divelab/Sys2Bench huggingface dataset:
Question: If the cost price of 40 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?
Options:
A)25% loss
B)25% profit
C)20% loss
D)60% profit
E)75% profit
Rationale: Let the cost price of 1 article be $1.
Therefore, cost price of 40 articles = 40 * 1 = $40
The selling price of 25 articles = cost price of 40 articles = $40.
Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.
Cost price of 25 articles = 25 * 1 = $25.
Therefore, profit made on sale of 25 articles = Selling price of 25 articles - cost price of 25 articles
= 40 - 25 = $15.
As the profit is in the positive, the merchant has made a profit of $15.
Therefore, % loss = loss/cp * 100
% loss = 15/25 * 100 = 60%profit.
D
Answer: D
Question: 27 is a perfect cube. When x is added to the prime factor of 27, the result is a prime number. What is x?
Options:
A)1
B)3
C)5
D)8
E)11
Rationale: 27 is 3*3*3
then
A 3+1 = 4
B 3+3 = 6
C 3+5 = 8
D 3+8 = 11
E 3+11= 14
here D is the only addition that gives a prime number.
Answer: D
Question: If 12 men do a work in 80 days, in how many days will 20 men do it?
Options:
A)18 days
B)38 days
C)42 days
D)48 days
E)44 days
Rationale: 12 * 80 = 20 * x
x = 48 days
ANSWER:D
Answer: D
Question: A life insurance company insured 25,000 young boys, 14,000 young girls and 16,000 young adults. The probability of death within 10 years of a young boy, young girl and a young adult are 0.02, 0.03 and 0.15 respectively. One insured person dies. What is the probability that the dead person is a young boy?
Options:
A)36/165
B)25/166
C)26/165
D)32/165
E)33/165
Rationale: The number of young boys that will die = 0.02 x 25,000 = 500
The number of young girls that will die = 0.03 x 14,000 = 420
The number of young adults that will die = 0.15 x 16,000 = 2400
The required probability = The number of young boys who will die / The total number of people who will die.
= 500 / (500 + 420 + 2400) = 25/166
ANSWER:B
Answer: B
Question: Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
Options:
A)0<y<4
B)4<y<10
C)10<y<20
D)20<y<30
E)y>30
Rationale: x = the product of all even numbers from 2 to n, where n is any even integer value from 2 to 60 including.
If x = 2, x - 1 = 2! -1
If x = 2x4, x - 1 = 2! (2^2) - 1
If x = 2x4x6, x - 1 = 3! (2^3) - 1
If x = 2x4x6x8, x - 1 = 4! (2^4) - 1
.
.
.
.
If x = 2x4x6x.......x60, x - 1 = 30! (2^30) - 1
Lets find y, a smallest prime factor of (x-1):
If y were 2, [(30!) (2^30) -(1)] would be divisible by 2 however thats not the case.
If y were 3, [(30!) (2^30) -(1)] would be divisible by 3 however thats not the case.
If y were 5, [(30!) (2^30) -(1)] would be divisible by 5 however thats not the case.
.
.
.
.
.
If y were 29, [(30!) (2^30) -(1)] would be divisible by 29 however thats not the case.
If none of the primes under 31 is a factor of (x-1), (x-1) must have a prime factore above 30.
ANSWER:E
Answer: E
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/8 then b= ?
Options:
A)-1/4
B)1/4
C)4
D)-4
E)12
Rationale: f(a) = -1/2 = -1/a, and thus a = 2
f(ab) = 1/8, and thus ab = -8
2b = -8
b = -4
The answer is D.
Answer: D
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
Options:
A)Rs.648
B)Rs.640
C)Rs.629
D)Rs.620
E)Rs.622
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer: B
Answer: B
Question: What is the place value of 9 in the numeral 2934?
Options:
A)600
B)900
C)700
D)760
E)768
Rationale: Option 'B'
9 * 100 = 900
Answer: B
Question: A certain football team played seven games and scored an average of 5 goals per game. If, in the team’s first five games, it scored 5, 4, 2, 5, and 4 goals, what was the average (arithmetic mean) number of goals scored over the last two games?
Options:
A)5
B)1
C)2
D)7.5
E)Cannot be determined from the information given.
Rationale: Avg goals for total of 7 games = 5
So A+B+C+D+E+F+G/7=5
and A+B+C+D+E+F+G = 35
Given A+B+C+D+E = 20
So F+G = 15
So average (arithmetic mean) number of goals scored over the last two games is 15/2 = 7.5
Correct answer is D) 7.5
Answer: D
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 9/11%
B)18 2/11%
C)18 2/81%
D)19 2/11%
E)38 2/11%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: B
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 32 pounds and 28 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
Options:
A)31
B)29
C)35
D)37
E)39
Rationale: Total weight of the 4 dogs = (25+31+32+28) = 132
Avg = 116/4 = 29
Total weight of 5 dogs = 116+y or 4(29)+y
Average of 5 dogs as per Question = 29
Equation:
4(29) + y = 5 (29), or y = 29.
