RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: a man have 8 t-shirt and some pant.he can dress in 72 ways.then tell me the no. of pant that man have.
A.8
B.9
C.10
D.11
Answer: B.9
Explanation: let he have x pant.
by fundamental principle total no. of ways in which he can dress=8x
8x=72
x=9pants
answer B
Question: If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 6 € (4 € 5) =
A.480
B.120
C.160
D.240
Answer: A.480
Explanation: working inside out,
(4 € 5) = 2*4*5 = 40
6 € 40 = 2*6*40 = 480
Hence, answer is A
Question: The line r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2) and is parallel to the line s ≡ mx + 2y − 13 = 0. Calculate the values of m and n.
A.-6,-1
B.-3,-2
C.3,2
D.6,1
Answer: A.-6,-1
Explanation: r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2)
3. 3 +nN . 2 - 7 = 0 n = -1
3/m = - 1/2
m=6
ANSWER : A -6,-1
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
A.7 kmph
B.4 kmph
C.8 kmph
D.3 kmph
Answer: B.4 kmph
Explanation: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer:B
Question: 1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams
A.48 paise
B.77 paise
C.96 paise
D.66 paise
Answer: A.48 paise
Explanation: Explanation:
Let 200 gm potato cost X paise
According to question,
Cost of 1/4 Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise
=> 1 Kg = 1000 gm
=> 1/4 Kg = 1000/4 gm = 250 gm
By direct proportion, more quantity, more cost
200 grams : 250 grams = X : 60
=> 200*60 = 250 X
=> 12000 = 250 X
=> X = 48
=> Thus, the cost of 200 grams is 48 paise.
ANSWER: A
Question: In how many ways can you line up 7 apples in a row if one of them cannot be in the middle or at the either end?
A.1,790
B.52
C.2,880
D.98
Answer: C.2,880
Explanation: Since the apple cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: C.
Question: A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest is 12% per annum,how much cash should he pay ?
A.Rs. 9025.20
B.Rs. 9200
C.Rs. 9600
D.Rs. 9560
Answer: B.Rs. 9200
Explanation: Solution
Required money = P.W. of Rs.10028 due 9 months hence
= Rs. [ 10028x 100/100+( 12 x9/12)] = Rs. 9200
Answer B
Question: The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?
A.440
B.512
C.620
D.700
Answer: C.620
Explanation: Solved it the prime factorization way
440= 2*2*2*5*11 Sum=22
512= 2^6 Sum=2*6=12
620=2*2*5*31 Sum=40>35
Hence correct.
Ans is C
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
A.2.15 p.m
B.1.15 p.m
C.4.15 p.m
D.3.15 p.m
Answer: A.2.15 p.m
Explanation: Suppose they meet x hours after 10 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Ans: A
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?
A.9! * ⁷P₆
B.6! * ⁷P₆
C.9! * ⁷P₆
D.6! * ⁷9₆
Answer: B.6! * ⁷P₆
Explanation: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
Answer:B
Question: Solve below question 2x + 1 = -15
A.-8
B.-9
C.9
D.8
Answer: A.-8
Explanation: 2x + 1 = -15
x = -8
A
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
A.2387
B.1640
C.2781
D.2778
Answer: B.1640
Explanation: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640
Answer: B
Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is?
A.23
B.25
C.27
D.31
Answer: A.23
Explanation: Let the numbers be x and y.
Then, xy = 120 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
x + y = 529 = 23.
Option A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
A.Insufficient data
B.3 : 1
C.1 : 3
D.3 : 2
Answer: D.3 : 2
Explanation: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
=> (27x + 17 y)/(x + y) = 23
=> (27x + 17 y) = 23(x + y)
=> 4x = 6y
=> x/y = 6/4 = 3/2
ANSWER:D
Question: Sentence B can only be a concluding sentence; we find in the answer choice–b, a sequence of the sentences logically leading to the concluding sentence
A.17
B.88
C.171
D.19
Answer: B.88
Explanation: Answer:B
Question: Two trains 130 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
A.10.9
B.10.7
C.10.3
D.10.44
Answer: D.10.44
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 130 + 160 = 290 m.
Required time = 290 * 9/250 = 261/25 = 10.44 sec.
'Answer: D
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
A.671.5
B.600
C.672.5
D.673
Answer: B.600
Explanation: Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds;
Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours;
So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: B.
