divelab/Sys2Bench huggingface dataset:
Question: Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 4. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?
Options:
A)3, 8, 24
B)7, 9, 17
C)6, 9, 12
D)5, 15, 18
E)9, 10, 13
Rationale: I didnt get your point on eliminating E.
The number of stamps only one purchased was divisible by 4.Could that not be Cecilia with 9 stamps.
I choose this and marked E.
Answer: E
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
Options:
A)48
B)49
C)50
D)51
E)52
Rationale: Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
= 10x5/18 m/sec
= 25/9 m/sec
= 2x/36 =25/9
2x =100
X=50
answer :C
Answer: C
Question: A fruit seller had some apples. He sells 30% and still has 420 apples. Originally, he had ?
Options:
A)30 apples
B)600 apples
C)420 apples
D)70 apples
E)None
Rationale: Answer
âˆµ 70% of N = 420
âˆ´ N = (420 x 100)/70 = 600
Correct Option: B
Answer: B
Question: A man, a woman and a boy can together complete a piece of work in 3 days. If a woman alone can do it in 6 days and a boy alone in 18 days, how long will a man take to complete the work?
Options:
A)5days
B)8days
C)7days
D)9days
E)8days
Rationale: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3
1wo man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/18
man alone can finish the work in 9 days.
Answer: Option D
Answer: D
Question: 9, 16, 18, 25, 36,49
Options:
A)9
B)16
C)18
D)25
E)36
Rationale: Each of the numbers except 18, is perfect square.
Answer: Option C
Answer: C
Question: A man can row downstream at 22 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)16, 2
B)16, 4
C)16, 8
D)16, 6
E)16, 7
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 22 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 32 => x = 16, y = 6.
Answer:D
Answer: D
Question: In how many ways 4 Indians and 2 Englishmen can be seated in a row so that they are alternate?
Options:
A)120
B)96
C)144
D)48
E)256
Rationale: number of ways = 4!*2! = 48
Answer is D
Answer: D
Question: A number x is 3 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)66.6%
C)80%
D)11%
E)1%
Rationale: Say y=1 and x=3.
Then y=1 is less than x=3 by (3-1)/3*100=2/3*100=66.6%.
Answer: B.
Answer: B
Question: The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is:
Options:
A)79.8cm3
B)79.4cm3
C)89.8cm3
D)89.4cm3
E)None of these
Rationale: Explanation:
Volume of the largest cone = Volume of the cone with diameter of base 7 and height 7 cm
Volume of cone =1/3πr2h
=1/3∗22/7∗3.5∗3.5∗7
=269.5/3cm3
=89.8cm3
Note: radius is taken as 3.5, as diameter is 7 cm
Option C
Answer: C
Question: Q' = 3Q - 3, what is the value of (6')' ?
Options:
A) 120
B) 150
C) 180
D) 210
E) 240
Rationale: (6')'=(3*6-3)'=15'=15*15-15=210
Answer D
Answer: D
Question: What is the remainder when 14,453 × 15,654 × 16,788 is divided by 5?
Options:
A)2
B)1
C)5
D)4
E)3
Rationale: Only the unit's digit of the product will decide the remainder when divided by 5.
Hence, 3*4*8= will give units digit as 5
So, whatever be the number, if it ends in 6, the remainder after dividing with 5 will be 1.
OptionB
Answer: B
Question: The ratio of the incomes of Uma and Bala is 8:7 and the ratio of their expenditure is 7:6. If at the end of the year, each saves $2000 then the income of Uma is?
Options:
A)$16800
B)$16500
C)$16000
D)$16300
E)$16200
Rationale: Let the income of Uma and Bala be $8x and $7x
Let their expenditures be $7y and $6y
8x-7y = 2000-------1)
7x-6y = 2000-------2)
From 1) and 2)
x = 1000
Uma's income = 8x = 8*2000 = $16000
Answer is C
Answer: C
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)7 sec
B)5 sec
C)4 sec
D)6 sec
E)2 sec
Rationale: Speed of train relative to man
= (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
= [55/3] m/sec.
Time taken to pass the man
= [110 * 3/55] sec
= 6 sec
Answer:D
Answer: D
Question: 10 People take a history test. The following are the scores:
40, 45, 45, 50, 50, 60, 70, 75, 95, 100
Using the mean and median scores, find the amount of scores that fall in between the range of the two
Options:
A)One
B)Three
C)Five
D)Seven
E)Nine
Rationale: The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.
Only 60 is between 55 and 63.
Answer: A
Question: A compact car uses 15 gallons of fuel in traveling 360 miles. In order for the truck to travel the same distance using 12 gallons of fuel, by how many miles per gallon must the car’s fuel mileage be increased?
