divelab/Sys2Bench huggingface dataset:
Question: Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A)120
B)116
C)108
D)107
E)72
Rationale: # of three-digit integers greater than 600 is 399 (999-600);
Numbers with all distinct digits: 4*9*8=288. First digit can take 4 values: 6, 7, 8 or 9, second digit can take 9 values (10 minus the one we used for the first digit) and third digit can tale 8 values (10 minus 2 digits we've already used for the first two digits);
Numbers greater than 600 which have all alike digits: 4 (666, 777, 888, 999);
{Total}-{all distinct}-{all alike}={two alike, one different} --> 399-288-4=107.
Answer: D.
Answer: D
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)287
B)288
C)500
D)277
E)121
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Answer: C
Question: For a sequence to be considered an arithmetic sequence, there must be a constant difference between the terms. If a,b,c,d,e is an arithmetic sequence, which of the following is also an arithmetic sequence?
I. 7a,7b,7c,7d,7e
II. a-5, b-5, c-5, d-5, e-5
III. a^3, b^3, c^3, d^3, e^3
Options:
A)III only
B)I and II
C)II and III
D)II only
E)I and III
Rationale: lets look at the three choices...
I. 7a,7b,7c,7d,7e
since the difference is constant, it is an arithmetic sequence...
II. a-5, b-5, c-5, d-5, e-5
since the difference is constant, it is an arithmetic sequence
III. a^3, b^3, c^3, d^3, e^3
since the difference is not constant it is not be an arithmetic sequence...
Answer is B)
Answer: B
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB < AX
B)XB < YD
C)AX > XB
D)AX < AB
E)AX > AB
Rationale: A--X------B
C------Y--D
AX < AB.
Answer: D.
Answer: D
Question: If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
Options:
A)20
B)40
C)15
D)16
E)12
Rationale: 100
125
-----
125 ----- 25
100 ------ ? => 20%
ANSWER A
Answer: A
Question: A train takes 18 seconds to pass completely through a statin 162 m long and 15 seconds through another station 120 m long. The length of the train is:
Options:
A)30
B)60
C)90
D)100
E)120
Rationale: Sol.
Let the length of the train be x metres.
∴ x + 162 / 18 = x + 120 / 15 ⇔ 15 (x + 162) = 18 (x + 120) ⇔ x = 90 m.
Answer C
Answer: C
Question: 20 machines can do a work in 5days. How many machines are needed to complete the work in 10days?
Options:
A)10
B)15
C)8
D)12
E)20
Rationale: Required number of machines = 20*5/10 = 10
Answer is A
Answer: A
Question: If x^2 - 1 = 0 and x > 0, which of the following must be equal to 0 ?
Options:
A) x^2 - 9x
B) x^2 - 9x + 8
C) x^2 - 2x + 3
D) x^2 + 2x - 3
E) x^2 + 5x + 6
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= 1 in the equation x^2 -9x+8 = 1-9+8 = 0
B is also the answer
Answer: B
Question: 12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
Options:
A)6
B)8
C)10
D)20
E)40
Rationale: we have 1 litre = 1000cm³ (thanks Bunuel)
=>12 litres = 12*1000 = 12000cm³
Let call the height of the water is x
the breadth and length of the water will equal the aquarium
The volume of the water:
50 * 30 * x = 12000cm³
=> x = 12000/(50*30) = 8 cm
Answer is B
Answer: B
Question: A travel agent offers a vacation plan which costs x dollars for the first day, and x/3 for each additional day. How much does a vacation of y days cost, where y > 1.
Options:
A)(yx-3x)/3
B)(yx+4x)/2
C)(yx+5x)
D)(yx+2x)/3
E)(yx-x)/3
Rationale: Cost = x + (y-1)*x/3 = (3x + (y - 1)*x)/3 = (yx+2x)/3
Answer is D
Answer: D
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
Options:
A)5
B)6
C)8
D)4
E)1
Rationale: 28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: D
Answer: D
Question: A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $6.00?
