divelab/Sys2Bench huggingface dataset:
Question: In an entrance test, Deepika came across a mathematical patter problem.
If
6 / 7 = 2
3 / 9 = 7
8 / 2 = 6
Then
4 / 5 = ?
She was able to solve it in less than a minute. Can you?
Options:
A)0
B)1
C)2
D)3
E)10
Rationale: A
The answer is 0.
As
6 / 7 = 42 but the answer is written as 2
3 / 9 = 27 but the answer is written as 7
8 / 2 = 16 but the answer is written as 6
If we look at the answers, the second digit has been used in the problem.
Now, as
4 / 5 = 20 and the second digit is 0, the answer is 0.
Answer: A
Question: The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
Options:
A)11
B)11.2
C)11.4
D)11.5
E)None
Rationale: Solution
Middle number	= [(10.5x6+11.4x6) - 10.9x11]
= (131.4 - 119.9)
= 11.5.
Answer D
Answer: D
Question: There are 145 bananas lying in a shop which is to be divided equally among 12 candidates. Find the extra number of bananas lying with the shop owner after distribution.
Options:
A)1
B)2
C)3
D)4
E)9
Rationale: 145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A.
Answer: A
Question: The ratio of male to female in a class is 2:4. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
Options:
A)a)160 degree
B)b) 168 degree
C)c)191 degree
D)d)192 degree
E)e)200 degree
Rationale: here is my approach => males => 2x and females =4x => total =6x
now 6x=> 360
therefore 10x/3 => 200 degree .
P.S => 10x/3 is nothing but total number of students with the given preference
Answer E
Answer: E
Question: If A speaks the truth 55% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
Options:
A)0.29
B)0.33
C)0.41
D)0.482
E)0.411
Rationale: Explanation:
Probability that A speaks truth is 55/100 = 0.55
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.55 × 0.6 = 0.33
Answer: B
Answer: B
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options:
A)76
B)35
C)25
D)28
E)62
Rationale: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76
Answer: A
Answer: A
Question: The speeds of 3 cars in the ratio 5:4:6. The ratio between time taken by them to travel the same distance is?
Options:
A)1:2:3
B)5:7:12
C)12:15:10
D)22:23:25
E)9:11:17
Rationale: Ratio of time taken is = 1/5 : 1/4 : 1/6 = 12:15:10
Answer is C
Answer: C
Question: If A and B are two prime numbers bigger than 2, which of the following can be true?
(1) A + B is an even number.
(2) A - B is also a Even number.
(3) A^B is also a prime number
Options:
A)1 only.
B)2 only.
C)3 only.
D)1 and 2 only
E)1, 2 and 3.
Rationale: (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A x B is also a prime number. : Beats the property of primes, so false
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans :D
Answer: D
Question: What is the sum of the different positive prime factors of 630?
Options:
A)7
B)10
C)17
D)20
E)24
Rationale: The prime factorization of 630
= 63 * 10
= 7*9 * 2*5
= 7*3^2 * 2*5
The sum of the different positive prime factors = 2+3+5+7 = 17
The answer is C.
Answer: C
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)178.89 cm
B)178.29 cm
C)178.79 cm
D)177.89 cm
E)178.69 cm
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: In how many ways can 10 engineers and 4 doctors be seated at a round table if all the 4 doctors do not sit together?
Options:
A)13! - (10! × 4!)
B)13! × 4!
C)14!
D)10! × 4!
E)None of these
Rationale: Explanation :
Initially let's find out the total number of ways in which 10 engineers and 4 doctors
can be seated at a round table
In this case, n = total number of persons = 10 + 4 = 14
Hence the total number of ways in which 10 engineers and 4 doctors can be seated at a round table
= (14-1)! = 13! ---(A)
Now let's find out the total number of ways in which 10 engineers and 4 doctors
can be seated at a round table where all the 4 doctors sit together.
Since all the 4 doctors sit together, group them together and consider as a single doctor.