Options:
A)10
B)6
C)15
D)36
E)27
Rationale: There are two sets 15G1 gallons and 12G2 gallons details given.
15 gallons covering 360 miles
Then 1 G1 is used to cover 24 miles.
Now for 12, G2 covering 360 miles.
then 1 G2 is used to cover 30 miles.
Therefore, 30 - 24 = 6 miles per gallon increment is needed for 12 gallons to improve the mileage to cover 360 miles.
Thus, B is the correct answer.
Answer: B
Question: Mangala completes a piece of work in 12 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)7.5 days
B)7.6 days
C)7.7 days
D)8.7 days
E)9.7 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 = 12 Ã— 20/32 = 7.5 days.
A)
Answer: A
Question: If selling price is doubled, the profit triples. Find the profit percent:
Options:
A)66 2/3
B)100
C)105 1/3
D)120
E)150
Rationale: Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
ANSWER:B
Answer: B
Question: X, Y and Z can do a work in 9 , 10 and 15 days respectively. They completed the work and got Rs.600. What is the total amount earned by X and Y?
Options:
A)476
B)356
C)456
D)466
E)450
Rationale: The ratio of their working rates = 1/9 : 1/10 : 1/15 = 10 : 9 : 6.
Since, they work together, the share of X
= 10/25 * 600 = Rs.240
the share of Y = 9/25 * 600 = Rs.216
total amount earned by X and Y = 240 + 216 = Rs.456
Answer: C
Answer: C
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $120, how much more remains to be paid?
Options:
A)$880
B)$990
C)$1,000
D)$1,100
E)$1,080
Rationale: 10/100P = 120 >> p= 120*100/10 = 1200
1200 - 120 = 1080
ANSWER:E
Answer: E
Question: How many odd 4-digit positive integers R that are multiples of 5 can be formed without using the digit 3?
Options:
A)648
B)729
C)900
D)1296
E)3240
Rationale: I choose A.
Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)
Possible n° of 2nd digit: 9 (3 is excluded)
Possible n° of 3rd digit: 9 (3 is excluded)
Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)
So, R=8*9*9*1=648 (A)
Answer: A
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by N percent, which of the following expressions represents the final price of the item?
Options:
A)(10,000z + 100z(x – y) – xyz)/10,000
B)(10,000z + 100z(y – x) – xyz)/10,000
C)(100z(x – y) – xyz)/10000
D)(100z(y – x) – xyz)/10000
E)(A+ Ax/100) - N/100 ( A +Ax/100)
Rationale: .value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by N% on Total N/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - N/100 ( A +Ax/100)
E
Answer: E
Question: Three pipes of same capacity A,B,C can fill a tank in 6 hours. If there are only two pipes B and C of same capacity, the tank can be filled in?
Options:
A)2
B)4
C)9
D)12
E)16
Rationale: The part of the tank filled by three pipes in one hour
= 1/6
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/6 = 1/9.
The tank can be filled in 9 hours.
Answer:C
Answer: C
Question: The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)1752
B)1799
C)1719
D)1750
E)1800
Rationale: Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 60 Ã¨ x = 60 * 60 / 2 = 1800
Answer: E
Answer: E
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)278
B)276
C)20
D)288
E)21
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: C
Question: In a fuel station the service costs $4.25 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
Options:
A)122.6$
B)128.9$
C)243.7$
D)298.85$
E)309.85$
Rationale: Service cost of 3 van and 2 truck = 4.25*(3+2)=21.25
Fuel in 3 Van = 3*65=195 litre
Fuel in 2 Trucks =2 * 65(1+120/100)= 286
Total fuel(Van+Truck) = 481 Litre
Total Fuel cost = 481*0.6 =288.6
TOTAL COST =FUEL+SERVICE=288.6+21.25=309.85
ANSWER IS E
Answer: E
Question: The speeds of 3 trains in the ratio 4:12:24. The ratio between time taken by them to travel the same distance is?
Options:
A)6:2:1
B)1:2:3
C)4:8:9
D)6:5:2
E)4:8:7
Rationale: Ratio of time taken is = 1/4 : 1/12 : 1/24 = 6:2:1
Answer is A
Answer: A
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x?
Options:
A)2/5
B)3/4
C)4/5
D)5/4
E)2/7
Rationale: a/b = 4/5
m/x = (2/5)*5 / (7/4)*4 = 2/7
The answer is E.
Answer: E
Question: The ratio of ages of A and B at present is 2:3. After five years the ratio of their ages will be 3:4 What is the present age of A in years?
