Profit % = 29%.
Answer: B
Answer: B
Question: On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000?
Options:
A)15
B)16
C)18
D)20
E)24
Rationale: x- interest rate
80.000= 10.000 (1+x)^year
=> 8=(1+x)^year
40.000=10.000 . (1+x)^12
=> 4= (1+x)^12
=>2= (1+x)^6
=> 8 = (1+x)^ 18
So, after 18 years, the total value of the investment plus interest will increase to $80,000.
ANSWER:C
Answer: C
Question: An Olympic diver received the following scores: 2, 4, 6, 8. The standard deviation of her scores is in which of the following ranges?
Options:
A)4.01 to 4.99
B)1.01 to 1.99
C)3.01 to 3.99
D)2.01 to 2.99
E)5.01 to 5.99
Rationale: 2+4+6+8/4=5
∣2-5∣^2 =3^2 = 9
∣4-5∣^2 =1^2 = 1
∣6-5∣^2 =1^2 = 1
∣8-5∣^2 =3^2 = 9
sqrt 20/4 =2.24
Answer : D
Answer: D
Question: According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?
Options:
A)30%
B)50%
C)25%
D)55%
E)62%
Rationale: A/B = 3/2 = x suppose
that for A=3x
B=2x
Total A+B=5x
Now 64% is happy with new president, 64%*(5x) =3.2x is happy with new present out of total population of A & B
now 70% of A is happy with new pres, so 70%*(3x) = 2.1x
Total happy people are 3.2x
so B=3.2x-2.1x=1.1x is happy
Now B's population is 2x
1.1x is 55% of total population of B
Answer : D
Answer: D
Question: A man swims downstream 96 km and upstream 40 km taking 8 hours each time; what is the speed of the current?
Options:
A)3.5 kmph
B)1.5 kmph
C)13 kmph
D)6.5 kmph
E)7:3kmph
Rationale: Explanation:
96 --- 8 DS = 12
? ---- 1
40 ---- 8 US = 5
? ---- 1 S = ?
S = (12 - 5)/2 = 3.5
Answer: Option A
Answer: A
Question: What is the area of a square field whose sides have a length of 11 meters?
Options:
A)225 sq m
B)205 sq m
C)121 sq m
D)167 sq m
E)156 sq m
Rationale: 11 * 11 = 121 sq m
The answer is C.
Answer: C
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 395 km of the tour is:
Options:
A)31.11 km/hr
B)87.8 km/hr
C)71.11 km/hr
D)36 km/hr
E)71 km/hr
Rationale: Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 395 x 2/9 = 87.8 km/hr.
Answer : B.
Answer: B
Question: A number when divided by a divisor leaves a remainder of 23. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)12
B)13
C)35
D)36
E)59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+23
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 36
as D is also integer and 36 is a prime number, the D should be 36 to satisfy the above equation.
Hence answer is 'D'
Answer: D
Question: Stacy has a 33 page history paper due in 3 days. How many pages per day would she have to write to finish on time?
Options:
A)9
B)8
C)11
D)8.5
E)6
Rationale: 33/3=11
Answer : C
Answer: C
Question: The population of a town has increased from 133575 to 138918. The percent increase in population is :
Options:
A)2.5
B)3
C)4.5
D)4
E)3.5
Rationale: (133575-138918)/138918*100=4
ANSWER:D
Answer: D
Question: How many three digit even numbers do not use any digit more than once
Options:
A)None of these
B)2160
C)2240
D)2460
E)2520
Rationale: The Way i solved it is
A B C ( hundreds, tens, units)
C can be 0 2 4 6 8 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 7 * 8 * 5 = 280
Ans :A
Answer: A
Question: A car traveled from San Diego to San Francisco at an average speed of 48 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 = 48x
Total distance traveled = 2 * 48x = 96x
Total time taken = x + 2x = 3x
Average speed = 96x/3x = 32
Answer: B
Answer: B
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)22
B)28
C)20
D)82
E)34
Rationale: M = 15
S = 5
DS = 15 + 5 = 20.Answer:C
Answer: C
Question: emblem is coded as 216;
crude is coded as 125
bat will be ?
Options:
A)45
B)32
C)27
D)56
E)64
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
bat = 3^3 =27
ANSWER:C
Answer: C
Question: What number should replace the question mark? 3, 30, 11, 24, 19, 18, ---?
Options:
A)24
B)22
C)27
D)25
E)28
Rationale: Answer: C
3, 30, 11, 24, 19, 18, 27?
There are two alternate sequences: +8 and -6.