Options:
A) 72
B) 60
C) 90
D) 120
E) 240
Rationale: Cost price of 1 pound of bananas = 0.5/3 = 1/6
Selling price of 1 pound of bananas = 1/4
Profit per pound = (1/4 - 1/6) = (1/12)
Total profit is given as 6
(1/12)*x = 6
x = 72
Answer: A
Answer: A
Question: The price of an article is cut by 10%. To restore it to the former value, the new price must be increased by
Options:
A)10%
B)9 1/11 %
C)11 1/9%
D)11%
E)None
Rationale: Explanation:
Let original price = Rs.100
Then, new price = Rs.90
Increase on Rs.90=Rs.100
Increase % = (10/90×100)% =11 1/9 %
Correct Option: C
Answer: C
Question: Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time V it could take for 10 cars to be complete?
Options:
A)111 1/9 minutes
B)115 2/5 minutes
C)116 minutes
D)120 minutes
E)125 minutes
Rationale: A builds 4 cars in 80 min
B builds 4 cars in 100 min
So A builds another car in another 20 min (i.e total 5 cars)
B builds another car in another 25 minutes (i.e, total 5 cars)
However, A can build another car in next 20 min (i.e total 6 cars)
So total time V= 125 min by B, which is > 120 min by A
B - 4 cars, A - 6 cars
Answer = D
Answer: D
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 69.12 = ?
Options:
A)229
B)225
C)235
D)220
E)240
Rationale: ? = 33 1⁄3% of 768.9 + 25% of 1691.2 – 69.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 6.12
= 256.3 + 40.3 – 69.12 ≈ 229
Answer A
Answer: A
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 16%?
Options:
A)26%
B)28%
C)27%
D)40%
E)70%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 84
2/3 SP1 = 84
SP1 = 126
100 --- 26 => 26%
Answer:A
Answer: A
Question: A vendor sells 20 percent of the pears he had and throws away 50 percent of the remainder. The next day, the vendor sells 20 percent of the remaining pears and throws away the rest. In total, what percent of his pears does the vendor throw away?
Options:
A)56
B)60
C)64
D)68
E)72
Rationale: Let x be the original number of pears.
On day one, the vendor throws away (0.5)(0.8)x=0.4x.
The remaining pears are (0.5)(0.8)x = 0.4x.
On day two, the vendor throws away (0.8)(0.4)x=0.32x.
The vendor throws away a total of 0.4x + 0.32x = 0.72x.
The vendor throws away 72 percent of the pears.
The answer is E.
Answer: E
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)6
B)5
C)7
D)8
E)2
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D
Answer: D
Question: At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 7:3. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?
Options:
A)45/21
B)46/2
C)13/30
D)23/6
E)4/6
Rationale: Red: Blue = 7:3
Let Red = 7x and Blue = 3x
1/3 of Red are left handed => 1/3 * 7x = 7x/3 Red left handed
2/3 of Blue are left handed => 2/3 *3x = 6x/3 blue left handed
fraction of participants who are left handed = total left handed/ total participants = (red left handed + blue left handed)/total participants = (7x/3 + 6x/3)/(7x+3x) = 13/30
Answer : C
Answer: C
Question: The perimeter of a semi circle is 113 cm then the radius is?
Options:
A)17
B)28
C)19
D)11
E)22
Rationale: 36/7 r = 113 => r
= 22
Answer: E
Answer: E
Question: A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders W when the order of the divisors is reversed.
Options:
A)8,5,3
B)4,2,1
C)W=3,2,1
D)W=6,4,2
E)None of above
Rationale: My approach would be
Three Divisors : 3, 5, 8
Three Remain: 1, 4, 7
Start from the bottom of the last column i.e. from the third remainder:
Go up diagonally and multiply by the second divisor: 5*7 = 35
Go down and add the second remainder: 35 + 4 = 39
Go up diagonally and multiply by the first divisor: 39* 3 = 117
Go down and add the first remainder: 117 + 1 = 118
Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2
Ans is D i.e. 6,4,2
Answer: D
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
Options:
A)7 years
B)5 years
C)4 years
D)6 years
E)3 years
Rationale: 100 ---- 300 --- 3
900 --- 3
----
6 years
Answer:D
Answer: D
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:12. If P invested the money for 5 months, find for how much time did Q invest the money?