Hence, n = total number of persons = 10 + 1 = 11
These 11 persons can be seated at a round table in (11-1)! = 10! ways ---(B)
However these 4 doctors can be arranged among themselves in 4! Ways ---(C)
From (B) and (C), the total number of ways in which 10 engineers and 4 doctors
can be seated at a round table where all the 4 doctors sit together
= 10! 4! ---(D)
From (A) and (D),
The total number of ways in which 10 engineers and 4 doctors can be seated at a round table
if all the 4 doctors do not sit together = 13! - (10! 4!)
Answer : A
Answer: A
Question: A pipe can fill a tank in 16 hours. Due to a leak in the bottom,it is filled in 24 hours. If the tank is full, how much time will the leak take to empty it ?
Options:
A)12 hrs
B)24 hrs
C)36 hrs
D)48 hrs
E)42 hrs
Rationale: Time taken by leak to empty tank = 1/(1/16-1/24) = 48 hrs
ANSWER:D
Answer: D
Question: In how many different ways can 3 physics, 2 math, and 3 chemistry books be arranged in a row so that all books of the same subject are together?
Options:
A)432
B)456
C)512
D)556
E)624
Rationale: Let's think of each subject as a group so there are 3 groups.
The number of ways to arrange these 3 groups is 3!
Within each subject the books can be re-arranged.
So we need to multiply 3! by 3!*2!*3! which is 3!*3!*2!*3! = 432
The answer is A.
Answer: A
Question: (11^2+12^2+13^2+......+20^2)=?
Options:
A)385
B)2485
C)2870
D)3255
E)None of them
Rationale: =(1^2+2^2+3^2+......+30^2)-(1^2+2^2+3^2+......+10^2)
=(20x21x41/6 - 10x11x21/6)
Therefore, (1^2+2^2+....+n^2)=1/6n(n+1)(2n+1)
=(2870-385) = 2485.
Answer is B
Answer: B
Question: Which of the following numbers is the number 2 not a prime factor?
Options:
A)30
B)48
C)76
D)82
E)99
Rationale: 30=2*3*5
48=2^4*3
76=2^2*19
82=2*41
99=3^3*11
99 has 2, none of which is 2.
Answer E
Answer: E
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 14 men
do it ?
Options:
A)65 hours
B)64 hours
C)30 hours
D)62 hours
E)66 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
14 : 36 : : 25 : x	(14 x x) = (36 x 25)	(36 x 25)/14 ~ 64
Answer is B.
Answer: B
Question: If $ 5,000 is invested in an account that earns 16% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
Options:
A)$ 4
B)$ 8
C)$ 12
D)$ 16
E)$ 432
Rationale: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.16/2)^2= 5416
Amount (SI) = P+PTR/100 = 5000+(5000*1*16/100)=5400
Difference = 5416-5400=16 $
D
Answer: D
Question: Consider below info to be a table:
AMOUNT OF BACTERIA
TIME - AMOUNT
1PM - 10gms
4PM - x gms
7PM - 16.9 gms
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ?
Options:
A)12.0
B)12.1
C)12.2
D)13.0
E)12.4
Rationale: let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =16.9 => x^2 =1.69 or x = 1.3 => @4PM quantity = 10x =10*1.3 =13.
Answer D
Answer: D
Question: If a discount of 16% is given on the marked price of a book, the publisher gains 20%. If the discount is increased to 20% the gain percent is
Options:
A)14 2/7%
B)14 1/7%
C)14 3/7%
D)14 4/7%
E)14 5/7%
Rationale: Let MP = 100, then SP = 100 - 16 = 84.
CP = SP*100/(100 + Gain%) = 8400/120 = 70.
When discount = 20, SP = 80.
Thus gain % = (80 - 70)/70 * 100 = 14 2/7 %.
ANSWER:A
Answer: A
Question: In a match in team X, 3% candidates got selected from the total appeared candidates. team X had an equal number of candidates appeared and 12% candidates got selected with 27 more candidates got selected than ream x. what was the number of candidates appeared from each team?
Options:
A)300
B)200
C)258
D)456
E)187
Rationale: Explanation :
Solution: Let the number of candidates appeared from each team be x.
then, 12% of x - 3% of x =26.