Options:
A)10
B)15
C)25
D)30
E)35
Rationale: ( 2x+5 ) /( 3x+5) = 3/4
or, 8x+20=9x+15
or,x=5
So, Present age of A = 2x = (2*5) = 10
ANSWER:A
Answer: A
Question: In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
Options:
A)24
B)144
C)292
D)584
E)None of these
Rationale: 5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
Answer:D
Answer: D
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.
Options:
A)37.5 %
B)38.5 %
C)42 %
D)27.5 %
E)none
Rationale: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 64. S.P = Rs. 88.
∴ Gain % = [24/64 * 100]% = 37.5%.
Answer A
Answer: A
Question: Combine terms: 12a + 26b -4b – 16a.
Options:
A)4a + 22b
B)-28a + 30b
C)-4a + 22b
D)28a + 30b
E)30a-28b
Rationale: 12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
correct answer C
Answer: C
Question: What least number must be added to the least number of six digits so that the resulting number may be a perfect square.
Options:
A)489
B)267
C)278
D)199
E)111
Rationale: The least number of six digits = 100000 3 10 00 00 317 9 61 100 61 627 3900 4389 – 489 Least number to be added = 489.
Answer:A
Answer: A
Question: what is the remainder when 789456123 is divided by 999
Options:
A)349
B)359
C)369
D)379
E)389
Rationale: there is a simple trick for 99 or 999..u have to add the digits from right side for 99 you will select the last 2 digits and add with next two last digits and go on..similarly for 999 u will add last three digits then its next two last digits and so on..
so you will get 123 + 456 +789 =1368 again select last 3 and add them u will get 368 + 001 i.e 369
ANSWER:C
Answer: C
Question: In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
Options:
A)19%
B)15%
C)25%
D)40%
E)9.4%
Rationale: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)
Originally,
C = FNP
When number of students decrease by 8%, and the price of food increases by 20%,
C = F(new) * (0.92N) * (1.2P)
=> F(new) = F/(0.92*1.2)
=> F(new) = 0.906F
Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4%
ANSWER:E
Answer: E
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Options:
A)6 days
B)10 days
C)15 days
D)16 days
E)20 days
Rationale: Work done by X in 4 days =(1/20)*4=1/5
Remaining work =1 -1/5=4/5	.
(X + Y)'s 1 day's work =1/20+1/12 =	8/60	=	2/15	.
Now,	2/15	work is done by X and Y in 1 day.
So,	4/5	work will be done by X and Y in	(15/2x4/5)= 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
Option B
Answer: B
Question: A toy store sells small, medium, and large toy trucks in each of the colors red, blue, black, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
Options:
A)2/5
B)7/15
C)11/15
D)7/20
E)11/30
Rationale: Probability of NOT selecting medium out of 3 sizes = 2/3
Probability of NOT selecting red out of 5 colours = 4/5
Total probability of NOT selecting red and medium = (2/3)*(4/5) = 8/15
Required probability = 1 - 8/15 (this will select at least one of red and medium)
= 7/15
The answer is B.
Answer: B
Question: A student scored an average of 60 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)86
B)160
C)76
D)140
E)26
Rationale: Given M + P + C = 60 * 3 = 180 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 180
= 140
Answer:D
Answer: D
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
Options:
A)4:8
B)4:3
C)4:2
D)4:1
E)4:6
Rationale: 4 πr2 : 3 πr2 => 4:3
Answer: B
Answer: B
Question: What least value should be replaced by * in 483*4312 so the number become divisible by 6
Options:
A)3
B)4
C)5
D)2
E)7
Rationale: Explanation:
Trick: Number is divisible by 6, if sum of all digits is divisible by 3 and 2,
Last digit is 2 so it is dividable by 2
so (4+8+3+*+4+3+1+2) = 25+* should be divisible by 6,
15+ will be divisible by ,
so that least number is 2.
Answer: Option D
Answer: D
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $80, and the total cost is $16,000, what is the value of n?
Options:
A) 30
B) 50
C) 60
D) 75
E) 100
Rationale: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $10,000 + n * $80 --> n = 75.
Answer: D.
Answer: D
Question: How many odd numbers are possible between 1 to 10000? find out the number of odd number of digits?
Options:
A)2999
B)3500
C)4000
D)4599
E)4999
Rationale: There are always one odd and one even no. And the question is odd no. Between 1 to 10000
So we have to find no. Between 1 to 10000 so we should not includes 1
10000/2 -1=4999
ANSWER:E
Answer: E
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 4x+ 4y > 4z
III. yz > xz
IV. xy > y + z
Options:
A) I only
B) II only
C) II and III only
D) II and IV only
E) III and IV only
Rationale: we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 4x+ 4y > 4z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B
Answer: B
Question: A large delicatessen purchased p pounds of cheese for K dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)
Options:
A)(p − d)(s − c)
B)s(p-d) - Kp
C)c(p − d) − ds
D)d(s − c) − pc
E)pc − ds
Rationale: Total cost price = K*p ............... (1)
Wastage = d pounds
Quantity sold = p-d
Selling price per pound = s
Total selling price = s(p-d) ........... (2)
Profit = (2) - (1)
= s(p-d) - Kp
B
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)88
B)27
C)36
D)31
E)12
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 190 + 120 = 310 m.