Options:
A)19
B)17
C)13
D)10
E)12
Rationale: 7*5: 5*x = 7:12
x = 12
Answer: E
Answer: E
Question: Jane started baby-sitting when she was 20 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Check two extreme cases:
Jane = 20, child = 10, years ago = 32-20 = 12 --> child's age now = 10+12 = 22;
Jane = 22, child = 11, years ago = 32-22 = 10 --> child's age now = 11+10 = 21.
Answer: C.
Answer: C
Question: The parameter of a square is equal to the perimeter of a rectangle of length 4 cm and breadth 2 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Options:
A)4.51
B)4.71
C)4.32
D)4.21
E)4.68
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(4+ 2) = 12 cm Parameter of the square = 12 cm
i.e. 4a = 12
a = 3
Diameter of the semicircle = 3 cm
Circimference of the semicircle
= 1/2(âˆ)(3)
= 1/2(22/7)(3) = 66/14 = 4.71 cm to two decimal places
Answer: B
Answer: B
Question: A group of 6 volunteers is to be interviewed and selected from a pool of 9 candidates. How many different volunteer groups are possible?
Options:
A)102
B)52
C)84
D)56
E)336
Rationale: Note that the volunteer groups must consist of 6 members, not at least 6 members. Hence, all you have to do is 9C6 = 84
Answer (C)
Answer: C
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
Options:
A)37
B)85
C)48
D)43
E)84
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer: Option C
Answer: C
Question: Six children — A, B, C, D, E, F — are going to sit in seven chairs in a row. The children CF have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
Options:
A)600
B)240
C)1440
D)4320
E)4800
Rationale: for such questions , we can treat both as one then total person=5..
these 5 can be arranged in 6! ways.. but within these 6 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =5!*2=240
ans B
Answer: B
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 14 charts have been brought to the meeting, how many people are present?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 10
Total charts are 11 so A + 2B = 14
Add both: 3A + 3B = 24 so A + B = 8
Total number of people = 8
C
Answer: C
Question: Find the cost price of an item if by selling at Rs.1255, a profit of 10% is made?
Options:
A)Rs. 1000
B)Rs.3000
C)Rs.2100
D)Rs.1129
E)Rs.1985
Rationale: SP = 1255
CP = (SP)*[100/(100+P)]
= 1255 * [100/(100+10)]
= Rs.1129
Answer: D
Answer: D
Question: The avg. age of a group of 24 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
Options:
A)22 years
B)23 years
C)24 years
D)25 years
E)27 years
Rationale: Total age of 12 students=24*20=480
If total age of 4 students=x
Then, (480+x)/(24+4) =(20+1), x=108
So average age of new students=108/4= 27 years
ANSWER:E
Answer: E
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 40% goods during theft. His loss percent is:
Options:
A)72%
B)42%
C)34%
D)12%
E)22%
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 60.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 60 = Rs. 66
Hence, loss % = 34/100 * 100 = 34%
Answer:C
Answer: C
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
Options:
A)90
B)100
C)120
D)160
E)200
Rationale: Solution:
Let x be the number he chose, then
2*x*138=102
2x=240
x=120
correct answer C
Answer: C
Question: The price of rice has increased by 60%. In order to restore to the original price, the new price must be reduced by ?
Options:
A)33 1/3%
B)37 1/2%
C)40%
D)45%
E)NONE
Rationale: Answer
Let original price = Rs. 100
⇒ Increase price = Rs. 160
⇒ Decrease on Rs. 160 = Rs. 60
∴ Decrease on Rs. 100 = (60/160) x 100 % = 37 1/2%
Correct Option: B
Answer: B
Question: If Feb 12th,1986 falls on Wednesday then Jan 1st,1987 falls on which day?
Options:
A)monday
B)friday
C)Thursday
D)saturday
E)0
Rationale: Explanation:
First,we count the number of odd days for the left over days in the given period.
