divelab/Sys2Bench huggingface dataset:
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 38 years now, the son's age five years back was?
Options:
A)14yr
B)15yr
C)20yr
D)25yr
E)30yr
Rationale: Let the son's present age be x years
Then, 38-x = x
x = 19
Son's age 5 years back = 19-5 = 14 years
Answer is A
Answer: A
Question: The value of “A” varies in inverse proportion as the square of “B”. If the value of “A” is equal to 40 when “B” is equal to 12. What would be the value of “A” when “B” is equal to 24 ?
Options:
A)10
B)88
C)26
D)27
E)28
Rationale: Explanation:
We have, A α 1/B2
A * B2 = K (constant)
When B = 12, A = 40 …..Given
K = 40 * (12)2 = 5760
Now, B = 24. Hence, A = 5760 / 576 = 10
ANSWER: A
Answer: A
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 55 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
Options:
A)9x/80
B)13x/20
C)80/9x
D)20x/13
E)80x/11
Rationale: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 55% of the sales of imported tools = 0.55*{total}/4 = 11/20*{total}/4 = 11*{total}/80.
Since the sales of of Japanese tools was x, then 11*{total}/80 = x --> {total} = 80x/11.
Answer: E.
Answer: E
Question: what is the smallest integer that is multiple of 5,7,9
Options:
A)A)70
B)B)315
C)C)200
D)D)280
E)E)140
Rationale: It is the lcm of 5, 7 and 9 which is 315.
The answer is B.
Answer: B
Question: What is the difference between the compound interest on Rs.12000 at 28% p.a. for one year when compounded yearly and half yearly?
Options:
A)399
B)383
C)235
D)288
E)133
Rationale: When compounded annually, interest
= 12000[1 + 28/100]1 - 12000 = Rs.3360
When compounded semi-annually, interest
= 12000[1 + 14/100]2 - 12000 = Rs.3595.2
Required difference = 3595.2 - 3360 = Rs.235.2
Answer: C
Answer: C
Question: Nelson borrowed some money at the rate of 6 p.c.p.a. for the first three years, 9 p.c.p.a. for the next five years and 13 p.c.p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is 8,160, how much money did he borrow?
Options:
A)12,000
B)10,000
C)8,000
D)Data inadequate
E)None of these
Rationale: Let ‘x’ be the amount borrowed by Nelson
and x×6×3/100+x×9×5/100+x×13×3/100=8160
⇒ 102⁄100x = 8,160
∴ x = 8,160×100102=8000
Answer C
Answer: C
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on?
Options:
A)3.
B)4.
C)5.
D)6.
E)7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 4 = 5x + 2
6x - 4 = 5x + 2
x = 6
Answer: D
Answer: D
Question: The present ages of A,B & C are in the ratio of 5:7:8. 7years ago, the sum oftheir ages was 59. What is the present age of eldest one?
Options:
A)30
B)31
C)32
D)35
E)36
Rationale: Let their present ages be 5x, 7x and 8x.
7 years ago, sum of their ages was 59.
Sum of their present ages = 59 +( 3 x 7) = 80
Sum of their present ages given is 5x + 7x + 8x = 20x
20x = 80 =>x = 80 20
=4
Age of the Eldest one= 8x = 8x 4 = 32 years.
C
Answer: C
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts six hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
Options:
A)3
B)4.5
C)4
D)d) 12
E)e) 5
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 6+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(6+T) = 40*T
T = 18 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*18/60 = 12 hrs
Time taken by A = 6+T = 6+18 = 24 hrs
Time taken by K = 12 hrs
So K starts 24-12 = 12 hrs after A. (ANSWER D)
Answer: D
Question: How long does a train 110 m long traveling at 72 kmph takes to cross a bridge of 170 m in length?
Options:
A)16.5
B)16.0
C)16.4
D)14
E)16.1
Rationale: D = 110 + 170 = 280 m
S = 72 * 5/18 = 20
T = 280 * 1/20 = 14 sec
Answer: D
Answer: D
Question: As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 30%, what is the probability that Karen will be accepted to at least one project?
