mathewhe/aqua_rat huggingface dataset:
Question: Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 05:00 and starts climbing at a constant pace. Ken starts climbing only at 07:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
(A) 13:00
(B) 13:30
(C) 14:00
(D) 15:00
(E) 12:00
Rationale: Both Sari and Ken climb in the same direction.
Speed of Sari = 700/2 = 350 meters/hr (since she covers 700 meters in 2 hrs)
Speed of Ken = 500 meters/hr
At 8:00, distance between Ken and Sari is 700 meters. Ken needs to cover this and another 50 meters.
Time he will take = Total distance to be covered/Relative Speed = (700 + 50)/(500 - 350) = 5 hrs
Starting from 7:00, in 5 hrs, the time will be 12:00
Answer (E)
Answer: (E) 12:00
Question: list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000
(A) $28,000
(B) $28,500
(C) $30,200
(D) $30,800
(E) $31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,000, $32,000, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,000 + $32,000 = $63,000
The median salary is $31,500.
E
Answer: (E) $31,500
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.64, find the sum of money?
(A) 328
(B) 262
(C) 72
(D) 205
(E) 267
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 64
41 ---- ? => Rs.328
Answer: A
Answer: (A) 328
Question: 3 persons (1 couple and 1 single) are seated at random in a row of 5 chairs. What is the probability that the couple does not sit together?
(A) 5/7
(B) 4/5
(C) 2/5
(D) 3/5
(E) 11/18
Rationale: The single person is no different from an empty chair :lol:
Thus, there are 202=10202=10 ways to pick two chairs for the couple, but only 4 in which they sit together (CCEEE, ECCEE, EECCE, EEECC).
1 - 4/10 = 3/5 is the answer.D
_
Answer: (D) 3/5
Question: The price of sugar is increased by 20%. If the expenditure is not allowed to increase, the ratio between the reduction in consumption and the original consumption is :
(A) 1:3
(B) 1:4
(C) 1:6
(D) 1:5
(E) None
Rationale: Explanation:
Reduction in consumption
=(20/120×100)%=50/3%
Reduction in consumption/Original consumption=(50/3×1/100)
=1/6=1:6
Correct Option: C
Answer: (C) 1:6
Question: A Man can row upstream at 87kmph and downward stream at 47 kmph. Find Man's rate of the current
(A) 87km/hr
(B) 20km/hr
(C) 65km/hr
(D) 2.8km/hr
(E) 4.4km/hr
Rationale: Rate of the current=1/2(87-47)km/hr
=20km/hr
correct option is :B
Answer: (B) 20km/hr
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 65 Kmph
(B) 68 Kmph
(C) 97 Kmph
(D) 16 Kmph
(E) 17 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: (B) 68 Kmph
Question: The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840. At what rate of intrest the same amount of interest can be received on the same sum after 5 years.
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 9%
Rationale: Explanation:
Here firstly we need to calculate the principal amount, then we can calculate the new rate.
P=S.I.∗100 /R∗T
P=840∗100/5∗8
P=2100
Required Rate = 840∗100/5∗2100R=8%
Option D
Answer: (D) 8%
Question: Three interviewers, A, B, and C are interviewing 50 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 20 applicants, B admitted 22 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
(A)  4
(B)  0
(C)  6
(D)  8
(E)  12
Rationale: If A admitted 20 are overlapping with B admission of 22 But C does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : B
Answer: (B)  0
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices?
(A) 10
(B) 15
(C) 14
(D) 16
(E) 18
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2=2^4=16.
Answer: D.
Answer: (D) 16
Question: For how many values of N, is |||N - 5| -10| -5| = 2?