Here,given period is 12.2.1986 to 1.1.1987
Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan
16 31 30 31 30 31 31 30 31 30 31 1 (left days)
2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 1(odd days) = 1 odd day
So,given day Wednesday + 1 = Thursday is the required result.
Answer: C) Thursday
Answer: C
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3400, A will get:
Options:
A)Rs.1200
B)Rs.1500
C)Rs. 2040
D)Rs.2000
E)None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 136
So, A’s amount = 120 × 15 = Rs.2040.
Answer: Option C
Answer: C
Question: 6 people can do work in 80 days how much people they required to complete the work in 16
days ?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Man and days concept ...
6M * 80D=M * 16D
solve it,
total no of people required is 30;
ANSWER:C
Answer: C
Question: A clock shows 5.20. After how much time both hands will coincide together?
Options:
A)6 2/11 minutes
B)5 5/11 minutes
C)3 2/11 minutes
D)4 2/11 minutes
E)7 2/11 minutes
Rationale: 60/55*(5)=5 5/11
ANSWER:B
Answer: B
Question: In an examination 35% of the students passed and 351 failed. How many students appeared for the examination?
Options:
A)A)540
B)B)400
C)C)700
D)D)650
E)E)840
Rationale: Let the number of students appeared be x
then, 65% of x = 351
65x/100 = 351
x = 351*100/65 = 540
Answer is A
Answer: A
Question: A boy rides his bicycle 10km at an average speed of 12km/hr and again travels 12km at an average speed of 10km/hr. His average speed for the entire trip is approximately?
Options:
A)8km/hr
B)10.8km/hr
C)12.6km/hr
D)15.6km/hr
E)14km/hr
Rationale: Total distance traveled = 10+12 = 22km
Total time taken = 10/12 + 12/10 = 61/30 hrs
Average speed = 22*30/61 = 10.8km/hr
Answer is B
Answer: B
Question: A grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ?
Options:
A)4991
B)5467
C)5987
D)6453
E)None of these
Rationale: Explanation:
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991. Answer: A
Answer: A
Question: Two persons enter the lift of a five storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
Options:
A)7
B)10
C)12
D)14
E)16
Rationale: Each person out of 2 has 4 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 4*4=4^2=16.
Answer: E.
Answer: E
Question: Rose and John had the same number of candies. Rose gave John 24 candies so that now John has five times as many candies as Tina has. John has now how many candies?
Options:
A)36
B)48
C)54
D)60
E)65
Rationale: T = R
T - 24 ;R + 24
R + 24 = 5 ( T - 24 )
R + 24 =5T - 120
R - 5T = - 144
We knowR = T, so
R - 5T = - 144
Or, R - 5R = -144
Or, - 4R = - 144
Or, R = 36( This is the initital no of Candies Rebecca had)
Candles now she possesses is36 + 24 = 60
So , Rebecca now has 60 candies.
Answer will be (D) 60
Answer: D
Question: X completes a work in 70 days and Y complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be?
Options:
A)20 days.
B)22 days.
C)25 days.
D)36 days.
E)21 days.
Rationale: If X can complete a work in x days and Y can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 70Ã— 30/ 100 = 21 days.
E)
Answer: E
Question: What is the length of the longest pole which can be kept in a room 6 m long, 4 m broad and 3 m high?
Options:
A)7
B)9
C)11
D)13
E)None
Rationale: Explanation:
d2 = 62 + 42 + 32 = 7.8
E)
Answer: E
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 26 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
Options:
A)32
B)40
C)48
D)54
E)60
Rationale: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.26(800) = 232
The answer is A.
Answer: A
Question: How many integers n are there such that 1< 4n + 4 < 16?
Options:
A)5
B)1
C)2
D)3
E)4
Rationale: 1< 4n + 4 < 16
1< 4n + 4 < 16
We first subtract 4 from all three parts of the inequality, and we obtain:
-3/4 < 4n < 12
Next, we divide both sides of the inequality by 4 and we get:
-4/4 < n < 3
The answer is D
Answer: D
Question: Fom the integer n, if n*n*n is odd, then what is true from below options?