Time taken = 310/10 = 31 sec.
Answer: D
Answer: D
Question: A new basketball cost increased 5% last week. A basketball coach wanted to buy two dozen basketballs in bulk for his team. He was able to negotiate paying only 90% of the posted price for the bulk purchase. How much did the coach save by purchasing in bulk?
Options:
A)2.5%
B)3.5%
C)4.5%
D)5.5%
E)6.5%
Rationale: Quantity X Rate = Price
1 X 1 = 1
0.9 X 1.05 = 0.945
Decrease in price = (0.055/1) Ã— 100 = 5.5%
Answer = Option D
Answer: D
Question: The average age 12 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)24 years
B)21 years
C)18 years
D)29 years
E)30 years
Rationale: 12 * 2 = 24 years
Answer:A
Answer: A
Question: 29 persons can repair a road in 16 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)12.88
B)3.88
C)13.88
D)15
E)18.8
Rationale: Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
Hence we can write as
(persons)29:30
}::x:16
(hours)5:6
29*5*16=30*6*x
x=12.88
ANSWER:A
Answer: A
Question: If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king?
Options:
A)6/13
B)7/10
C)4/11
D)7/13
E)5/26
Rationale: There are 26 black cards and 2 red kings.
P(black card or king) = 28/52 = 7/13
The answer is D.
Answer: D
Question: Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)
Options:
A)14/15
B)15/14
C)4/5
D)21/25
E)Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 42 /5
Average Speed of Jill = 42/(4.2) = 10
Ratio of Average speed of Jack to Jill = (42/5)/10 =42/50 =21/25
Answer D
Answer: D
Question: The S.I. on a certain sum of money for 2 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
Options:
A)2197
B)1267
C)1750
D)2267
E)2625
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(2 * 8) = Rs. 2625
Answer:E
Answer: E
Question: The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is
Options:
A)2488
B)378
C)739
D)474
E)291
Rationale: Explanation:
Area of 4 walls = 2(l+b)h
=2(10+7) x 5 = 170 sq m
Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m
area to be planted = 170 -12 = 158 sq m
Cost of painting = Rs. 158 x 3 = Rs. 474
Answer:D
Answer: D
Question: In how many ways can the letters of the word AEOGHYI be rearranged such that the vowels always appear together?
Options:
A)254
B)576
C)476
D)765
E)398
Rationale: AEOGHYI
AEOI will come together as a group which can be arranged in 4!=24ways.
AEOI, G,H,Ycan be arranged in 4!=24 ways.
total possible arrangements = 24*24=576 ways
ANSWER:B
Answer: B
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Options:
A)50400
B)50420
C)50500
D)50540
E)50590
Rationale: The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.
Number of ways to arrange these letters
=
7
!
2
!
=
7
×
6
×
5
×
4
×
3
×
2
×
1
2
×
1
=
2520
=7!2!=7×6×5×4×3×2×12×1=2520
In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves
=
5
!
3
!
=
5
×
4
×
3
×
2
×
1
3
×
2
×
1
=
20
=5!3!=5×4×3×2×13×2×1=20
Hence, required number of ways
=
2520
×
20
=
50400
=2520×20=50400
A)
Answer: A
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 1/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Options:
A)7/17
B)14/31
C)7/15
D)14/19
E)1/2
Rationale: # of basic stereos was 1/3 of total and # of deluxe stereos was 2/3 of total, let's assume total=15, then Basic=5 and Deluxe=10.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 5*1=5 and total time for Deluxe would be 10*7/5=14 --> total time for both of them would be 5+14=19--> deluxe/total=14/19.
Answer: D.
Answer: D
Question: A corporation that had $10 billion in profits for the year paid out $200 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
Options:
A)50%
B)20%
C)5%
D)2%
E)0.2%
Rationale: required answer = [employee benefit/profit] *100
=[(200 million)/(10 billion)]*100
=[(200*10^6)/(10*10^9)]*100
=(20/1000)*100
=2%
So answer is (D)
Answer: D
Question: What will come in place of the x in the following Number series? 177147 ,59049 ,19683 ,6561, 2187 , x
Options:
A)727
B)729
C)726
D)722
E)723
Rationale: Go on dividing by 3 to the next number
Answer : B
Answer: B