Question: In a sequence of 11 numbers, each term, except for the first one, is 11^11 less than the previous term. If the greatest term in the sequence is 11^12, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
A.−12^11
B.0
C.11^11
D.11·12^11
Answer: C.11^11
Explanation: there are total 11 terms. andgreatestterm is 11^12. Each term is 11^11 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 11^11 less than previous one')
Therefore, 11^12 is the first term of the AP and -11^11 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 11^12 + 10*(-11^11)
=> Last term = 11^12 - 10*11^11
=> Last term = 11^11 (11-10) = 11^11
Which is the smallest term.
Hence Ans C it is.
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 10. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 13. How many cooks does the restaurant have?
A.4
B.6
C.9
D.12
Answer: D.12
Explanation: Originally there were 3k cooks and 10k waiters.
13k = 10k+12
k=4
There are 12 cooks.
The answer is D.
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,U,R,S,and T so that letter P is to the left of letter R?
A.60
B.30
C.90
D.120
Answer: A.60
Explanation: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
A
Question: If the product 4864*9 P 2 is divisible by 12, the value of p?
A.1
B.5
C.6
D.7
Answer: A.1
Explanation: Explanation:
clearly 4864 is divisible by 4
So 9 P 2 must be divisible by 3.So(9+P+2) must be divisible by 3.
so P=1.
Answer: A) 1
Question: The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 156.4, what is the average of the other half?
A.12.8
B.24.2
C.49.1
D.72.1
Answer: C.49.1
Explanation: The average of this half is 156.4/4 = 39.1
This is 5 below the overall average, thus the average of the other half of the numbers must be 5 above the overall age, that is 44.1+5 = 49.1
The answer is C.
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87, and 98
A.80
B.85
C.92
D.97
Answer: C.92
Explanation: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median quiz score was 92. (Four quiz scores were higher than 92 and four were lower.)
C
Question: 12 men can complete any work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only the women were to complete the remaining work in 4 days, then how many women would be required?
A.60
B.74
C.68
D.75
Answer: B.74
Explanation: 1 Man, 1 Day work=1/(12*36)
1 Woman, 1 Day work=1/(18*60)
So 8 men and 20 women's 20 days work= 20[ 8/(12*36) + 20/(18*60) ] =20/27
Remaining work= 7/27
If remaining work is to be completed by 'x' women in 4 days, then 4*x/(18*60)= 7/27
=> x=(7*18*60)/(27*4)=70
ANSWER:B
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.7 sec.
B.6 sec
C.3 sec.
D.1 sec.
Answer: B.6 sec
Explanation: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Question: An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
A.23.000 degrees / second
B.43.000 degrees / second
C.52.000 degrees / second
D.18.000 degrees / second
Answer: D.18.000 degrees / second
Explanation: 3000 revolutions / minute
= 3000*360 degrees / 60 seconds
= 18,000 degrees / second
correct answer D
Question: A car traveled the first quarter of a certain distance at five times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
A.1/14
B.1/15
C.1/16
D.1/17
Answer: C.1/16
Explanation: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be five times, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 2 km/h for the remaining quarters.
He'll take 1 hour to do the first quarter and then 15 hours for the second ,third and fourth quarter. On total he will take 16 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/16. Answer C.
Question: Jerry received a 10% raise each month for two consecutive months. What was his starting salary if after the two raises his salary is $1452?
A.$1,200
B.$1,300
C.$1,331
D.$1,380
Answer: A.$1,200
Explanation: S * 1.1 * 1.1 = 1452 so,
S = 1200
Answer: A
Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
A.32
B.28
C.40
D.27
Answer: C.40
Explanation: S = (200 + 300)/45 = 500/45 * 18/5 = 40
Answer: C
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
A.11
B.10
C.19
D.187
Answer: B.10
Explanation: Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days. Answer: B
Question: A baseball player just signed a new contract in which he will earn a 12% raise in base pay over last year. Last year he earned no performance bonus, but this year he will have the opportunity to earn up to $50,000 in extra pay through performance. If he earns the full performance bonus, his salary will effectively have been raised by 12.5% from the last year. Assuming he earns the full performance bonus, what will his new salary be?