Options:
A)729/1000
B)657/1000
C)343/500
D)123/250
E)17/100
Rationale: Since the probability of Karen's being accepted to each individual project is 30%, the probability of her not being accepted to each project is 70%. The probability that she will be accepted to none is, therefore, (7/10)*(7/10)*(7/10)=343/1000.
P(Karen will be accepted to at least one project) = 1 - (343/1000) = 657/1000.
The answer is B.
Answer: B
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 25 percent of the seeds in the first plot germinated and exactly 40 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
Options:
A)12%
B)26%
C)29%
D)31%
E)60%
Rationale: In the first plot 25% of 300 seeds germinated, so 0.25 x 300 = 75 seeds germinated.
In the second plot, 40% of 200 seeds germinated, so 0.4 x 200 = 80 seeds germinated.
Since 75 + 80 = 155 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (155/500) x 100%, or 31%.
Answer: D.
Answer: D
Question: Which of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460?
Options:
A)797
B)798
C)799
D)796
E)795
Rationale: 5678 - 35 + (one of the answer option) should be divisible by 460. Only option C satisfies.
Answer:A
Answer: A
Question: How many multiples of 3 are less than 6500, and also multiples of 7?
Options:
A)104
B)208
C)310
D)340
E)454
Rationale: LCM of 3 & 7 = 21
Tried dividing 6500 by 21
Got quotient 309.5'So C is answer
Answer: C
Question: If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2?
Options:
A)4.
B)8.
C)12.
D)16
E)64
Rationale: A-B-C+D = 13 -- equation 1
A+B-C-D = 5 -- equation 2
Adding 1 and 2 , we get
2A - 2C = 18
=> A-C = 9 -- equation 3
Using equation 3 in 2 , we get
B-D = 5 - 9 = -4
=>(B-D)^2 = 16
Answer D
Answer: D
Question: What is the sum of all the multiples of 7 between 30 and 100?
Options:
A)692
B)700
C)677
D)654
E)665
Rationale: You first have to know all the multiples of 7 between 30 and 100. They are 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98. If you add all these numbers together, you get 665.
Final Answer:
E
Answer: E
Question: In how many different number of ways 1 boys and 2 girls can sit on a bench?
Options:
A)700
B)7
C)6
D)8
E)1
Rationale: npn = n!
3p3 = 3 × 2 × 1 = 6
C)
Answer: C
Question: A bangle was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)Rs.800
B)Rs.700
C)Rs.1000
D)Rs.1100
E)Rs.1200
Rationale: 90%
104%
--------
14% ---- 140
100% ---- => Rs.1000
C
Answer: C
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
Options:
A)8 years
B)10 years
C)12 years
D)14 years
E)15 years
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6)	...(j)
and Rupesh + 6 = | (Ravi + 6)	...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: C
Question: The length of rectangle is thrice its breadth and its perimeter is 80 m, find the area of the rectangle?
Options:
A)300 sq m
B)356 sq m
C)452 sq m
D)428 sq m
E)528 sq m
Rationale: 2(3x + x) = 80
l = 30 b = 10
lb = 30 * 10 = 300
ANSWER:A
Answer: A
Question: A goods train runs at the speed of 72 km/hr and crosses a 220 m long platform in 26 sec. What is the length of the goods train?
Options:
A)382
B)782
C)300
D)270
E)881
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 220)/26 = 20
x = 300 m.
Answer: C
Answer: C
Question: Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other?
Options:
A)300 kms from A
B)280 kms from A
C)305 kms from A
D)295 kms from A
E)265 kms from A
Rationale: DETAILED SOLUTION
Bus A
Travels 200km @ 40kmph
the next 200km @ 50kmph and
the final 200km @ 60kmph
So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins
Bus B
Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip.
So, Bus B will travel
160 kms in the first 4 hours
200 kms in the next 4 hours
and 240 in the final 4 hours
So, both buses cross each other when they are in their middle legs.
After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50).
The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50 = 100 kmph.
Time taken = 190/100 = 1.9 hours. = 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95 = 305 kms. So, the two buses will meet at a point that is 305 kms from City N and 295 kms from city A.