Answer: C
Question: The price of an item is discounted 3 percent on day 1 of a sale. On day 2, the item is discounted another 3 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Options:
A)85.1%
B)86.9%
C)87.3%
D)88.8%
E)89.5%
Rationale: Let initial price be 100
Price in day 1 after 3% discount = 97
Price in day 2 after 3% discount = 94.09
Price in day 3 after 10% discount = 84.68
So, Price in day 3 as percentage of the sale price on day 1 will be = 84.68/97*100 => 87.3%
Answer will definitely be (C)
Answer: C
Question: If a and b are integers and (a*b)^5 = 48y, y could be:
Options:
A)8
B)16
C)162
D)144
E)100
Rationale: Distribute the exponent.
a^5 * b^5 = 48 y
Find the prime factorization of 48. This is 2^4 *3^1.
We need 2^1*3^4 (or some other power of 3 that will give us a multiple of 3^5 as our second term).
3^4*2 = 81*2= 162
The answer is C.
Answer: C
Question: The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
Options:
A)16
B)12
C)20
D)24
E)35
Rationale: Side of first square = (40/4) = 10 cm;
Side of second square = (32/4)cm = 8 cm.
Area of third square = [(10) 2 - (8) 2] cm2 = (100 - 64) cm2 = 36 cm2.
Side of third square = (36)(1/2) cm = 6 cm.
Required perimeter = (6 x 4) cm = 24 cm.
Ans: D
Answer: D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 21 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)877 m
B)225 m
C)167 m
D)887 m
E)265 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 21)m = 315 m. Let the length of the platform be x meters. Then, (x + 315)/36 = 15
==> x + 315 = 540 ==> x
= 225 m.
Answer: B
Answer: B
Question: 7 3/4 + 7 2/17 - 9 1/15=?
Options:
A)7 719/1020
B)9 817/1020
C)9 719/1020
D)5 817/1020
E)None of them
Rationale: Given sum=7+3/4+7+2/17-(9+1/15)
=(7+7-9)+(3/4+2/17-1/15)
=5+(765+120-68/1020
=5 817/1020
Answer is D
Answer: D
Question: If daily wages of a man is five times to that of a woman, how many men should work for 20 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
Options:
A)12
B)14
C)16
D)8
E)20
Rationale: Explanation :
Wages of 1 woman for 1 day = 21600/40Ã—30
Wages of 1 man for 1 day = 21600Ã—5/40Ã—30
Wages of 1 man for 20 days = 21600Ã—5Ã—20/40Ã—30
Number of men = 14400/(21600Ã—5Ã—20/40Ã—30)=144/(216Ã—100/40Ã—30)=8
Answer : Option D
Answer: D
Question: Convert 300 miles into meters?
Options:
A)784596
B)845796
C)804670
D)482802
E)864520
Rationale: 1 mile = 1609.34 meters
300mile = 300*1609.34 = 482802 meters
Answer is D
Answer: D
Question: The average of 11 results is 55, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
Options:
A)4
B)5
C)7
D)8
E)9
Rationale: 1 to 11 = 11 * 55 = 605
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 605 = 4
ANSWER:A
Answer: A
Question: 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is ?
Options:
A)7 years
B)5 years
C)3 years
D)4 years
E)2 years
Rationale: Explanation:
Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be years.
Then, age of the elder child = years.
So,
Age of younger child = 3 years.
Answer: C
Answer: C
Question: Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?
Options:
A)8 min 15 sec
B)7 min 15 sec
C)6 min 15 sec
D)5 min 15 sec
E)4 min 15 sec
Rationale: Explanation:
Part filled in 3 minutes =
3∗(1/12+1/15)=3∗9/60=9/20
Remaining part =1−9/20=11/20
=>1/15:11/20=1:X
=>X=11/20∗15/1
=>X=8.25mins
So it will take further 8 mins 15 seconds to fill the bucket.
Option A
Answer: A
Question: What is the speed of the stream if a canoe rows upstream at 6km/hr and downstream at 12km/hr
Options:
A)1 kmph
B)4 kmph
C)3 kmph
D)2 kmph
E)1.9 kmph
Rationale: Sol.
Speed of stream = 1/2(12 -6) kmph = 3 kmph.
Answer C
Answer: C
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 68 with him, what was the average amount with the group before his joining the group?
Options:
A)s.13
B)s.11
C)s.15
D)s.22
E)s.12
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 68. So, the amount with remaining 6 people = 140 - 68 = Rs. 72
The average amount with them = 72/6 = Rs.12.
