mathewhe/aqua_rat huggingface dataset:
Question: In how many different E ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
(A) 70
(B) 288
(C) 576
(D) 10,080
(E) 20,160
Rationale: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves
Answer E= (4!)^2 = 576 or C
Answer: (C) 576
Question: 0.999991+0.111119=?
(A) 1
(B) 1.0001
(C) 1.0021
(D) 1.11111
(E) 1.1111
Rationale: 0.999991 + 0.111119
= 0.999991 + 0.11111 + 0.00009
= (0.999991 + 0.00009) + 0.11111
= 1 + 0.11111
= 1.11111
D
Answer: (D) 1.11111
Question: If c persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
(A) z
(B) x
(C) x/y
(D) z/x
(E) y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
c person can do z jobs in y days..
so c person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: (E) y/z
Question: Which of the following inequalities is equivalent to –2 < y< 4 ?
(A)  | y– 2 | < 4
(B)  | y– 1 | < 3
(C)  | y+ 1 | < 3
(D)  | y+ 2 | < 4
(E)  None of the above
Rationale: First remove the mod
then set the expression to 0
then get a value of y
then add and subtract the value from the given number on the RHS
Lets try with an example (B) --------------> | y– 1 | < 3
First remove the mod -------------------> y-1
then set the expression to 0--------------> y-1=0
then get a value of y---------------------> y=1
then add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2
the range become -2 to 4 correct answer
Now try its with an incorrect option (C) | ----------> |y+ 1 | < 3
First remove the mod --------------------------> y+1
then set the expression to 0----------------------> y+1=0
then get a value of y------------------------------> y=-1
then add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4
the range become -4 to 2 Incorrect
THE CORRECT ANSWER IS B
Answer: (B)  | y– 1 | < 3
Question: If Suresh distributes his pens in the ratio of 1/2 : 1/4 : 1/5 : 1/7 between his four friends A, B, C and D, then find the total number of pens Suresh should have?
(A) 153
(B) 150
(C) 100
(D) 125
(E) 135
Rationale: EXPLANATION:
Here, A : B : C : D = 1 / 2 : 1 / 4 : 1 / 5 : 1 / 7
1) L.C.M of 2, 4, 5, 7 is 140
2) Find the number of pens each friend received --------- (To find no. of pens each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/2) x 140 = 70
B = (1/4) x 140 = 35
C = (1/5) x 140 = 28
D = (1/7) x 140 = 20
3) Total number of pens = (70 x + 35 x + 28 x + 20 x) = 153 x
Minimum number of pens (x) = 1
Therefore, total number of pens = 153 pens.
ANSWER IS A
Answer: (A) 153
Question: A tin of oil was 4/5 full. When 6 bottles of oil were taken out and four bottles of oil were poured into it, it was 3/4 full. how many bottles of oil can the tin contain?
(A) 10
(B) 40
(C) 46
(D) 36
(E) 25
Rationale: Suppose X bottles can fill the tin completely
Then Present oil = 4/5 X
after 6 bottles taken out it is 4/5 X - 6
after four bottles poured in it is 4/5 X - 6 + 4
now the oil level is 3/4X
so 4/5 X - 6+4 = 3/4X ===> 4/5 X - 3/4 X = 6-4
X/20=2
X=40
Therefore required no of bottles = 40
so 40 bottles of oil can fill the tin.
the answer is option B) 40.
Answer: (B) 40
Question: The total number of problems in the mathematics and algebra books is 28 more than the total number of problems in the algebra and geometry books. How much lesser is the number of problems in the geometry book as compared to the mathematics book?
(A) 30
(B) 18
(C) 28
(D) 25
(E) 32
Rationale: (Mathematics + Algebra) - (Algebra + Geometry) = 28
Mathematics - Geometry = 28
Answer: C
Answer: (C) 28
Question: With both inlets open, a water tank will be filled with water in 20 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
(A) 9,000
(B) 1,500
(C) 1,750
(D) 1,200
(E) 1,300
Rationale: The work Done by Inlet A and B together in 1 min = 1/20
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/20)- (1/120) =1/24
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/24)- (1/120) = 50 Cubic meter
i.e. 1500 Cubic Meter
Answer: option B
Answer: (B) 1,500
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.3 km?