(Those ls are mods)
(A)  0
(B)  2
(C)  4
(D)  8
(E)  More than 8
Rationale: I think its 8
|||N-5|-10|-5| =2
let |N-5| = a which makes above
||a-10|-5| =2
let |a-10| = b which makes
|b-5| = 2
now for the above b can take 3, 7
for every b =3 a can have 13, 7
and for b = 7 a can have 17 and 3
so 'a' has four solutions 13, 7, 17 and 3
for a = 13; x has 18 or -8 thus has 2 for every combination hence 4x2 = 8
answer D
Answer: (D)  8
Question: Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder
(A) 1235
(B) 1456
(C) 1567
(D) 1678
(E) 1631
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 35
5x = 1330
x = 266
Large number = 266+1365 = 1631
E
Answer: (E) 1631
Question: Praveen starts business with Rs.3780 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
(A) s.7500
(B) s.8000
(C) s.8500
(D) s.9720
(E) s.6000
Rationale: Let Hari’s capital be Rs. x. Then, 3780 * 12/7x = 2/3
=> 14x = 136080
=> x = 9720.
ANSWER:D
Answer: (D) s.9720
Question: A 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 287
(B) 350
(C) 828
(D) 277
(E) 400
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/42 = 50/3
3x + 900 = 2200 => x = 400 m.
Answer: E
Answer: (E) 400
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
(A) 6
(B) 5
(C) 2
(D) 7
(E) 2
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs. Answer: A
Answer: (A) 6
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
(A) 12
(B) 88
(C) 66
(D) 44
(E) 12
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12
Answer:C
Answer: (C) 66
Question: The average score of a cricketer for ten matches is 38.9 runs. If the average for first six matches is
42, then average for last four matches is
(A) 33.25
(B) 32.25
(C) 34.25
(D) 34.5
(E) None of these
Rationale: Explanation:
=(38.9×10)−(42×6)4
=(1216−750)4=34.25
Answer: Option C
Answer: (C) 34.25
Question: If a is an even integer and b is an odd integer which of the following must be an even integer :
(A) a/b
(B) ab
(C) 2a+b
(D) 2(a+b)
(E) option A B and D
Rationale: a=even = e.g 6
b= odd = e.g 3
A. even/odd for example 6/3 = 2 =even
B. even * odd = 6 * 3 = 18 = even
C. 2*even + odd = even + odd = odd
D. 2(even + odd) = 2(odd) = even
Hence E it is.
Answer: (E) option A B and D
Question: a, b, c, and d are positive consecutive odd integers and a < b < c < d.
If you take away the last number from the square of the first number, you get a number that is three more than the sum of the last three numbers. What is the product of ac?
(A) 35
(B) 77
(C) 101
(D) 39
(E) 18
Rationale: aa - d = b + c + d + 3
Simplify: aa = b + c + 2d + 3
We know that aa is the square of an odd number. Here are some possibilities: 3x3 = 9, 5x5 = 25, 7x7 = 49, 9x9 = 81, 11x11 = 121.
We want to find a sequence where the following odd numbers are very close to the square.
The sequence 11, 13, 15, 17 won't work because 121 is much bigger than 45 (the sum of the other three).
The sequence 3, 5, 7, 9 won't work because 9 is much smaller than 21 (the sum of the other three).
The sequence 7, 9, 11, 13 puts us on the right track: 49 is not that much bigger than 33 (the sum of the other three). So let's try the rest of the equation:
49 = 9 + 11 + 13x2 + 3
Simplify: 49 = 20 + 26 + 3
Add: 49 = 46 + 3
Add: 49 = 49
Done! The sequence is 7, 9, 11, 13. The question asked for the product of ac, or 7x11 = 77 (option B).
Answer: (B) 77
Question: The averge score of a cricketer for ten matches is 41 runs. If the average for the first six matches is 35. Then find the average for the last four matches?
(A) 50
(B) 55
(C) 60
(D) 45
(E) 48
Rationale: sum of last 4 matches = (10 × 41) – (6 × 35)=200
Average =200/4
= 50
ANSWER:A
Answer: (A) 50
Question: A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week?
