divelab/Sys2Bench huggingface dataset:
Question: What percent of a day is 5 hours?
Options:
A)12%
B)12.5%
C)13%
D)20.8%
E)None of these
Rationale: Explanation :
Solution: required percentage = (5/100 * 24) = 20.8%
Answer : D
Answer: D
Question: Find the highest common factor of 36 and 84.
Options:
A)12
B)10
C)16
D)19
E)18
Rationale: 36 = 2^2 x 3^2
84 = 2^2 x 3 x 7
H.C.F. = 2^2 x 3 = 12.
Answer: Option A
Answer: A
Question: A passenger train takes two hours less for a journey of 300km if its speed is increased by 5 kmph from its normal speed. The normal speed is
Options:
A)35 kmph
B)50 kmph
C)25kmph
D)30 kmph
E)38 kmph
Rationale: let normal speed = x
Increased speed = x + 5
Initial => x = 300/t1
=> t1 = 300/x
After => (x + 5) = 300/(t1 - 2)
=> (x + 5) = 300 / [ (300/x) - 2]
=> x = 25kmph
ANSWER:C
Answer: C
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)9 days
C)12 days
D)14 days
E)16 days
Rationale: 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 = 10 × 40/50 = 8 days.
A)
Answer: A
Question: A card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox. Find the total number of pins used .
Options:
A)135
B)136
C)137
D)138
E)139
Rationale: (35*4)-4=136
ANSWER:B
Answer: B
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is?
Options:
A)11 years
B)88 years
C)38 years
D)17 years
E)18 years
Rationale: Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years.
x = 6/5 (x - 8)
5x = 6x - 48 => x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.
Rajan's sister's present age = (30 + 8) = 38 years.
Answer: C
Answer: C
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 15?
Options:
A)A)100
B)B)150
C)C)250
D)D)200
E)E)160
Rationale: Then, 10% of x= 15
(10/100)x = 15
x = (15*100*)/10= 150
Answer is B
Answer: B
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?
Options:
A)13
B)18
C)40
D)82
E)43
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (83 - 63)
=> x/2 = 20
=> x = 40
Answer:C
Answer: C
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)7
B)9
C)8
D)6
E)4
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: C
Question: In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 6 boys when a boy gets any no. of prizes?
Options:
A)1296
B)1678
C)1456
D)1200
E)1340
Rationale: Ans.(A)
Sol. In this case, repetitions are allowed, so all the 4 prizes can be given in 6 ways, i.e. (6 x 6 x 6 x 6) ways = 64 ways = 1296 ways Or nr ways = 64 ways = 1296 ways
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 3 sec. What is the length of the train?
Options:
A)50
B)75
C)100
D)120
E)25
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 3 = 50 m
Answer: A
Answer: A
Question: From a nine-member dance group, six will be chosen at random to volunteer at a youth dance event. If Kori and Jason are three of the nine members, what is the probability that three will be chosen to volunteer?
Options:
A)a) 1/21
B)b) 100/7
C)c) 4/21
D)d) 2/7
E)e) 3/7
Rationale: Total number of ways to choose 6 out of 9 = 9C6 = 21/5.
Number of ways to choose 3 (any but Kori and Jason) out of 6 (excluding Kori and Jason) = 6C3 = 60.
P = favorable/total = 60/(21/5) = 100/7.
Answer: B.
Answer: B
Question: 400 + 5 × 4 = ?
Options:
A)820
B)202
C)420
D)209
E)None of these
Rationale: 400 + 5 × 4 = ?
or, ? = 400 + 20 = 420
Answer C
Answer: C
Question: A certain team has 10 members, including Joey. A three-member relay team will be selected as follows: one of the 10 members is to be chosen at random to run first, one of the remaining 9 members is to be chosen at random to run second, and one of the remaining 8 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
Options:
A)1/1320
B)1/132
C)1/110
D)1/12
E)1/5
Rationale: Total outcomes= 10*9*8
Favorable Outcomes= 9*1*8 and 9*8*1
P=2*9*8*1/10*9*8
P=1/5
Ans E
Answer: E
Question: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 28, what is the common ratio of the G.P?
Options:
A)3
B)1/3
C)2
D)9
E)1/9
Rationale: 28=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)
Factorize the same terms
28=1+(a4+a5+a6)/(a1+a2+a3)
Write every term with respect to r
a1=a1
a2=a1*r^1
a3=a1*r^2
.........