(A) 600 m
(B) 325 m
(C) 300 m
(D) 400 m
(E) 100 m
Rationale: B
325 m
Distance covered by Amar = 18/4.8 (1.3km) = 3/8(1300) = 325 m
Answer is B
Answer: (B) 325 m
Question: Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank ?
(A) 8 hrs
(B) 9 hrs
(C) 18 hrs
(D) 36 hrs
(E) 33 hrs
Rationale: 2 taps can fill in 4 hrs
With leak it will take 4 1/2 hrs
now leak can empty in 1/4-1/(4 (1/2))
1/4-8/9=1/36. so it an empty tank in 36 hrs
ANSWER:D
Answer: (D) 36 hrs
Question: A merchandise feedback online portal accords ‘ratings’ to a product by recording the percentage of customers who have reported their views as either ‘satisfied’ or ‘unsatisfied’ only. The portal rounds off the exact percentage value calculated to the closest integral value. If the percentage of unsatisfied customers as recorded by the portal is 57%, what is the LEAST possible number of people that could have reported their views as ‘satisfied’ ?
(A) 2
(B) 3
(C) 12
(D) 43
(E) 57
Rationale: 57% unsatisfied . So ~43% satisfied
But 100% should be an integer only and since the above percentages are approximations 100% should be as close as possible to an integer.
Now substitute value
[1] If 43% is 2 what is 100% -> 200/43 is not giving a number which is closest to an integer.
[2] If 43% is 3 what is 100% -> 300/43 [43*7=301] ...therefore closest possible to an integer. [It also satisfies the least possible and hence we need not check for other choices which are greater than 3]
Therefore Ans is B.
Answer: (B) 3
Question: There are 780 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 75
(B) 100
(C) 125
(D) 130
(E) 225
Rationale: female = x
Male = 780-x
x/2 + 780-x/4 = 1/3* (780)= 260
x= 260
x/2 = 130 is supposed to be the answer
M is missing something
Correct Option D
Answer: (D) 130
Question: Find the odd man out. 742, 743, 633, 581, 871, 990, 532
(A) 532
(B) 990
(C) 581
(D) 743
(E) None of these
Rationale: Explanation :
In all numbers except 581, the difference of third and first digit is the middle digit. Answer : Option C
Answer: (C) 581
Question: A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 400 miles apart, at what time will the trains pass each other?
(A) 12:40pm
(B) 12:49pm
(C) 12:55pm
(D) 1:00pm
(E) 1:04pm
Rationale: Train A: going from K to T
Train B: going from T to K
First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles
They have 400-40=360 miles to travel to meet each other.
I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph
Divide Distance/Rate to find total time each will travel:
360/400>>> 54 Minutes to meet
12:10+54 minutes = 01:04 or Answer E
Answer: (E) 1:04pm
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
(A) 8 balls.
(B) 4 balls.
(C) 7 balls.
(D) 5 balls.
(E) 6 balls.
Rationale: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) * x = 26
x = 26 * (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by
(1 / 8) of 48 = 6 balls. correct answer E
Answer: (E) 6 balls.
Question: Each employee of Company X is a member of precisely 1 of 3 shifts of employees. Among the 60 members of the first shift, 20 percent participate in the pension program; among the 50 members of the second shift, 40 percent participate in the pension program; and among the 40 members of the third shift, 10 percent participate in the pension program. What percent of the workers at Company X participate in the pension program?
(A) 20%
(B) 24%
(C) 36%
(D) 37.5%
(E) 70%
Rationale: 60 members & 20 percent = 12
50 members & 40 percent = 20
40 members & 10 percent = 4
=> 36/150∗100 = 24%
Answer B
Answer: (B) 24%
Question: Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 2/5 of the juniors is equal to 1/3 of the seniors, what fraction of the students in the room are juniors?