Answer:E
Answer: E
Question: The average expenditure of a man for the first five months is Rs.360 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
Options:
A)Rs.140
B)Rs.150
C)Rs.250
D)Rs.350
E)none
Rationale: Explanation:
Total income = Rs.(360Ã—5+130Ã—7+290)=Rs.3000
Average monthly income
= Rs. (3000/12)=Rs.250
Correct Option: C
Answer: C
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
Options:
A)4:9
B)4:3
C)4:5
D)4:0
E)4:1
Rationale: Explanation:
4 πr2 : 3 πr2 => 4:3
Answer: Option B
Answer: B
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 360 m long?
Options:
A)30 Seconds
B)22 Seconds
C)41 Seconds
D)24 Seconds
E)29 Seconds
Rationale: 30 Seconds
Distance travelled = 140 + 360m = 500m
Speed = 60 * 5/8 = 50/3m
Time = 500 * 3/50 = 30 Seconds
ANSWER A
Answer: A
Question: A boat running up stram takes 6 hours to cover a certain distance, while it takes 7 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
Options:
A)2 : 3
B)5 : 6
C)4 : 5
D)13 : 1
E)8 : 1
Rationale: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
6(x+y) = 7(x-y)
6x+6y = 7x-7y
13y = x
13y = x
x/y = 13/1
13 : 1
Answer: Option D
Answer: D
Question: There are some people in party, 1/3rd left the party . Then 2/5th of the remaining left the party , then 2/3rd of the remaining left the party . At last 10 were remaining . How many people were in total ?
Options:
A)45
B)27
C)28
D)26
E)75
Rationale: Sol:
45
If x persons were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 10
x×2/3 × 3/5 × 1/3 = 10
x = 75
Answer:E
Answer: E
Question: How long will it take a sum of money invested at 8% p.a. S.I. to increase its value by 80%?
Options:
A)12 years.
B)11 years.
C)8 years.
D)10 years.
E)9 years.
Rationale: Sol.
Let the sum be x. Then, S.I. = 80% of x = 4x/5; Rate = 8%.
âˆ´ Time = [100 * 2x/5 * 1/x*8 = 10 years.
Answer D
Answer: D
Question: What least number must be subtracted from 9671 so that the remaining number is divisible by 2?
Options:
A)3
B)1
C)16
D)11
E)15
Rationale: On dividing 9671 by 2, we get remainder = 1.
Required number be subtracted = 1
ANSWER:B
Answer: B
Question: If x and y are integers such that x^2-4x+2y+6=2x^2-5x+y-6, we can deduce that y is
Options:
A)not an even
B)an even
C)a perfect square
D)an odd
E)a prime
Rationale: x^2 - 4x + 2y + 6 = 2x^2 - 5x + y - 6
y = x^2 - x - 12
y = (x-4)(x+3) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B.
Answer: B
Question: If 5th March, 2009 is Tuesday, what was the day of the week on 5th March, 2008?
Options:
A)Sunday
B)Saturday
C)Tuesday
D)Wednesday
E)Monday
Rationale: Solution
The year 2008 is a leap year. So, it has 2 odd days.
But, Feb 2008 not included because we are calculating from March 2008 to March 2009. So it has 1 odd day only.
The day on 5th March, 2009 will be 1 day beyond the day on 5th March, 2008. Given that, 5th March, 2009 is Tuesday.
5th March, 2008 is Monday (1 day before to 5th March, 2009)
Answer E
Answer: E
Question: If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)
Options:
A)0.25
B)1.5
C)2
D)2.5
E)3
Rationale: (a-b)-(c-d)=6 and (c-d)-(a+b)=3
(a-c)-(b+d)=6 and (c-a)-(b+d)=3
(b+d)= (a-c)-6 and (b+d)=3-(c-a)
2(a-c)=3
(a-c)=1.5
ANSWER B 1.5
Answer: B
Question: If x is less than y by 50% then y exceed x by:
Options:
A)33.33%
B)100%
C)75%
D)66.66%
E)None of these
Rationale: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 50(100-50)*100
=100%
ANSWER:B
Answer: B
Question: Given that a/b < 1, and both a and b are positive integers, which one of the following must be greater than 1?
Options:
A)a/b^2
B)a^2/b
C)a^2/b^2
D)b/a
E)√(a/b)
Rationale: Since a/b is a fraction b must always be > 1
Given -
Which one of the following must be greater than 1
We can get the result one only when the denominator in a/b ( Which is less than 1 ) becomes numerator..
Among the given options only (D) has the required characteristic we are looking for...