CORRECT ANSWER D
Answer: D
Question: Sum of two numbers is 25. First exceeds by 5 from the other. Then the numbers will be?
Options:
A)20, 5
B)10, 15
C)15, 10
D)5, 20
E)12, 13
Rationale: Explanation:
x + y = 25
x - y =5
x = 15 y = 10
Answer: C
Answer: C
Question: In how many different ways can the letter of the word 'CONCEALED ' be arranged in such a way that the vowels occupy the odd positions?
Options:
A)7412
B)4596
C)5760
D)4563
E)8521
Rationale: In the given word there 5 letters in that there are 4 vowels and 5 consonants
no of ways of arranging the vowels=4P4=48
no of ways of arranging the consonants=5P5=120
total number of ways 120*48=5760
Answer(C)
Answer: C
Question: In a shop 90% of the articles are sold at a profit of 20% and the remaining at a loss of 40%.what is the overall profit/loss?
Options:
A)14% profit
B)10% loss
C)18% profit
D)7% loss
E)2% Profit
Rationale: 90*1.05+10*0.6/100=1.14
ANSWER:A
Answer: A
Question: The sum of the first 50 positive even integers is 2550. What is the sum W of even integers from 102 to 200 inclusive?
Options:
A)5100
B)7550
C)10100
D)15500
E)20100
Rationale: My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
W=2550+(100*50)=7550.B
Answer: B
Question: The inner circumference of a circular race track, 25 m wide, is 880 m. Find radius of the outer circle?
Options:
A)165m
B)120m
C)100m
D)190m
E)220m
Rationale: Let inner radius be r metres. Then, 2Πr = 880 ⇔ r = (880 x (7/44))= 140 m.
Radius of outer circle = (140 + 25) m = 165 m.
hence A
Answer: A
Question: To a sugar solution of 3 liters containing 40% sugar, one liter of water is added. The percentage of sugar in the new solution is?
Options:
A)20%
B)30%
C)25%
D)15%
E)50%
Rationale: Quantity of sugar = 40*3/100 = 1.2kg
New percentage = 1.2/4 * 100 = 30%
Answer is B
Answer: B
Question: A can do a certain job in 10 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
Options:
A)7 1/2 days
B)8 days
C)6 1/4 days
D)9 days
E)None of them
Rationale: Ratio of times taken by A and B = 160 : 100 = 8 : 5.
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 10 : x = 8x = 5 x 10 =x = 6 1/4 days.
Answer is C.
Answer: C
Question: A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?
Options:
A)200
B)400
C)500
D)600
E)800
Rationale: With mixture problems I usually take following approach
10%=Total mix of acid/Total amount of mixture.
With X= amount of 12% acidic solution we have:
10%=(400*0.06+.12*X)/400+X)
40+0.1X=24+0.12X
16=0.002X
X=800
Answer E
Answer: E
Question: If a2 + b2 + c2 = 941 and ab + bc + ca = 10, then a + b + c is
Options:
A)44
B)56
C)16
D)32
E)31
Rationale: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 941 and ab + bc + ca = 10,
(a + b + c)^2 = 941 + 2(10)
= 961
=31^2
therefore: a + b + c = 31
ANSWER:E
Answer: E
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
Options:
A)144 min
B)145 min
C)150 min
D)200 min
E)250 min
Rationale: slower pipe alone fill the tank = x
faster pipe will fill in x/3 min
1/x+3/x=1/36
x=144 min
ANSWER A
Answer: A
Question: A machine that produces silicon bottle stoppers, makes 36 stoppers weighing 6y grams each, and 9x stoppers weighing 12 grams each. What is the average weight (arithmetic mean) per stopper?
Options:
A)(36y + 18x)/(y + 2)
B)(18y + 9x)/4
C)(36x)/(2y + 3x)
D)(24y + 12x)/(4 + x)
E)6 + 3y
Rationale: The total number silicon stoppers weighing 6y grams is 36 and 12 grams is 9x
Average weight = (36*6y + 9x*12)/36+9x
= (9(24x + 12y))/(9(4+x))
= 24x+12y/4+x
(Option D)
Answer: D
Question: An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank?