28=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))
27=(r^3 (1+r^1+r^2))/((1+r^1+r^2))
27=r^3
r=3
A
Answer: A
Question: A trader sells 23 meters of cloth for Rs. 529 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)26
B)88
C)90
D)42
E)18
Rationale: SP of 1m of cloth = 529/23 = Rs. 23
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 23 - Rs. 5 = Rs. 18
Answer:E
Answer: E
Question: How many natural numbers are there between 43 and 200 which are exactly divisible by 6?
Options:
A)28
B)26
C)24
D)22
E)21
Rationale: Explanation :
43/6 = 7, remainder = 1. Hence 5 more should be added to 43 to get the minimum
number divisible by 6 between 43 and 200.
=> Minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48
200/6 = 33, remainder = 2. Hence 2 should be decreased from 200 to get the maximum
number divisible by 6 between 43 and 200.
=> Maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198
Hence, natural numbers numbers divisible by 6 between 43 and 200 are 48, 54, 60,...198
This is Arithmetic Progression with a = 48, d = 6, l=198
Number of terms = (l − a)/d + 1 = (198 − 48)/6 + 1 = 150/6 + 1 = 25 + 1 = 26. Answer : Option B
Answer: B
Question: Jack and Christina are standing 360 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 5 feet per second and Christina walks in a straight line toward Jack at a constant speed of 7 feet per second. Lindy runs at a constant speed of 12 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
Options:
A)270
B)300
C)330
D)360
E)390
Rationale: The relative speed of Jack and Christina is 5+ 7 = 12 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 360/12 = 30 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 12*30 = 360 feet.
Answer: D.
Answer: D
Question: The product of x and y is a constant. If the value of x is increased by 40%, by what percentage must the value of y be decreased?
Options:
A)34%
B)36%
C)28.57%
D)30%
E)32%
Rationale: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.4x (140)
i.e. 140*New 'y' = 10000
i.e. New 'y' = 10000/140 = 71.43
i.e. y decreases from 100 to 71.43 i.e. Decrease of 28.57%
C
Answer: C
Question: Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase?
Options:
A)3
B)4
C)6
D)9
E)10
Rationale: We have 5, 10, 10 and 20 to work with
From least to greatest, we have...
5 (the least)
10
15
20
25
30
35
40
45 (the greatest)
Total options = 9
Final Answer:D
Answer: D
Question: M is the sum of the reciprocals of the consecutive integers from 301 to 400, inclusive. Which of the following is true?
Options:
A)1/3 < M < 1/2
B)1/5 < M < 1/3
C)1/7 < M < 1/5
D)1/9 < M < 1/7
E)1/4< M < 1/3
Rationale: M = 1/301 + 1/302 + 1/303 + ...... + 1/400
If we replace the first 99 terms by 1/400, then we get a sum = 100/400 = 1/4. Since the actual terms are larger than 1/400, the sum is larger than 1/4.
If we replace the all the 100 terms by 1/300, we get a sum = 100/300 = 1/3. Since the actual terms are smaller than 1/200, the sum is less than 1/3.
Therefore 1/4 < M < 1/3
Choice E
Answer: E
Question: If â€œ*â€ is called â€œ+â€, â€œ/â€ is called â€œ*â€, â€œ-â€ is called â€œ/â€, â€œ+â€ is called â€œ-â€. 240*80 / 60 + 40 / 10 = ?
Options:
A)-2305
B)-2407
C)2509
D)-2101
E)None of these
Rationale: Explanation:
Given : 240*80 / 60 + 40 / 10 = ?
Substituting the coded symbols for mathematical operations, we get,
240 / 80 - 60 * 40 - 10 = ?
3 - 2400 - 10 = -2407
ANSWER : B
Answer: B
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places)?
Options:
A)178.88
B)178.29
C)188.29
D)178.2
E)178.12
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35
= 180 cm - 60 /35 cm
= 180 cm - 1.71 cm
= 178.29 cm.