Hence answer will be (D)
Answer: D
Question: What is the HCF of 2/3, 4/9 and 6/5
Options:
A)7/45
B)2/45
C)4/15
D)8/45
E)9/45
Rationale: Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 9, 5) = 2/45
Answer: Option B
Answer: B
Question: P, Q and R have Rs.9000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options:
A)Rs.3000
B)Rs.3600
C)Rs.2400
D)Rs.4000
E)None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(9000 - r) => 3r = 18000 - 2r
=> 5r = 18000 => r = 3600.
ANSWER:B
Answer: B
Question: Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
Options:
A)4328
B)5382
C)6174
D)7690
E)8436
Rationale: The number of ways for the ships to go to the ports is 3! = 6.
At Port A, the number of ways to choose two winners is 7C2 = 21.
At Port B, the number of ways to choose one winner is 7.
At Port C, the number of ways to choose one winner is 7.
The total number of ways to give out gift certificates is 6*21*7*7 = 6174
The answer is C.
Answer: C
Question: Calculate the average of all the numbers between 11 and 27 which are divisible by 2.
Options:
A)11
B)10
C)18
D)19
E)21
Rationale: Explanation:
numbers divisible by 2 are 12,14,16,18,20,22,24,26,
Average = (12+14+16+18+20+22+24+26, ) / 8 = 152/8 = 19
ANSWER: D
Answer: D
Question: Every day Daniel drives 120 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
Options:
A)10%
B)20%
C)30%
D)40%
E)60%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 120 miles at 4 miles/hour.
D = (R)(T)
120 = (4)(T)
120/4 = 30 = T
It takes 30 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (88 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
88 = (2)(T)
88/2 = 44 = T
It takes 44 hours for the second part
Total time to drive home on Monday = 4+44 = 48 hours
We're asked by what percent 48 hours is greater than 30 hours.
48/30 = 1.6, so it is 60% greater.
answer:E
Answer: E
Question: A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that Exactly three are not spoiled.
Options:
A)116/495
B)224/495
C)129/495
D)187/495
E)197/495
Rationale: equired probability = 8C3 . 4C1/12C4 = 56 x 4/495
= 224/495.
ANSWER:B
Answer: B
Question: At a meeting, 8 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
Options:
A)12
B)72
C)120
D)1440
E)5040
Rationale: The number of arrangements of n distinct objects in a row is given by n!
The number of arrangements of n distinct objects in a circle is given by (n−1)!
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
R=n!-n=(n−1)!
(n−1)!=(8−1)!=5040
Answer: E
Answer: E
Question: A train 120 m long crosses a platform 220 m long in 20 sec; find the speed of the train?
Options:
A)87 kmph
B)65 kmph
C)54 kmph
D)61 kmph
E)18 kmph
Rationale: D = 120 + 220 = 340
T = 20
S = 340/20 * 18/5 = 61 kmph
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. 6970, then what will be the share of Sameer in the profit?
Options:
A)2318
B)2380
C)1277
D)2662
E)1321
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer: B
Answer: B
Question: A man buys a cycle for Rs. 1800 and sells it at a loss of 25%. What is the selling price of the cycle?
Options:
A)s. 1090
B)s. 1160
C)s. 1190
D)s. 1350
E)s. 1256
Rationale: S.P. = 75% of Rs. 1800 = Rs.75/100x 1800	= Rs. 1350
ANSWER :D
Answer: D
Question: Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%?
Options:
A)10liters
B)15liters
C)20liters
D)18liters
E)22liters
Rationale: Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters
Let x liters of pure milk be added.
Then, 0.5/(10+x) = 2/100
2x = 30
x=15 liters
Answer is B
Answer: B
Question: Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the pipes are opened simultaneously, and the pipe A is closed after 3 minutes, then how much more time will it take to fill the tank by pipe B?
Options:
A)5 minute 25 second
B)5 minute 45 second
C)5 minute 35 second
D)6 minute 45 second
E)7 minute 45 second
Rationale: Part filled by pipe A in 1 minute =1/8
Part filled by pipe B in 1 minute =1/14
Part filled by pipe A and pipe B in 1 minute =1/8+1/14=11/56
Pipe A and B were open for 3 minutes.
Part filled by pipe A and B in 3 minute=3 Ã— 11/56=33/56
Remaining part =1-33/56=23/56
Time taken by pipe B to fill this remaining part=(23/56)/(1/14)=23/4
=5 3/4 minutes
=5 minute 45 second
Answer is B
Answer: B
Question: If x > 3000, then the value of (x)/(2x-42) is closest to?
Options:
A)1/6
B)1/3
C)10/21
D)1/2
E)3/2
Rationale: assume x = 3002
(x)/(2x-42) = 3002 / (3002*2-42)
=3002 / 5962
= = 1/2
Ans - D
Answer: D