=>9% of x =27
=>9x/100 =27 => x =27*100/9 = 300
Answer : A
Answer: A
Question: In a college the ratio of the numbers of boys to the girls is 8:5. If there are 175 girls, the total number of students in the college is?
Options:
A)562
B)356
C)455
D)416
E)512
Rationale: Let the number of boys and girls be 8x and 5x
Then , 5x = 175
x= 35
Total number of students = 13x = 13*35 = 455
Answer is C
Answer: C
Question: 16.02 Ã— 0.1 = ?
Options:
A)0.1602
B)0.001602
C)1.6021
D)0.01602
E)None of these
Rationale: 16.02 Ã— 0.1 = 1.602
The answer is C.
Answer: C
Question: The maximum numbers of students among them 781 pens and 710 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options:
A)71
B)910
C)1001
D)1911
E)None
Rationale: olution
Required number of students.
= H.C.F of 781 and 710.
â€¹=â€º 71.
Answer A
Answer: A
Question: R is the set of positive even integers less than 51, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Options:
A) None
B) Three
C) Four
D) Five
E) Seven
Rationale: R is the set of positive even integers less than 51, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?
R=2,4,6,8,10,12...
S=4,16,36,64...
Numbers: 4, 16, and 36 are even integers (less than 51) that are in both sets.
Solution: Three
Answer: B
Answer: B
Question: If 6x = 10y = 14z, then what is a possible sum of positive integers x, y, and z?
Options:
A)213
B)58
C)84
D)122
E)168
Rationale: Answer = D = 122
6x = 10y = 14z
3x = 5y = 7z
3(5*7) = 5(3*7) = 7(3*5)
Addition = 35+21+15 = 71
Answer would be multiple of 71 which is 213
Answer : A
Answer: A
Question: In an examination 30% failed in Math and 70% failed in French. If 20% failed in both. What % of students passed in both.
Options:
A)25%
B)15%
C)20%
D)30%
E)10%
Rationale: Passed in Math = 100 - 30 = 70%
Passed in French = 100 - 70 = 30%
Students who passed Math or French = 100 -20 = 80%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 70+30-80 =20%
ANSWER:C
Answer: C
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)87
B)44
C)88
D)76
E)54
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352
=> T = 44.
Answer:B
Answer: B
Question: Winchard's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Winchard's average score on the 5 tests to be 80?
Options:
A) 80
B) 82
C) 84
D) 86
E) 88
Rationale: E. 88
Winchard must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88.
Answer: E
Question: Should a total ban be put on traping wild animals?
Arguments:
1. Yes. Trappers are making a lot of money
2. No. Bans on hunting and trapping are not effective
Options:
A)Only 1 is true
B)Only 2 is true
C)Either 1 or 2 is true
D)Neither 1 or 2 is true
E)Either 1 or 6 is true
Rationale: Explanation:
Ban is necessary to protect our natural envoirnment .So none of the argument is strong enough
Answer: D) Neither 1 or 2 is true
Answer: D
Question: In one hour, a boat goes 11 km along the stream and 5 km against the stream. the sped of the boat in still water (in km/hr) is :
Options:
A)3
B)5
C)8
D)9
E)10
Rationale: Solution
Speed in still water= 1/2(11+5) km/hr= 8kmph. Answer C
Answer: C
Question: Find the odd man out. 13, 16, 12, 24, 12, 34, 46
Options:
A)16
B)46
C)24
D)13
E)18
Rationale: Explanation :
13 is the only odd number in the given series
Answer : Option D
Answer: D
Question: the two sides of a triangle are 32 and 68. the area is 960 sq.cm. find the third side of triangle?
Options:
A)45
B)50
C)60
D)70
E)80
Rationale: we see 68^2-32^2=(68+32)*(68-32)=100*36=60^2
now (1/2)*60*32=960(match with given options)
(i.e area of a right angled triangle whose sides are 32,60,68)
third side=60
ANSWER:C
Answer: C
Question: The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 54
2L^2/3 = 54
L^2 = 81
L = 9 cm
The answer is D.
Answer: D
Question: Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?