(A) 605
(B) 505
(C) 105
(D) 100
(E) 200
Rationale: earning 35 surveys using her cell phone = 13*35 = 455
balance 15 surveys = 10 x 15 = 150
Total = 455+150 = 605
Answer : A
Answer: (A) 605
Question: Along a yard 255 metres long, 18 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
(A) 18
(B) 15
(C) 10
(D) 11
(E) 12
Rationale: Explanation:
18 trees have 17 gaps between them,
Required distance (281/17) = 15
Option B
Answer: (B) 15
Question: Lucas and David are partners in a business, they invested Rs. 30,000 and Rs. 45,000 respectively.If the business yielded a total profit of Rs. 18,500, what is David's share?
(A) 13400
(B) 11520
(C) 15700
(D) 11100
(E) 11142
Rationale: Explanation:
Ratio of their shares = 30,000 : 45,000 = 2 : 3.
David's share = Rs. (18,500 * 3/5) = Rs. 11100.
Answer: D) 11100
Answer: (D) 11100
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 46 years now, the son's age five years back was?
(A) 16 years
(B) 14 years
(C) 18 years
(D) 19 years
(E) 15 years
Rationale: Let the son's present age be x years.
Then, (46 - x) = x
2x = 46 => x = 23
Son's age 5 years back = (23 - 5)
= 18 years.
Answer: C
Answer: (C) 18 years
Question: If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?
(A) 10
(B) 13
(C) 18
(D) 26
(E) 50
Rationale: a/b = 2.86
a/b = 286/100
a/b = 143/50
a = 143/50*b
We require to find from the available 5 options that must be a divisor of a"
This also means which of the following 5 options can divide 143 evenly
(Ignore b as its value unknown; Ignore 50 as in denominator)
Only option B = 13 best fits in
Answer = 13
ANSWER:A
Answer: (A) 10
Question: A metallic sheet is of rectangular shape with dimensions 50 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
(A) 5440
(B) 5120
(C) 6420
(D) 7500
(E) 8960
Rationale: l = (50 - 16)m = 34 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (34 x 20 x 8) m3 = 5440 m3.
Answer: Option A
Answer: (A) 5440
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49 m2
(B) 50 m2
(C) 53.5 m2
(D) 55 m2
(E) 57 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2.
Answer: Option A
Answer: (A) 49 m2
Question: A monkey ascends a greased pole 18 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
(A) 21st
(B) 22nd
(C) 33rd
(D) 24th
(E) None of these
Rationale: In 2 minutes, he ascends = 1 metre
âˆ´ 16 metres, he ascends in 32 minutes.
âˆ´ He reaches the top in 33rd minute.
Answer C
Answer: (C) 33rd
Question: If u r genius solve it:-
50 * 15 = 12
40 * 14 = 11
30 * 13 = ?
(A) 2
(B) 12
(C) 6
(D) 8
(E) 10
Rationale: Logic :
50*15=750=7+5+0=12
40*14=560=5+6+0=11
So 30*13=390=3+9+0=12
Answer : B
Answer: (B) 12
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
(A) 21
(B) 77
(C) 99
(D) 17
(E) 13
Rationale: Let the pipe B be closed after x minutes.
30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24 = 21.
Answer: E
Answer: (E) 13
Question: Five little kids were walking down the street. At a shop, they saw three brands of chocolates viz. Cadbury, Nestle and Ferrero there. The shopkeeper has three chocolates which are of three different flavors of each brand. The kids bought all the chocolates available and decided to play a game. The chocolates will be distributed only to the winners of that game. Also they have decided that any winner cannot have all three brands of chocolates as his prize. Find the number of ways in which the chocolates can be distributed when there are four winners of the game and the best of them gets at least 4 chocolates?
(A) 12312
(B) 22536
(C) 4320
(D) 11268
(E) 45072
Rationale: Since, one child cannot have more than two brands of chocolates, therefore, one child can get a maximum of six chocolates.
When there are four winners, the winners can have the chocolates in the following possible way
Case I
One of them gets six chocolates and the other three get one each.
The one who gets six chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.
The three chocolates of the same brand will be distributed among the other three in 3! ways.