Options:
A)50%
B)40%
C)33.5%
D)37.5%
E)None of these
Rationale: Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8
∴ required% = 3A⁄ (8 × A) × 100 = 37.50%
Answer D
Answer: D
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Options:
A)228 Sec
B)190 Sec
C)167 Sec
D)767 Sec
E)328 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: B
Question: In Net's hair salon 40% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?
Options:
A)5%
B)7%
C)12%
D)15%
E)21%
Rationale: Let a total of 100 people visit the salon.
Total = 100
Dye hair blonde (A) = 40 % = 40
Dye Eyebrows blonde (B) = 36% = 36
Straighten Hair (C) = 35% = 35
Neither = 20% = 20
All Three = 12% =12
Total = A+B+C - (Sum of Exactly Two group overlaps) - 2*(All three) + Neither
100 = 40+36+35 - (Sum of Exactly Two group overlaps) - 2*12 + 20
(Sum of Exactly Two group overlaps) = 9
%of customers coming for exactly 2 of the 3 procedures =7%
B
Answer: B
Question: The greatest possible length which can be used to measure exactly the length 5m ,2m 19cm, 4m 20 cm is?
Options:
A)25cm
B)1cm
C)56cm
D)42cm
E)35cm
Rationale: Required length = H.C.F of 500cm, 219cm, 420cm = 1cm
Answer is B
Answer: B
Question: If x/4 years ago Roger was 14 years old and x/4 years from now he will be 4x years old, how old will he be 6x years from now?
Options:
A)32
B)39
C)30
D)40
E)28
Rationale: Assume the current age = a
a - x/4 = 14 (i)
a + x/4 = 4x
Or a = 15x/4 (ii)
Putting the value of a from (ii) in (i)
15x/4 - x/4 = 14
Or 14x/4 = 14 Therefore x = 4 and a = 15
6x years from now, age will be 15 + 6*4 = 39
Option B
Answer: B
Question: There are 5 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
Options:
A)90
B)120
C)150
D)180
E)200
Rationale: Number of ways of selecting 2 fiction books = 5C2
Number of ways of selecting 2 non fiction books = 6C2
5C2 * 6C2 = 10 * 15 = 150
Answer: C
Answer: C
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Options:
A)276
B)299
C)322
D)345
E)258
Rationale: Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer: Option C
Answer: C
Question: The length, breadth and height of a room are in ratio 3:2:1. If breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
Options:
A)remain the same
B)decrease by 13.64%
C)decrease by 15%
D)decrease by 18.75%
E)decrease by 30%
Rationale: Solution: Let length, breadth and height of the room be 3, 2, 1 unit respectively.
Area of walls = 2(l+b)*h = 2(3+2)*1 = 10 sq. unit.
Now, length, breadth and height of room will become 6, 1 and 1/2 respectively.
Now, area of walls = 2(6+1)*1/2 = 7 sq. unit.
% decrease in the area of walls = (10-7)*100/10 = 30%.
Answer: Option E
Answer: E
Question: Lisa is 10 yaers older than Joey. If the sum of their age is 40 , what is the age of Joey?
Options:
A)15 years
B)25 years
C)10 years
D)20 yaers
E)5 years
Rationale: Let Joey's age be x.
x + x + 10 = 40
x = 15
Hence Joey's age is 15 years
Answer : A
Answer: A
Question: Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?
Options:
A)3 days
B)6 days
C)8 days
D)4 days
E)9 days
Rationale: 12/ (2 * 2) = 3 days
Answer:A
Answer: A
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)169
B)175
C)544
D)166
E)121
Rationale: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer:B
Answer: B
Question: Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 56 workers in the Palabras bookstore, how many of them have read both books?
Options:
A)13
B)12
C)9
D)8
E)17
Rationale: There are total 56 workers.
Half of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 28 have read Saramago.
5/8 of the workers have read the latest book by H. Kureishi.
So (5/8) * 56 = 35 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 20 - B have read Saramago but not Kureishi.