Options:
A)761 min
B)100 min
C)167 min
D)367 min
E)178 min
Rationale: Work done by the third pipe in 1 min
= 1/50 - (1/60 + 1/75)
= - 1/100.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 100 min.
Answer: B
Answer: B
Question: The grade point average of the entire class is 85. If the average of one third of the class is 97, what is the average of the rest of the class?
Options:
A)76
B)77
C)78
D)79
E)80
Rationale: Let x be the number of students in the class.
Let P be the average of the rest of the class.
85x = (1/3)97x + (2/3)(P)x
255 = 97 + 2P
2P = 158
P = 79.
The answer is D.
Answer: D
Question: The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
Options:
A)872
B)876
C)440
D)157
E)452
Rationale: r = 7 h = 3
2πr(h + r) = 2 * 22/7 * 7(10)
= 440
Answer: C
Answer: C
Question: A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 10 months?
Options:
A)18:13
B)18:16
C)18:10
D)18:14
E)14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only.
A : B
8000*18 : (8000*8) + (4000*10)
14400 : 104000
A:B = 18:13
Answer: A
Answer: A
Question: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 40 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
Options:
A)40
B)33
C)50
D)51
E)52
Rationale: Yes, ensure that you understand the relation thoroughly!
Cost per liter = K * Fraction of Spirit
40 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 20 cents. Fraction of spirit is 1/2.
20 = K * (1/2)
K = 40
Cost per liter = 40 * (1/3) (1 part spirit, 2 parts water)
Cost for 3 liters = 40 * (1/3) * 3 = 40 cents
A. 40 cents
Answer: A
Question: A real number x satisfying 1- (1/n) ≤ 3 + (1/n), for every positive integer n, is best described by ≤
Options:
A)1 < x < 4
B)1 < x ≤ 3
C)0 < x ≤4
D)1 ≤ x ≤ 3
E)None of these
Rationale: Explanation :
1- (1/n) ≤ 3 + (1/n)
Put n =1 , we get 0 < x ≤4.
Answer : C
Answer: C
Question: Two locomotives are moving in the same direction at 62 mps and 26 mps. The faster train crosses the slower train in 8 seconds. What is the length of the faster train in meters?
Options:
A)247 m
B)316 m
C)194 m
D)270 m
E)288 m
Rationale: Relative speed = (62 - 26) = 36 mps.
Distance covered in 8 sec = 36 * 8 = 288 m.
The length of the faster train = 288 m.
Answer:E
Answer: E
Question: In a six-sided polygon CQRSTV ∠C measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠C equal to, in degrees?
Options:
A) 72
B) 80
C) 88
D) 96
E) 104
Rationale: The sum of interior angle in a polygon is (n-2)*180
so for a six sided figure, (6-2)*180 = 720
let the A.M of the other 5 angles be 'm'
--> m*5 + ∠C = 720, we know ∠C=m-48
--> m*5 + m - 48 = 720, solving we get m=128
hence ∠C= 128-48 = 80
Ans B.
Answer: B
Question: There are 3 sections with 5 questions each. If three questions are selected from each section, the chance of getting different questions is________
Options:
A)10
B)100
C)1000
D)10000
E)6000
Rationale: we have to select three questions from each section so the chances are 5C3.5C3.5C3=1000
ANSWER:C
Answer: C
Question: An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 48$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?
Options:
A)52
B)75
C)92
D)100
E)184
Rationale: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (48 - 40)/(40 - 36) = 8/4 = 2/1 = Number of MicroTron stocks/Number of Dynaco stocks
So for every 2 MicroTron stock, she sold 1 Dynaco stock.
So out of 300 total stocks, (1/3)th i.e. 300/3 = 100 must be Dynaco stock.
Answer (D)
Answer: D
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Options:
A)13 min
B)7 min
C)9 min
D)12 min
E)15 min
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
ANSWER C
Answer: C
Question: The triplicate ratio of 1:2 is?
Options:
A)1:5
B)1:8
C)1:3
D)1:4
E)1:1
Rationale: 13: 23 = 1:8
Answer: B
Answer: B
Question: The number of sequences in which 5 players can throw a ball, so that the youngest player may not be the last is ?