Answer:B
Answer: B
Question: A rectangular with dimensions 10 inches by 15 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
Options:
A)a) 4 inches
B)b) 6 inches
C)c) 7 inches
D)d) 8 inches
E)e) 5 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
10=2*5
15=3*5
GCF = 5
P.S you can make squares with side of 5
Answer : E
Answer: E
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
Options:
A)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
B)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.759
C)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.758
D)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.752
E)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.122
Rationale: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer: A
Answer: A
Question: A lady who lived in a shoe had to buy Christmas gifts for her big family. She selected the cheapest stocking stuffers. The bill was still high. There was an addition of 15 percent of the sales tax and an addition of the 5 percent of the luxury tax to the actual amount. She paid $100.
Find out the original price of the stuffers without the taxes ?
Options:
A)$55.26
B)$83.33
C)$45.87
D)$90.12
E)$95>50
Rationale: B
The original price is $83.33.
(20 percent of the taxes are added to the selling price.)
Answer: B
Question: A number when divided by 133 leaves 16 as a remainder. What will be the remainder if the number is divided by 50?
Options:
A)51
B)56
C)49
D)17
E)7
Rationale: 133+16=149
Dividing 149 evenly into whole numbers is 2 and leaves 49 remaining.
The correct answer is C.
Answer: C
Question: Two-third of a positive number and 25/216 of its reciprocal are equal. The number is:
Options:
A)5/12
B)12/5
C)25/144
D)144/25
E)146/25
Rationale: Let the number be x. Then,
2/3 x = 25/216 * 1/x
x2 = 25/216 * 3/2 = 25/144
x = 5/12
ANSWER:A
Answer: A
Question: If x^2 = y^3 , where x and y are non negative and non zero integers, what is the greatest possible value of x / y from options below?
Options:
A)1
B)3
C)2
D)4
E)5
Rationale: B. x=27, y=9
27^2=729
9^3=729
x / y=27 / 9=3
My Answer is (B) 3
Answer: B
Question: 39! is divided by 41 then find the remainder?
Options:
A)1
B)3
C)5
D)6
E)7
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: A
Question: C individuals pledged to pay equal contributions so that a charity’s goal of $Q could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
Options:
A)dQ / C
B)Q / (C-d)
C)d / (C-dQ)
D)Q / (C(C-d))
E)dQ/C(C - d)
Rationale: Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = Q
n = Q/C
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dQ/C --> Additional amount
Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dQ/C(C - d)
Answer: E
Answer: E
Question: Two cubes each with side b are joined to form a cuboids. What is the surface area of this cuboids?
Options:
A)12b^2
B)10b^2
C)6b^2
D)4b^2
E)2b^2
Rationale: l=2b; b=b; h=b;
surface area=2*(lb+bh+hl)
=2*(2b^2+b^2+2b^2)
=10 b^2
ANSWER:B
Answer: B
Question: 10 men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa?
Options:
A)22
B)20
C)10
D)15
E)none
Rationale: it is written that 10 men and 10 women dance with each other. so there is no chance of matching more than 2 partners at a time. so 2 men & 1 women is not possible.
ANSWER:E
Answer: E
Question: Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book?
Options:
A)20
B)18
C)16
D)15
E)15.39
Rationale: Actually u can set up 2 equation
P--stands for the pages
D--stands for the days
1) P*D=480 (we want to find the Days, soP=480/D)
2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000
as the 1) stated u can put 1) into 2)
=> 1000-5P+15D-75=1000 => 15D-5P=75
put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16)
=> D^2-5D-160=0
so D=15.39days. Ans: (E)
Answer: E
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 7 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
Options:
A)1/3
B)2/5
C)3/7
D)1/2
E)7/13
Rationale: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 7*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 7x
=13x
August tips as a fraction of total tips = 7x/13x =7/13. So E
Answer: E
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
Options:
A)195 m
B)145 m
C)175 m
D)179 m
E)125 m
Rationale: Explanation:
RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer: Option C
Answer: C
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
Options:
A)40%
B)60%
C)80%
D)20%
E)28%
Rationale: A B C D
90 100 80 100
A D
90 ---------100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer:C
Answer: C
Question: A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability R that both selected dogs are NOT littermates?
Options:
A)1/6
B)2/9
C)5/6
D)7/9
E)8/9
Rationale: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.
So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.
Work with probabilities:
Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).
The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).
The probability R of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).
The required probability is 1/2 + 1/3 = 5/6.
Find the probability for the complementary event: choose AA or BB.
Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.
Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 = 1/12.