Choose B
Answer: B
Question: List I: 3, 6, 14, 19
List II: x, 3, 14, 8, 19
Options:
A) 6
B) 7
C) 8
D) 9
E) 10
Rationale: We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.
median = (6 + 14)/2
median = 20/2
median = 10
The median of list I is 7.
Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10.
The answer is E.
Answer: E
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
Options:
A)5%
B)10%
C)13%
D)14%
E)20%
Rationale: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Answer: B
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?
Options:
A)8%
B)16%
C)20%
D)24%
E)40%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.7x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.7x = 1.3x
The number of students in advanced trigonometry is 0.2x
The percentage in advanced trigonometry is 0.2x / 2.5x = 8%
The answer is A.
Answer: A
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)Rs.1014
B)Rs.1140
C)Rs.999
D)Rs.1085
E)Rs.1185
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999
ANSWER:C
Answer: C
Question: When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $94.50, what was the total value of the item?
Options:
A)$2,350
B)$2,850
C)$3,250
D)$3,400
E)$3,750
Rationale: Let x be the value in excess of $1,000.
0.07x = 94.5
x = $1,350
The total value was $1,350 + $1,000 = $2,350.
The answer is A.
Answer: A
Question: A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container.
Options:
A)26.34 litres
B)27.36 liters
C)28 litres
D)29.16 litres
E)cannot be determined
Rationale: Solution
Amount of milk left after 3 operations
[40 (1-4/40)3] litres = (40x9/10x9/10x9/10)= 29.16 litres
Answer D
Answer: D
Question: If the average of 744, 745, 747, 748, 749, 752, 752, 753, 755 and x is 750, what is the value of x?
Options:
A)750
B)752
C)754
D)755
E)756
Rationale: Sum of the deviations of the numbers in the set from the mean is always zero
744, 745, 747, 748, 749, 752, 752, 753, 755
mean is 750
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 750 + 5 =755
D
Answer: D
Question: Two bullet trains of equal lengths take 10 seconds and 30 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)13 sec.
B)14 sec.
C)12 sec.
D)15 sec.
E)19 sec.
Rationale: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.
Speed of the second bullet train = 120/30 m/sec = 4 m/sec.
Relative speed = (12 + 4) = 16 m/sec.
Required time = (120 + 120)/16 sec = 15 sec.
D
Answer: D
Question: What will be the length of the mini-train, if it crosses a pole in 3 sec while travelling at a speed of 75 kmph?
Options:
A)60 m
B)65 m
C)63.5 m
D)64 m
E)62.5 m
Rationale: Explanation:
D = 75 * 5/18 * 3 = 62.5 m
Answer: Option E
Answer: E
Question: 30 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
Options:
A)33
B)34
C)26
D)10
E)19
Rationale: Explanation:
Let the two parts be (30- x) and x.
Then, 10 (30 - x) + 22x = 780
=> 12x = 480
=> x = 40.
Bigger part = (30- x) = 10.
Answer: D) 10
Answer: D
Question: Find the least number which when divided by 20,25,35,40 leaves remainder 14,19,29,34 respectively.
Options:
A)1394
B)1450
C)1245
D)2564
E)1256
Rationale: The difference of 20-14 = 6 , 25-19 = 6 , 35-29 = 6 , 40-34 = 6
LCM of 20,25,35,40 = 1400
Required number = 1400 - 6 = 1394
Answer is A
Answer: A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)54
B)31
C)36
D)25
E)24
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (180 + 180)/12 => x = 15
Speed of each train = 15 m/sec.
= 15 * 18/5 =54 km/hr.
Answer: Option A
Answer: A
Question: In a party, there are rows arranged with 12,20 and 30 chairs and there were 3 left in all the cases. When there were 11 rows. There were no chair left. If 30 chairs were added. Then what will be the reminder?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: LCM of 12,20,30 is 120.so the number is in the form of 120x+3 which is divisible by 11,by placing x=3, we get 363 which is divisible by 11 and the multiple of 120 when 3 is subtracted from 363.so the no. is 363.so when 30 is added to it and is divided by 11 we get remainder as 8
ANSWER:A
Answer: A
Question: David leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. David, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of David is 30 km\hr, find the speed of his son.