Options:
A)100
B)96
C)8
D)62
E)10
Rationale: x Not younger
The last ball can be thrown by any of the remaining 5 players. The first 4 players can throw the ball in 4P4 ways.
The required number of ways = 4(4!)
= 96
Answer:B
Answer: B
Question: If x is an integer, which of the following must also be an integer?
I. xy
II. y/x
III. y
Options:
A)I alone
B)II alone
C)III alone
D)I and III
E)None of the above
Rationale: Lets take X = 11 and Y = 2
Then XY = 22 which is an integer.
But X/Y = 11/2 --> Not an integer.
Y/X = 2/11 --> Not an integer.
y alone is 2. which is an integer.
Hence D.
Answer: D
Question: If x^2 – 2y^2 = 2xy, then (x - y)^2 =
Options:
A)x^2
B)3x^2
C)4xy
D)3y^2
E)– y^2
Rationale: (x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2- x^2+2y^2 = 3y^2
Correct option : D
Answer: D
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Options:
A)4/5
B)4/9
C)4/8
D)4/1
E)4/2
Rationale: x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
Answer: A
Question: if
21=3
32=7
82=22
92=25
than
72=?
Options:
A)17
B)19
C)21
D)23
E)25
Rationale: (2*1)+(2-1)=3
(3*2)+(3-2)=7
(8*2)+(8-2)=22
(9*2)+(9-2)=25
(7*2)+(7-2)=19
ANSWER:B
Answer: B
Question: A van takes 6 hours to cover a distance of 180 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)50 Kmph
B)60 Kmph
C)70 Kmph
D)80 Kmph
E)20 Kmph
Rationale: Time = 6
Distence = 180
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 180/9 = 20 Kmph
E
Answer: E
Question: Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 20%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved?
Options:
A)56.8%
B)64%
C)62.2%
D)68%
E)61%
Rationale: If initial cost is Rs 100, then
Final cost will be 100*0.8*0.6*0.9 = Rs. 43.2
savings = 100-43.2=56.8
so 56.8%
ANSWER:A
Answer: A
Question: You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 5 baseball cards. How many baseball cards do you have at the end?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Solution
Start with 16 baseball cards.
John takes 5 baseball cards from you: 16 - 5 = 11 baseball cards.
So you have 11 at the end.
Correct answer : A
Answer: A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 36 km/hr, what is the length of the platform?
Options:
A)338
B)60
C)287
D)267
E)191
Rationale: Speed = (36* 5/18) m/sec = 10 m/sec. Length of the train = (10 x 10)m = 100 m. Let the length of the platform be x meters. Then, (x + 100)/36 = 10==> x + 300 = 360 ==> x = 60 m.
Answer: B
Answer: B
Question: In how many ways can the letters of the word INTELLIGENCE be arranged?
Options:
A)2580
B)2500
C)200067
D)9979200
E)3420456
Rationale: INTELLIGENCE has 12 words, but I, N and L are repeated two times and E is repeated three times. Thus ways = 12! / 2!*2!*2!*3! = 9979200ways
D
Answer: D
Question: A certain list of 300 test scores has an arithmetic mean of 70 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?
Options:
A) 70 and 70
B) 80 and 85
C) 70 and 75
D) 75 and 75
E) 70 and 80
Rationale: Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 70 and 70 are the most close numbers and they will increase the number of elements in the set without changing the median value.
A
Answer: A
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
Options:
A)2880.
B)4860.
C)5780
D)5760
E)6380.
Rationale: Normal Day = 400 kw/h
Stormy Day = 400*1.2=480 kw/h
3 windmills for 2 hours on stormy day
480*3*2=2880
Answer: A
Answer: A
Question: Mike had 200 watermelons. Sally came over and took some. After Sally left mike had 136 watermelons. How many watermelons did Sally take?
Options:
A)33
B)87
C)264
D)5
E)64
Rationale: 200-X=136
X=200-136
X=64
Sally took 64 watermelons
E.64
Answer: E