A.5,150,000
B.10,550,000
C.11,250,000
D.11,450,000
Answer: C.11,250,000
Explanation: let x = the old salary
the new base pay + 50,000 = the new pay
(1+.12)*x + 50,000 = (1+.125)*x
1.12x + 50,000 = 1.125x
50,000 = .005x
10,000,000 = x
thus the new pay = (1+.125)*10,000,000 = 11,250,000
C
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
A.6620
B.6628
C.6520
D.6629
Answer: A.6620
Explanation: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Question: The average of 6 observations is 12. A new observation is included and the new average is decreased by 1. The seventh observation is?
A.1
B.3
C.5
D.6
Answer: C.5
Explanation: Let seventh observation = X.
Then, according to the question we have
=> (72 + X) / 7 = 11
=> X = 5.
Hence, the seventh observation is 5.
ANSWER:C
Question: Company A has 13 employees, 8 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 3 union members work each shift, then how many different combinations of employees might work any given shift?
A.56
B.231
C.336
D.350
Answer: C.336
Explanation: Looks easy: -- 8C3*5C1 + 8C5 -- 336 (C).
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
A.20
B.30
C.40
D.50
Answer: A.20
Explanation: Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
(a + b + c) = 400 = 20
Answer:A
Question: A new apartment complex purchased 60 toilets and 20 shower heads. If the price of a toilet is three times the price of a shower head, what percent of the total cost was the cost of all the shower heads?
A.9%
B.10%
C.11%
D.13%
Answer: B.10%
Explanation: LET PRICE OF SHOWER HEADS=X
THEN ,, ,, TIOLETS=3X
TOTALCOST=20*X+60*3X=200x
% OF TOTAL COST WAS THE COST OF ALL THE SHOWER HEADS=(20X/200X)*100=10%
ANSWER:B
Question: If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
A.1
B.7
C.3
D.14
Answer: B.7
Explanation: Explanation :
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
⇒ 7 × 1 × 7 = 1 × 7 × x
⇒x=7. Answer : Option B
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
A.7
B.8
C.5
D.6
Answer: B.8
Explanation: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2
= 8
Answer:B
Question: The difference between the place values of two threes in the numerical 40378273 is
A.29997
B.299997
C.297
D.0
Answer: B.299997
Explanation: Required difference = (300000-3)
=299997.
Answer is B
Question: Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
A.Rs.1978
B.Rs.1979
C.Rs.1951
D.Rs.1968
Answer: C.Rs.1951
Explanation: P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25)
= Rs. 17576 C.I.
= 17576 - 15625 = Rs. 1951.
Answer:C
Question: Kiran, an eight years old boy has 27 toys. He gave 19 toys to his brother Gourav, while Gourav playing all but 6 got destroyed. While Kiran playing all but 3 got destroyed. Finally how many toys left with both of them?
A.9
B.1
C.8
D.76
Answer: A.9
Explanation: While Gourav playing 'All but 6 got destroyed' means 'All except 6 got destroyed'. i.e., 13 toys got destroyed. It means now Gourav has 6 toys. While Kiran is playing 'All but 3 got destroyed' means 'except 3 all are not working i.e; 3 toys are good working so total toys at both of them is 6 + 3 = 9.
Answer:A
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. 3
II. -4
III. 8
IV. 5
A.I and II only
B.I and III only
C.II and III only
D.II and IV only
Answer: A.I and II only
Explanation: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 3 satisfy both inequalities.
Answer: A.
Question: If x < 0 and 0 < y < 1, which of the following has the greatest value W?
A.x^2
B.(xy)^2
C.(x/y)^2
D.x^2/y
Answer: C.(x/y)^2
Explanation: Given, x < 0 and 0 < y < 1
Let, x = -2 and y = 1/2
A. x^2 = (-2)^2 =4
B. (xy)^2 = (-2*1/2)^2 =1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16
D. x^2/y = (-2)^2 / (1/2) = 4*2 =8
E. x^2*y = (-2)^2*(1/2) =2
Answer: option C
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
A.23
B.25
C.40
D.46
Answer: C.40
Explanation: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Question: In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and chuck are not seated next to each other?
A.72
B.48
C.56
D.76
Answer: A.72
Explanation: When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....
These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
Answer :A
Question: The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is :
A.6 months
B.8 months
C.9 months
D.10 months
Answer: D.10 months
Explanation: Solution
P.W = Rs. (1760 - 160) = Rs. 1600.
∴ S.I on Rs.1600 ar 12% is Rs. 160.
∴ Time = 100 x 160/1600x12 ) = 5/6years = ( 5/6x12 ) months = 10 months.