(A) 3/20
(B) 1/3
(C) 5/12
(D) 12/17
(E) 5/11
Rationale: Let total number of juniors= J
total number of seniors =S
(2/5) J = (1/3) S
=> S = 6/5 J
Total number of students = J+S = (11/5) J
Fraction of the students in the room are juniors = J/(J+S) = J/[(11/5) J]
=5/11
Answer E
Answer: (E) 5/11
Question: A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?
(A) 76 days
(B) 21 days
(C) 97 days
(D) 45 days
(E) 97 days
Rationale: WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer:B
Answer: (B) 21 days
Question: The total of the ages of Jayant,Prem and Saransh is 93 years.Ten years ago,the ratio of their ages was 2:3:4.What is the present age of Saransh ?
(A) 24 years
(B) 32 years
(C) 34 years
(D) 38 years
(E) None of these
Rationale: Solution
Let the ages of Jayant,Prem and Saransh 10 years ago be 2x,3x and 4x years respectively.
Then,(2x +10)+ (3x +10) +(4x +10)= 93 ⇔ 9x = 63 ⇔ x =7.
∴ Saransh's present age = (4x +10)=38 years. Answer D
Answer: (D) 38 years
Question: A copy machine, working at a constant rate, makes 25 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
(A) 90
(B) 2,400
(C) 4,500
(D) 5,400
(E) 324,000
Rationale: Together the two machines make 25+55=80 copies per minute. So, in half an hour they will make 80*30=2,400 copies.
Answer: B.
Answer: (B) 2,400
Question: 3,7,12,18,25,33,..............7th terms
(A) 43
(B) 42
(C) 63
(D) 65
(E) 78
Rationale: 3+4=7
7+5=12
12+6=18
18+7=25
25+8=33
33+9=42
ANSWER:B
Answer: (B) 42
Question: Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 24 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
(A) 64
(B) 72
(C) 86
(D) 98
(E) 101
Rationale: Use the options.
The options which after getting added to 24 shows a cube of a number could be right.
Here
64+24 = 88
72+24 = 96
86+24 = 110
98+24 = 122
101+24=125 ---(5*5*5)
So we have 101 as the answer!
E
Answer: (E) 101
Question: If a function f is defined by f(x)= (2x-1)/3 for all non zero numbers x. If f(a) = 1 and f(ab) = 1/9 then b= ?
(A) 3
(B) 1/3
(C) -1/3
(D) -3
(E) -12
Rationale: Given that f(x)= (2x-1)/3 and f(a) = 1, then f(a) =(2a-1)/3=1 ===> a=2, then backsolve using the answer choices:
f(ab) = f(2b) = 1/6
A) 3 ===> f(2*3) = f(6) = (12-1)/3 = 11/3
B) 1/3 ===> f((2*1/3) = f(2/3) = (4/3-1)/3 = 1/9 WINS
C) -1/3 ===> f(2*-1/3) = f(-2/3) = (-4/3-1)/3 = -7/9
D) -3 ===> f(2*-3) = f(-6) = (-12-1)/3 = -13/3
E) -12 ===> f(2*-12) = f(-24) = (-24-1)/3 = -25/3
Answer: B
Answer: (B) 1/3
Question: A small company reduced its faculty by approximately 13 percent to 263 employees. What was the original number of employees?
(A) A)182
(B) B)208
(C) C)220
(D) D)224
(E) E)302
Rationale: If x is the original number of employees, then after 13% reduction in employees number is .87x
but we are given .87x = 263
x = 302
So the original number of employees is 302
Correct Answer - E
Answer: (E) E)302
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 221.8
(B) 127.5
(C) 881.2
(D) 223.1
(E) 122.5
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.Answer:B
Answer: (B) 127.5
Question: A number a is squared and then multiplied by negative 3. The result of this operation is equal to three times the sum of three times a and 1. What is one possible value of a ?