So, (28 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
56 = 28 + 35 - B + (28 - B - 1)
B = 17
Answer (E)
Answer: E
Question: In the rectangular coordinate system, points (5, 0) and (– 5, 0) both lie on circle C. What is the maximum possible value of the radius of C ?
Options:
A)2
B)4
C)8
D)16
E)None of the above
Rationale: The answer is B
It takes 3 distinct points to define a circle. Only 2 are given here.
The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius isgreater 5 B
Answer: B
Question: What decimal of an hour is a second ?
Options:
A)0.00027
B)0.00025
C)0.00026
D)0.00024
E)None of these
Rationale: Explanation :
1 hour = 60 minutes = 3600 seconds
Hence, required decimal = 1/3600 = 0.00027. Answer : Option A
Answer: A
Question: Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 60% savings. Assuming that they operate independently, what is the net saving achieved?
Options:
A)56%
B)64%
C)62.2%
D)83.2%
E)61%
Rationale: If initial cost is Rs 100, then
Final cost will be 100*0.7*0.6*0.4 = Rs. 16.8
savings = 100-16.8=83.2
so 83.2%
ANSWER:D
Answer: D
Question: How many three letter words are formed using the letters of the word MOUSE?
Options:
A)120
B)125
C)130
D)150
E)91
Rationale: Explanation:
The number of letters in the given word is five.
The number of three letter words that can be formed using these five letters is Ã¢Â´PÃ¢â€šÆ’ = 5*4 * 3 = 120.
Answer: A
Answer: A
Question: Find the number of square tiles to cover the floor of a room measuring 3.75 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Options:
A)478
B)376
C)442
D)471
E)445
Rationale: 3 1/4 * 8 1/2 = 1/4 * 1/4 * x => x
= 442
Answer:C
Answer: C
Question: A school has 4 section of Chemistry in Class X having 50, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
Options:
A)50.12
B)52.12
C)51.12
D)53.12
E)None of the above
Rationale: Required average marks
= 50Ã—50+35Ã—60+45Ã—55+42Ã—45/50+35+45+42
= 2500+2100+2475+1890/172
= 8965â„172 = 52.12
Answer B
Answer: B
Question: What percent of the different arrangements of the letters of the word AKACUL are those in which the vowels appear together?
Options:
A)50%
B)40%
C)30%
D)25%
E)20%
Rationale: let's determine the number of total possibilities in arranging the letters. There are six spaces, so the total number of arrangements is 6!, or 360.
Next, we need to figure out how to determine the number of ways that we can arrange the 3 vowels together - simply place them together (as in AAU) and call that a single place.
Next, we must determine the number of ways to arrange the now 4 units (i.e., AAU, B, C, S). Like above, there are 4 units and 4 places so the number of arrangements is 4!, or 24.
Finally, we need to account for the number of ways we can arrange AAU. We can either write out each unique iteration (AAU, AUA and UAA) or calculate as 3!/2! and get 3.
Putting this all together, we get the number of ways to arrange the letters so that the vowels are together is 4! x 3 ==> 72
the number of total arrangements of all the letters is 6! ==> 360
72/360 = 1/5, or 20%
Correct answer is E
Answer: E
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 21,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
Options:
A)5,476,811 kilometers squared
B)11,500,148 kilometers squared
C)9,843,123 kilometers squared
D)1,878,965 kilometers squared
E)4,787,900 kilometers squared
Rationale: he difference between the areas of Russia and China is given by
21,098,242 - 9,598,094 = 11,500,148 kilometers squared
correct answer B
Answer: B
Question: A car travels uphill at 30 km/hr and downhill at 60 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
Options:
A)32kmph
B)33kmph
C)34kmph
D)35kmph
E)36kmph
Rationale: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/60=5/6;
avg speed=150/(10/3+5/6)=36kmph
ANSWER:E
Answer: E
Question: A shopkeeper sold an article for Rs 2564.36. Approximately what was his profit percent if the cost price of the article was Rs 2200
Options:
A)17%
B)5%
C)6%
D)7%
E)8%
Rationale: Explanation:
Gain % = (364.36*100/2200) = 16.56 % = 17% approx
Option A
Answer: A