Hence, the total number of ways = 4 × 3 × 6 = 72
Case II
One of them gets 5 chocolates, one of them gets 2 chocolates and the other two get 1 each.
Kid with 5 chocolates:
The one who gets five chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.
After choosing the two brands (say AB), he can get all three chocolates of one brand in 2 ways (i.e. either A or B). The other two chocolates can be chosen from the second brand in 3 ways. Thus, there are 4 × 3 × 2 × 3 = 36 ways
Kid with 2 chocolates:
This person can be chosen in 3 ways. Now, he can either get two chocolates from the same brand or from two different brands.
Thus, there are 6 × 3 = 18 ways
Kids with 1 chocolate each
The remaining chocolates can be distributed between the two remaining winners in 2 ways.
Therefore, total number of ways = 36 × 18 × 2 = 1296 ways.
Case III
Similarly for four chocolates the following combinations are possible:
a) 4 3 1 1
The number of ways = 4 × 3 × [{6 × 3(1 + ( 6 + 3))} + {1 × 9 × 3 (1 + 6)}] × 2 = 8856
b) 4 2 2 1
The number of ways = 4 × 3 × [{6 × 3(2 × 6 × 3 + (3 + 9))} + {9 × (9 + 9)}] = 12312
Since, the best of them can’t have less than 4 chocolates the above are the only cases applicable.
Hence, the total number of ways = 72 + 1296 + (8856 + 12312) = 22536.
answer B
Answer: (B) 22536
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
(A) 7%
(B) 5%
(C) 9%
(D) 4%
(E) 1%
Rationale: Explanation:
SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100 =
0.04 * 100 = 4%
Answer: D
Answer: (D) 4%
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.3 m and its walls are 5 cm thick. The thickness of the bottom is:
(A) 90 cm
(B) 3 dm
(C) 1 m
(D) 1.1 cm
(E) None of these
Rationale: Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (130 - x)] = 8000 × 1000
=> 320 × 250 × (130 - x) = 8000 × 1000
=> (130 - x) = 8000×1000/320=
100
=> x = 30 cm = 3 dm.
Answer: B
Answer: (B) 3 dm
Question: A man sells a horse for Rs.680 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 287
(B) 679
(C) 780
(D) 860
(E) 898
Rationale: CP = SP + 1CP = SP - g
680 + x = 980 - 2x
3x = 300 => x
= 100
CP = 680 + 100
=780
Answer:C
Answer: (C) 780
Question: John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 60 miles per hour, what is v in miles per hour?
(A) 30
(B) 40
(C) 50
(D) 55
(E) 70
Rationale: Let distance be D.
We can find the total time & equate it, which comes as:
0.8D / 80 + 0.2D / v = D / 60
=> v = 30
ANSWER:A
Answer: (A) 30
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
(A) 60 gallons
(B) 100 gallons
(C) 120 gallons
(D) 180 gallons
(E) 130 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
ANSWER:C
Answer: (C) 120 gallons
Question: The speeds of three motor bikes are in the ratio 6 : 4 : 2. The ratio between the time taken by them to travel the same distance is :
(A) 2 : 5 : 6
(B) 2 : 4 : 6
(C) 2 : 3 : 6
(D) 2 : 3 : 7
(E) 1 : 3 : 6
Rationale: Ratio of time taken :
1/6 :1/4 : 1/2 = 2 : 3 : 6
ANSWER:C
Answer: (C) 2 : 3 : 6
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
(A) 20/65
(B) 20/63
(C) 20/68
(D) 20/66
(E) 20/29
Rationale: Required probability
= (5C3 . 4C1)/9C4
= (10 * 4)/126
= 20/63
Answer:B
Answer: (B) 20/63
Question: An arithemetic sequence of numbers begins p, 2p + 3, 4p + 4... What is the 12th member of this sequence?
(A) A)57
(B) B)40
(C) + 13
(D) D)53
(E) + 13
Rationale: Common difference of an arithmetic series is constant.