(A) 25
(B) 3
(C) 4
(D) 1
(E) 8
Rationale: -3*a^2=3(3a+1)
a= -1 or -1
a=-1=B
ANSWER:D
Answer: (D) 1
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped four times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 7?
(A) 3/8
(B) 1/16
(C) 1/8
(D) 1/2
(E) 1/4
Rationale: There are 16 possible outcomes but only one outcome (2222) has a sum greater than 7.
P(the sum is greater than 7) = 1/16
The answer is B.
Answer: (B) 1/16
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 7 liters
(B) 15 liters
(C) 10 liters
(D) 9 liters
(E) 19 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
ANSWER:C
Answer: (C) 10 liters
Question: Find the remainder R when 12^190 is divided by 1729 ?
(A) 12
(B) 1
(C) 1728
(D) 1717
(E) 4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder R -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: (D) 1717
Question: The compound interest on Rs.30,000 at 7% per annum is Rs. 4347. The period (in years) is:
(A) 2
(B) 2 ½
(C) 3
(D) 4
(E) 3 ½
Rationale: Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 (1 + 7/100)^n = 34347
(107/100)^ n = 34347/30000 = 11449/10000 = (107/100)^2
So the period is 2 years.
ANSWER:A
Answer: (A) 2
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $9,000, what is the bonds face value?
(A)  $6,000
(B)  $6,750
(C)  $7,425
(D)  $7,200
(E)  $9,375
Rationale: Interest = 0.05*face value = 0.04*9,000 --> face value = 0.04*9,000/0.05 = 7,200.
Answer: D.
Answer: (D)  $7,200
Question: A work which could be finished in 7 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 22
(B) 20
(C) 60
(D) 71
(E) 11
Rationale: x ------- 7
(x + 10) ---- 6
x * 7 = (x + 10)6
x = 60
\Answer: C
Answer: (C) 60
Question: A basket contains 6 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: The total number of ways to choose 2 apples is 6C2 = 15
The number of ways that include the spoiled apple is 5C1 = 5
P(the spoiled apple is included) = 5/15 = 1/3
The answer is A.
Answer: (A) 1/2
Question: The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is
(A) 3 10
(B) 2 10 – 1
(C) 3 10 – 1
(D) 2 10
(E) None of these
Rationale: Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions.
Hence, the number of all possible selections is 3 10 – 1.
Answer C
Answer: (C) 3 10 – 1
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 277
(B) 278
(C) 245
(D) 278
(E) 251
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x)
= 750 => x
= 245 m
Answer: Option C
Explanation:
Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer:C
Answer: (C) 245
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) 11292
(B) 31292
(C) 11392
(D) 11750
(E) 11729
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Answer: (D) 11750
Question: In one hour,a boat goes 13 km along the stream and 5 km against the stream.The speed of the boat in still water (in km/hr) is :
(A) 3
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: Solution
Speed in still water =1/2(13+5)kmph.= 9 kmph. Answer D
Answer: (D) 9
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-4)(x+10)(2x-5) = 0?
(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=4,x=-10andx=5/2=2.5. So, three solutions present in our set of 12 distinct numbers, therefore P=3/12=1/4.
Answer: C.
Answer: (C) 1/4
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 69. What is that number?
(A) 3.5
(B) 6
(C) 8
(D) 7
(E) 4
Rationale: Let the number be x. Then,
3(2x + 9) = 69
2x = 14 => x = 7
ANSWER:D
Answer: (D) 7
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 75% profit on the first article and 75% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 768
(C) 276
(D) 750
(E) 279
Rationale: Profit on first article = 75% of 1000 = 750.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: D
Answer: (D) 750
Question: If the day before yesterday was Thursday, when will Sunday be?
(A) Day after tomorrow
(B) Tomorow
(C) Two days after today
(D) Today
(E) none
Rationale: Explanation:
Day before yesterday was Thursday
=>Yesterday was a Friday
=> Today is a Saturday
=> Tomorrow is a Sunday
Answer: Option B
Answer: (B) Tomorow
Question: Ms. Lily sold two properties, X and Y, for $26,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
(A) $2166.67
(B) $2226.67
(C) $2326.67
(D) $2426.67
(E) $2526.67
Rationale: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...