Options:
A)15km/hr
B)6 km/hr
C)4.28 km/hr
D)9 km/hr
E)4.12 km/hr
Rationale: David leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. David, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of David is 30 km\hr, find the speed of his son.
The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.
Because we are dealing with a round trip here,David would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour
3.75km/52.5 = .07 km/minute
.07km/minute*60 minutes = 4.28 km/hour.
Answer: C. 4.28 km/hr
Answer: C
Question: If the time is currently 1:30pm, what time will it be in exactly 479 hours?
Options:
A)12:30am
B)1:30am
C)12:30pm
D)2:30pm
E)10:30pm
Rationale: Every 24 hours will bring us to the same 1:30pm. 480 is divisible by 24 (20*24=480), so if it were 480 hours we would have 1:30pm, but since it's 479 hours then it will be 1 hour less, so 12:30pm.
Answer: C.
Answer: C
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Options:
A)120 kmph
B)150 kmph
C)50 kmph
D)80 kmph
E)75 kmph
Rationale: Let speed of the car be x kmph.
Then, speed of the train =	150/100x	= 3/2 x	kmph.
75/x - 75/(3/2)x = 125/10 x 60
75/x	-50/x = 5/24
x =	25 x24/5	= 120 kmph.
answer :A
Answer: A
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers ?
Options:
A)7
B)8
C)5
D)4
E)2
Rationale: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8
Answer: B
Answer: B
Question: Given that 1.75 x 10(power 8), Which of the following options is equal to it?
Options:
A)171000000
B)172000000
C)176000000
D)175000000
E)177000000
Rationale: = 1.75 x 10(power 8)
= 1.75 x 100000000
= 175000000.
Answer is D.
Answer: D
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
Options:
A)110
B)115
C)120
D)130
E)145
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: C
Question: Two positive integers differ by 4, and sum of their reciprocals is 2. Then one of the numbers is
Options:
A)a) 3
B)2
C)c) 5
D)d) 21
E)e) 28
Rationale: Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 2
or ((n+4)+n)/n(n+4) =2 or (n^2+4n)*2 =2n+4 or n=2 as n cannot be -negative
Solve for n => n=2. Hence,
B
Answer: B
Question: A Hotel has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
Options:
A)10
B)12
C)15
D)24
E)30
Rationale: A Hotel has 6 employees;for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B
total = 10*1
= 10 - answer=A
Answer: A
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Options:
A)9
B)9.2
C)10
D)11.5
E)12
Rationale: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
D)
Answer: D
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value W?
Options:
A)2r
B)2s
C)r +s
D)2r-s
E)2s-r
Rationale: The simplest way to do this is to assume values.
We are told that r and s are positive integers W.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.
Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4
Hence option A is the greatest.
Answer: A
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)6
B)7
C)8
D)4
E)2
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: C
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 80 questions and secures 120 marks, the number of questions he attempts correctly, is:
Options:
A)35
B)46
C)42
D)30
E)40
Rationale: Let the number of correct answers be x.
Number of incorrect answers = (80 â€“ x).
4x â€“ 1(80 â€“ x) = 120 or 5x = 200 or x = 40.
ANSWER:E
Answer: E
Question: In a hostel, there is a meal for 120 men or 200 boys. If 150 boys have taken the meal, how many men will be catered to with remaining meal?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Explanation :
There is a meal for 200 boys. 150 boys have taken the meal.
Remaining meal is to be catered to 50 boys.
Now, 200 boys 120 men.
So 50 boys => 120 x 50/200 = 30 men.
Answer : B
Answer: B
Question: If the average (arithmetic mean) of a and b is 160, and c – a = 200, what is the average of b and c?
Options:
A)260
B)250
C)150
D)225
E)325
Rationale: a+b/2 = 160
=> a+b = 320
a = c - 200...sub this value
c-200+b =320
=>c+b = 520
=>c+b/2 = 260
Answer : A
Answer: A
Question: Find the ratio in which rice at Rs.7.10 a kg be mixed with rice at Rs.5.70 a kg to produce a mixture worth Rs.6.30 a kg?
Options:
A)1 : 3
B)2 : 3
C)3 : 4
D)4 : 5
E)None of these
Rationale: Solution
Required ratio = 60 : 80 = 3 : 4
Answer C
Answer: C
Question: Share Rs.4800 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
Options:
A)900
B)980
C)1600
D)1240
E)1400
Rationale: Amount received by sanjay.
4 / 12 X 4800 = 1600= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1600.
C
Answer: C
Question: A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform m calculations?
Options:
A)60ms/c
B)ms/c
C)ms/60c
D)60c/ms
E)m/60cs
Rationale: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.
We're told that a computer can perform C calculations in S seconds.
Let's TEST....