2p+3-p=4p+4-2p-3
p=2
1, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57
Ans:A
Answer: (A) A)57
Question: The sector of a circle has radius of 18 cm and central angle 135o. Find its perimeter?
(A) 78.4 cm
(B) 11.5 cm
(C) 91.8 cm
(D) 92.5 cm
(E) 99.5 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 18) + 2(18)
= 42.4 + 36
= 78.4 cm
Answer:A
Answer: (A) 78.4 cm
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) 59005
(B) 59007
(C) 59002
(D) 59000
(E) 59001
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000.Answer: D
Answer: (D) 59000
Question: Question: What is the remainder when I= (1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
(A)  0
(B)  25
(C)  49
(D)  81
(E)  100
Rationale: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when I=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Answer: (D)  81
Question: A shop owner buys a 1280 ounce bag of sugar for resale. How many 1 pound containers can she sell?
(A)  80
(B)  90
(C)  100
(D)  110
(E)  120
Rationale: 1 pound = 16 ounces.
1280 ounces / 16 = 80 pounds.
Answer: A.
Answer: (A)  80
Question: A hostess must seat 10 people around 2 circular tables. Table 1 can hold 6 people, table 2 can hold 4 people. If the hostess always seats people at Table 1 first and 2 seating arrangements are said to be different only when the positions of people are different relative to each other at the table, how many seating arrangements are possible?
(A) 5*210
(B) 15!*210
(C) 120*3!
(D) 5!*3!*210
(E) 5!*5!*3!
Rationale: 1)since there are two tables, the hostess has to choose 6 out of 10 and the remaining 4 will go to other table..
so WAYS= 10C6=10!/6!4!=210..
2)now 6 on the Table 1 can be seated in (6-1)! ways
3)and 4 on the Table 1 can be seated in (4-1)! ways
TOTAL ways=210*5!*3!
D
Answer: (D) 5!*3!*210
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
(A) 21 years
(B) 31 years
(C) 44 years
(D) 48 years
(E) 75 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row
= 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102 = 31 years.
Answer:B
Answer: (B) 31 years
Question: If DHOOM is coded as 25 and RACE is coded as 14, then FASHION is coded as
(A) 12
(B) 14
(C) 36
(D) 48
(E) None
Rationale: DHOOM = 4+8+15+15+13=55 i.e 5*5=25
RACE= 18+1+3+5=27 i.e 2*7=14
Fashion 6+1+19+8+9+15+14 =72 7*2=14
ANSWER:B
Answer: (B) 14
Question: 1=6,2=36,3=363,4=364,5=365, then 36=?
(A) 1
(B) 2
(C) 345
(D) 445
(E) 235
Rationale: 1=6,2=36,3=363,4=364,5=365, then 36=?
36=2
check the second eqn.
ANSWER:B
Answer: (B) 2
Question: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 4200 envelopes.
(A) 2
(B) 3
(C) 4
(D) 6
(E) 60/7
Rationale: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter
1. Work done in 1 hr by A is 2000 envelopes
2. Work done in 1 hr by A and C is 3000 envelopes
3. So work done in 1 hr by C is 1000 envelopes
4. Work done in 1 hr by B and C is 2400 envelopes
5. So work done in 1 hr by B is 1400 envelopes
6. So to process 4200 envelopes B will take 4200/1400 hrs = 3 hrs
So the answer is choice B
Answer: (B) 3
Question: Truck P and Truck Q drive on the highway in the same direction at respective rates of 70 kph and 75 kph. If Truck Q is 5 km behind Truck P, by how much does Truck P need to increase the speed to catch up with Truck P in 20 minutes?
(A) 6 kph
(B) 8 kph
(C) 10 kph
(D) 12 kph
(E) 14 kph
Rationale: Truck Q needs to gain 5 km in 20 minutes.
The relative speed difference needs to be 5 km / 20 minutes = 15 km/hour
Truck Q needs to increase up to 85 kph, thus an increase in 10 kph.
The answer is C.
Answer: (C) 10 kph