Total %Loss = (Common Gain% or Loss%/10)^2
Hence Here Loss% = (20/10)^2 = 4%
which means he recovered only 96% of his investment which amount to a total revenue = 26000 + 26000 = 52000
i.e. 96% of cost = 52000
therefore, 4% of cost (Loss) = $2166.67
Answer: A
Answer: (A) $2166.67
Question: A certain basketball team played seven games and scored an average of 50 points per game. If, in the team’s first five games, it scored 45, 39, 61, 50, and 43 points, what was the average (arithmetic mean) number of points scored over the last two games?
(A) 65
(B) 81
(C) 82
(D) 56
(E) Cannot be determined from the information given.
Rationale: Avg points for total of 7 games = 50
So A+B+C+D+E+F+G/7=50
and A+B+C+D+E+F+G = 350
Given A+B+C+D+E = 238
So F+G = 112
So average (arithmetic mean) number of points scored over the last two games is 112/2 = 56
Correct answer is D) 56
Answer: (D) 56
Question: In the graph below, no axes or origin is shown. If point B's coordinates are (11,3), which of the following coordinates would most likely be A's?
(A) (17, -2)
(B) (10, 6)
(C) (6, 8)
(D) (-10, 3)
(E) (-2, -17)
Rationale: wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10.
D rules..
Answer: (D) (-10, 3)
Question: A student travels from his house to school at 12 km/hr and reaches school 2 hours late. The next day he travels 20 km/hr and reaches school 1 hour early. What is the distance between his house and the school?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: Let x be the distance from his house to the school.
x/12 = x/20 + 3
5x = 3x + 180
2x = 180
x = 90 km
The answer is A.
Answer: (A) 90
Question: In how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5?
(A) 720
(B) 120
(C) 108
(D) 84
(E) 48
Rationale: 6 People in a round table can be seated in (6 - 1) ! ways = 120.
Now we need to subtract the number of cases when one of those is sitting next to 2 of the other 5.
We can consider as if 5 people are sitting in a row because it is round table.
Again consider 3 people, those who can not sit together, as a single unit â€“
So the possible arrangements among remaining people 5 â€“ 3 + 1 Unit are = 3 !
And the 3 people unit can arrange among themselves in 3 ! ways.
So the possible cases when one of those is sitting next to 2 of the other 5 = 3 ! * 3 ! = 36
Total possible cases = 120 -36 = 84 ANS:D
Answer: (D) 84
Question: 64 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 66
(B) 26
(C) 42
(D) 28
(E) 11
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 64 = 28
Answer: D
Answer: (D) 28
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 150 m
(B) 200 m
(C) 350 m
(D) 400 m
(E) 300 m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
ANSWER:C
Answer: (C) 350 m
Question: There are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
(A) 53
(B) 54
(C) 55
(D) 56
(E) 57
Rationale: First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 8
and for second = 7
so total methods = 8*7 = 56
ANSWER:D
Answer: (D) 56
Question: Arjun started a business with Rs. 10,000 and is joined afterwards by Anoop with Rs.40, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
Rationale: Suppose Anoop joined after 3 months.
Then, 10000 * 12 = 40000 * (12 – x)
=> x = 9.
ANSWER:E
Answer: (E) 9
Question: Of the diplomats who attended a summit conference: 20 spoke Spanish, 32 did not speak Russian and 20% of the diplomats spoke neither Spanish nor Russian. If 10% of the diplomats spoke both Spanish and Russian, then how many diplomats attended the conference?
(A) 70
(B) 96
(C) 108
(D) 120
(E) 150
Rationale: 2X2 matrix will be the easiest way to calculate this.
Text in black: given statements
Text in red: calculated values
Thus D=120 is the correct answer
Answer: (D) 120