Options:
A)n is odd and n*n is even
B)n is odd
C)n*n is even
D)n is even
E)n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: A
Question: A can have a piece of work done in 7 days, B can work five times faster than the A, C can work six times faster than A. How many days will they take to do the work together ?
Options:
A)3/2 days
B)8/9 days
C)4/3 days
D)can't say
E)none
Rationale: A's 1 day work is 1/18
B's 1 day work is 5/18
C's 1 day work is 6/18
(A+B+C)'s 1 day work(1/18+5/18+6/18) is 2/3
so, they can finish the work in 3/2 days
ANSWER:A
Answer: A
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)Rs.229
B)Rs.285
C)Rs.228
D)Rs.217
E)Rs.123
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160
= Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100]
= Rs.285.
Answer:D
Answer: D
Question: Mandrake has to choose from 4 from 14 people. There are 3 girls, 5 boys , 6 children. What is total probability that he will choose 1G , 2B , 1C?
Options:
A)1/7
B)2/7
C)3/7
D)4/7
E)16/89
Rationale: (3C1 * 5C2 * 6C1)/ 14C4 = 3*10*6/1001 = 180/1001=16/89
ANSWER:E
Answer: E
Question: How many numbers between 1000 and 5000 are exactly divisible by 225?
Options:
A)16
B)18
C)19
D)12
E)21
Rationale: Explanation: First multiple of 225 after 1000 is 1125 (225 Ã— 5 ) and last multiple of 225 before 5000 is 4950 (225 Ã— 22)
Total number are l+a/d=4950-1125/225+1=18
ANSWER IS B
Answer: B
Question: Doughnuts, Cookies and Muffins in a pastry shop are in the ratio of 5: 3 : 1. If there are 50 Doughnuts, the number of Muffins in the shop is:.
Options:
A)25
B)30
C)10
D)15
E)20
Rationale: Explanation :
Let Doughnuts = 5x, Cookies = 3x & Muffins = 1x. Now, 5x = 50 hence x = 10.
Number of Muffins = 1x which is 10.
Answer : C
Answer: C
Question: Exactly 36% of the numbers in set R are even multiples of 3. If 40% of the even integers in set R are not multiples of 3, what percent of the numbers in set R are not even integers?
Options:
A) 76%
B) 60%
C) 50%
D) 40%
E) 24%
Rationale: Everything is correct except the red part with a typo: it should be N=0.6R --> even numbers are 60% of R --> 40% of R are not even integers.
Answer: D.
Answer: D
Question: A man walking at a rate of 15km/hr crosses a bridge in 40 minutes. The length of the bridge is?
Options:
A)1250m
B)1110m
C)2000m
D)1000m
E)1300m
Rationale: Speed = 15*5/18 = 15/18 m/sec
Distance covered in 40 minutes = 15/18 *40 *60 = 2000m
Answer is C
Answer: C
Question: A box contains 3 yellow balls and 7 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
Options:
A)3/5
B)7/10
C)5/8
D)2/3
E)3/7
Rationale: Each ball has an equal chance (1/10) of being selected fourth.
The probability that a black ball is selected fourth is 7/10.
The answer is B.
Answer: B
Question: A circle graph shows how the budget of a certain company was spent: 15 percent for transportation, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for salaries. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent salaries?
Options:
A)216°
B)222°
C)228°
D)234°
E)240°
Rationale: The percent of the budget for salaries is 100 - (15+9+5+4+2)= 65%
100% of the circle is 360 degrees.
Then (65%/100%)*360 = 234 degrees
The answer is D.
Answer: D
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Options:
A)1:2
B)4:5
C)1:3
D)1:1
E)1:4
Rationale: Let the third number be x.
Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2
Therefore, Ratio of first two numbers = (6x/5 : 3x/2)
= 12x : 15x = 4 : 5.
Answer is B.
Answer: B
Question: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 16 cm height. What is the diameter of each sphere?
Options:
A)4 cm
B)6 cm
C)8 cm
D)10 cm
E)12 cm
Rationale: Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
12*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 16 = 64 cm^3
R = 4 cm
D = 8 cm
The answer is C.
Answer: C