C = 2
S = 3
2 calculations every 3 seconds =
40 calculations every 1 minute
We're asked how many MINUTES it will take to perform K calculations.
Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...
m = 80
So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80
Answer A: 60mS/C = 60(80)(3)/2 = 7200 This is NOT a match
Answer B: mS/C = (80)(3)/2 = 120 This is NOT a match
Answer C: mS/60C = (80)(3)/(60)(2) = 2 This IS a match
Answer D: 60C/mS = 60(2)/(80)(3) = 1/2 This is NOT a match
Answer E: m/60CS = 80/(60)(2)(3) = a fraction. This is NOT a match
C
Answer: C
Question: If −y ≥ x, and −x < −9, then which of the following must be true?
Options:
A)y = −9
B)y > −9
C)−y > 9
D)y ≤ −9
E)y ≥ −9
Rationale: −y ≥ x, and −x < −9
y <= -x < -9
As '-x' is less than '-9' and Y is less than or equal to '-x'
we have y < -9 which is similar to -y > 9.
C) -y > 9
Answer: C
Question: When x is divided by y, the quotient is u with remainder r. What is x in terms of r, y, and u?
Options:
A)y + r + u
B)yu + r
C)x/y+r
D)y/u+r
E)ru + y
Rationale: (x/y) = u + r
solve for x
x=(u*y)+r
Ans B.
Answer: B
Question: A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price.
Options:
A)$1,000
B)$960
C)$240
D)$200
E)$150
Rationale: Cost price=1000
Profit=20% =20% of 1000=200
selling price=CP+ Profit
SP=1200
a Discount of 20% to employees means 20% off on 1200
so 20% of 1200= 240
so a employee thinks he saved 240..
Answer: C
Answer: C
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)28%
B)20%
C)80%
D)70%
E)30%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: B
Question: If two times A is equal to three times of B and also equal to four times of C, then A:B:C is
Options:
A)2:3:4
B)3:4:2
C)4:6:3
D)6:4:3
E)None
Rationale: Solution: 2A = 3B;
Or, B = (2/3)A; And, 2A = 4C;
Or, C = (1/2)A;
Hence, A:B:C = A:2A/3:A/2 = 1:2/3:1/2 = 6:4:3
Answer: Option D
Answer: D
Question: if p/q=3/4
then3p+5q=?
Options:
A)25/4
B)29/4
C)20/4
D)35/4
E)25/3
Rationale: 3p+5q=?
Divided by q,
3(p/q)+5=x
3*(3/4)+5=29/4
ANSWER:B
Answer: B
Question: Harkamal purchased 9kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1120
B)B)1065
C)C)1070
D)D)1075
E)E)1080
Rationale: Cost of 9 kg grapes = 70 × 9 = 630.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 630 + 490 = 1120
A
Answer: A
Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options:
A)3.2 km
B)3 km
C)2.4 km
D)3.6 km
E)None of these
Rationale: Explanation :
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph
Let the requited distance be x km
Total time taken = 1 hour
=> x/6 + x/4 = 1
=> 2x + 3x = 12
=> 5x = 12
=> x = 2.4 km. Answer : Option C
Answer: C
Question: A certain list of 100 data has an average (arithmetic mean) of 9 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 108 data with standard deviation less than d?
Options:
A)-9 and 0
B)0 and 0
C)0 and 9
D)0 and 18
E)9 and 9
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 9 and 9 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: E
Question: A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun five times, approximately what is the probability that the product of the five winning sectors’ integers will be even?
Options:
A)50%
B)67%
C)85%
D)91%
E)97%
Rationale: The only way to have an odd product is if all 5 integers are odd.
P(odd product) = 1/2*1/2*1/2*1/2*1/2 = 1/32
P(even product) = 1 - 1/32 = 31/32 which is about 97%
The answer is E.
Answer: E
Question: If the given two numbers are respectively 8% and 16% of a third number, then what percentage is the first of the second ?
Options:
A)20%
B)25%
C)18%
D)50%
E)none of these
Rationale: Here, l = 8 and m = 16
Therefore, first number = l/m x 100% of second number = 8/16 x 100% of second number = 50% of second number
ANSWER:D
Answer: D
Question: What should come in place of the question mark (?) in the following equation?
6 5⁄6 × 5 1⁄3 + 17 2⁄3 × 1⁄2 = ?
Options:
A)112 1⁄3
B)663
C)240
D)116 2⁄3
E)None of these
Rationale: ? = 41⁄6 × 16⁄3 + 53⁄3 × 9⁄2 = 41×16+53×9×3 /6×3
= 656+1431 /18=2087/18=11517/18
Answer E
Answer: E