Again, we obtain 1 - (1/12 + 1/12) = 5/6.
Answer: C
Answer: C
Question: three men invested sum. and their ratio is 5:7:6. profit is 2700.then b's share
Options:
A)2000
B)2100
C)2200
D)2300
E)1050
Rationale: b's share =7/18*2700=1050
ANSWER:E
Answer: E
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 5 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--
Options:
A)12
B)19
C)60
D)180
E)300
Rationale: 5C3 * 5C2 * 3C2 = 10*10*3 = 300.
Answer: E.
Answer: E
Question: When 24 is divided by the positive integer a, the remainder is 4. Which of the following statements about a must be true?
I. a is even
II. a is a multiple of 5
III. a is a factor of 20
Options:
A)III only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: 24= m*a + 4
m*a=20
put values of m
m=1 a=20
m=2 a=10
m=4 a=5
I. not true
II. true
III. true
D. correct
Answer: D
Question: The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P +9, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)
Options:
A)41
B)47
C)58
D)65
E)72
Rationale: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.
Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.
As given that N = P + 9, then N=2*N/2.54+9--> N=~41.
Answer: A.
Answer: A
Question: Which of the following is closest to 1/8+1/88+1/888
Options:
A)1/8
B)1/2.5
C)1/5
D)1/7.3
E)1/9
Rationale: 1/8+1/88+1/888=0.125+0.01136+0.001126=0.137486=1/7.3
Answer D
Answer: D
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ6, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
Options:
A)I only
B)II only
C)III only
D)I , II and III
E)I and II only
Rationale: it can be a combination of 9,7 or 8,8
I choose D as an answer.
Answer: D
Question: A jeweler has a 20 gram ring that is 60% gold and 40% silver. He wants to melt it down and
add enough gold to make it 80% gold. How many grams of gold should be added?
Options:
A)4 grams
B)8 grams
C)12 grams
D)16 grams
E)20 grams
Rationale: Gold concentration = weight of gold/total weight
0.80 =20*0.60+x/20+x
12 + x = 16 + 0.8x
0.2x = 4
x = 20 grams
correct answer E
Answer: E
Question: At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 145 male associates, how many female managers are there?
Options:
A)15
B)20
C)25
D)30
E)35
Rationale: 250 Employees:
90 Male, 160 Female
40 Managers, 210 Associates
145 Male Associates implies 65 Female Associates which means the remaining 25 females must be Managers
C. 25
Answer: C
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
Options:
A)33
B)28
C)24
D)97
E)16
Rationale: Explanation:
2c = Â¼ + 1/6 â€“ 1/3 = 1/12
c = 1/24 => 24 days
Answer:C
Answer: C
Question: If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio J of the resistors’ sum of A and C to the resistors’ sum of A and B?
Options:
A)2(R1+R2):(R1+2R2)
B)(R1+R2):(R1+2R2)
C)(2R1+R2):(R1+2R2)
D)2(R1+R2):(2R1+R2)
E)2(R1-R2):(R1+2R2)
Rationale: two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio J of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
=2(r1+r2)/2r2+r1.A
Answer: A
Question: Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
Options:
A)5!*6!
B)6!*6!
C)5!*7!
D)6!*7!
E)7!*7!
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: n!/n=(n-1)!
Now, 7 men in a circle can be arranged in (7-1)! ways and if we place 7 women in empty slots between them then no two women will be together. The # of arrangement of these 7 women will be 7! and not 6! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 6!*7!. ANS:D
Answer: D
Question: P is four times as fast as Q and working together, they can complete a work in 8 days. In how many days can Q alone complete the work?
Options:
A)35 days
B)15 days
C)10 days
D)25 days
E)18 days
Rationale: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 8 days, which means Q can do the work in 40 days.
Hence, P can do the work in 10 days.
ANSWER:C
Answer: C
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)49
B)48
C)47
D)50
E)52
Rationale: Total age of students is 32 Ã— 16 = 512 Years
Total age inclusive of teacher = 33 Ã— (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33 Ã— 1) = 49 Years
ANSWER IS A
Answer: A
Question: At a dinner party, 4 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)1) 6
B)2) 10
C)3) 24
D)4) 32
E)5) 120
Rationale: for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!
in this case, there are 4 guests, so number of distinct arrangements = 3! = 6
hence A
Answer : A
Answer: A