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?
A.532 m
B.537 m
C.500 m
D.846 m
Answer: C.500 m
Explanation: 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
Question: Amithab's average expenditure for the January to June is Rs. 4200 and he spends Rs.1200 in January and Rs.1500 in july.The average expenditure for the months of febraury to July is
A.Rs. 4250
B.Rs. 4228
C.Rs. 4128
D.Rs. 4988
Answer: A.Rs. 4250
Explanation: Amithab's total expenditure for Jan - June = 4200 x 6 = 25200
Expenditure for Feb - June = 25200-1200 = 24000
Expenditure for the months of Feb - July = 24000 + 1500 =25500
The average expenditure = {25500}/{6}=4250
Answer: A
Question: A taxi driver states that his cab number is divisible by the no 2,3,4,5,6 with a remainder of 1 and when the number is divided by 11 it does not give any remainder
A.101
B.11
C.121
D.111
Answer: C.121
Explanation: on finding the LCM of 2,3,4,5 & 6 we get the value as 60 ,on adding 1 to 60 satisfy the first condition
Now 61 not divisible by 11
Then multiply 60 by 2,
we get 120: 120+1, 121 is exactly divisible by 11
ANSWER:C
Question: Company S produces two kinds of radios: basic and deluxe. Of the radios produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe radio as it does to produce a basic radio, then the number of hours it took to produce the deluxe radio last month was what fraction of the total number of hours it took to produce all the radios?
A.7/17
B.2/3
C.8/17
D.6/17
Answer: A.7/17
Explanation: No of basic radios was 2/3 of total and # of deluxe radios was 1/3 of total, let's assume total=12, then Basic=8 and Deluxe=4.
Now, if time needed to produce one Deluxe rdio is 1 unit than time needed to produce one Basic radio would be 7/5 units. Total time for Basic would be 8*1=8 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 8+28/5 -->68/5 deluxe/total=28/5 / 68/5 = 28/68 =7/17
Answer: A.
Question: A train 100 meters long completely crosses a 300 meters long bridge in 12 seconds. What is the speed of the train is?
A.32 kmph
B.76 kmph
C.120 kmph
D.43 kmph
Answer: C.120 kmph
Explanation: S = (100 + 300)/12
= 400/12 * 18/5
= 120
Answer:C
Question: One student to pass the subject as probability 1/4. another man to get driving licence and student passed subject probability 1/6. find the probability man get driving licence.
A.1/3
B.2/3
C.4/3
D.5/3
Answer: B.2/3
Explanation: Let the probability of the man get driving licence is x.
so, 1/4 * x = 1/6
x = 2/3.
ANSWER:B
Question: In how many ways can be 5 boys and 5 girls sit around circular table so that no two boys sit next to each other?
A.(5!)^2
B.(6!)^2
C.5!4!
D.11!
Answer: C.5!4!
Explanation: first fix one boy and place other 4 in alt seats so total ways is 4!
now place each girl between a pair of boys... total ways of seating arrangement of girls 5!
total is 5!*4!
ANS C
Question: R is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in R?
I. 9
II. 15
III. 27
A.I only
B.II only
C.I and II only
D.I and III only
Answer: C.I and II only
Explanation: Ans: C
R->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Question: A waiter's salary consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips ?
A.4/9
B.5/4
C.5/8
D.5/9
Answer: D.5/9
Explanation: Income = salary (s) +tips = s + s*5/4 = s*9/4
Tips = s*5/4
fraction of his income came from tips = (s*5/4)/(s*9/4)= 5/9
ANSWER:D
Question: What will come in place of (a) in the following expression?
a - 796.21 + 498.05 = 215.50 – 300.01
A.431.65
B.488.6
C.388.67
D.431.2
Answer: A.431.65
Explanation: Explanation:
a - 796.21 + 498.05 = 215.50 - 425.01
a = 413.65
ANSWER: A
Question: Mangala completes a piece of work in 30 days, Raju completes the same work in 45 days. If both of them work together, then the number of days required to complete the work is
A.18 days
B.6 days
C.8 days
D.10 days
Answer: A.18 days
Explanation: 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.
That is, the required No. of days = 30 × 45/75 = 18 days.
Answer : A
Question: In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5
B.3
C.4
D.5
Answer: B.3
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 120/40 = 3 sec.
Answer: Option B