RikoteMaster/aqua-rat-mcqa huggingface dataset:
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?
A.5
B.6
C.7
D.9
Answer: B.6
Explanation: 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: B
Question: A certain debt will be paid in 65 installments from January 1 to December 31 of a certain year. Each of the first 20 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 20 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
A.443
B.455
C.465
D.468
Answer: B.455
Explanation: Total number of installments = 65
Payment per installment for the first 20 installments = 410
Payment per installment for the remaining 45 installments = 410+65=475
Average = (20*410 + 45*475)/65 = 455
Answer B
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum s of all the even integers between 99 and 301?
A.10,100
B.20,200
C.22,650
D.40,200
Answer: B.20,200
Explanation: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum s= Average*total count = 200*101 = 20,200
Answer is B
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
A.216
B.125
C.729
D.316
Answer: C.729
Explanation: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans: C
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
A.91
B.87
C.90
D.17
Answer: C.90
Explanation: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer: C
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 7?
A.y = -1/2*x + 3
B.y = 1/2*x - 7
C.y = 1/2*x + 3
D.y = 2x + 3
Answer: B.y = 1/2*x - 7
Explanation: Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)
y-intercept of line L is same as y intercept of line y = 2x − 7
y - intercept of line L = -7
Required line = 1/2* x - 7
Answer B
Question: In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10 kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was :
A.10
B.27
C.87
D.23
Answer: A.10
Explanation: Explanation:
Let the original quantity be x kg. Vanaspati ghee in x kg = (40x / 100 )kg = (2x / 5) kg.
Now, (2x/5)/(x + 10) = 20/100 <=> 2x / (5x + 50) = 1/5 <=> 5x = 50 <=> x = 10.
Answer: A) 10 kg
Question: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
A.2/3
B.5/6
C.7/12
D.11/12
Answer: C.7/12
Explanation: (1/2)X = (1/4)Y
(1/4)Y + (1/3)Y = (7/12)Y
The answer is C.
Question: The sum of two numbers is 73 and their difference is 28. Find the difference between their squares.
A.101
B.45
C.2044
D.2048
Answer: C.2044
Explanation: Explanation:
Let x and y be the two given numbers
(x + y) = 73; (x – y) = 28
(x2 – y2) = (x + y) (x – y) = 73*28 = 2044
ANSWER:C
Question: A man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock?
A.4
B.8
C.6
D.10
Answer: B.8
Explanation: By investing Rs.1552, income = Rs.128
By investing Rs.97, income = 128×97/1552=8
ie, dividend = 8%
Answer is B.
Question: Krishnakumar, Raghunandan, Chinnan and Aibak had an interesting discussion on the following:
Find the range of real values of x not satisfying even one of the inequalities 6x - 8 > 40 and 9x - 19 > 80"
A.x greater than 8
B.x lesser than or equal to 8
C.x lesser to 8
D.x greater than or equal to 8
Answer: C.x lesser to 8
Explanation: 6x – 8 > 40 => 6x >48 => x > 8 ...(1)
And 9x – 19 > 80 = > 9x >99 => x >11 ...(2)
For both the inequalities to hold true, x should be greater than 11, and for values of x greater than 8, at least the first inequality (1) will be satisfied.
For x not to satisfy both the inequalities, it has to be equal to or lesser than 8.
Therefore, our answer is x lesser than or equal to 8
ANSWER:C
Question: If x < y < 0, which of the following must be true?
A.2x+y is a negative integer
B.2xy is a negative integer
C.x-y is a positive integer
D.(-x)+ (-y) is positive integer
Answer: D.(-x)+ (-y) is positive integer
Explanation: Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
x-y is false since xSo, option D is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)
Answer : D
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.
B.
C.
D.
E.
A.210
B.1050
C.25200
D.21400
Answer: C.25200
Explanation: 7C3 * 4C2 * 5!
(7 * 6 * 5)/3! * 4!/2!2! * 120
35 * 6 * 120
= 210 * 120
= 25200
ANSWER:C
Question: For any real number x, the operatoris defined as:
(x) = x(2 − x)
If p + 1 =(p + 1), then p =
A.5
B.0
C.1
D.2
Answer: C.1
Explanation: (x) = x(2 − x)
(p + 1) = (p + 1)(2 - p - 1) = (1-p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (1-p)(p+1) = (p + 1)
Or (p + 1) + (p-1)(p+1) = 0
(p + 1)(p-1) = 0
p = -1,p=1
Option C
Question: 9 people decided to split the restaurant bill evenly. If the bill was $514.16 dollars, how much money did they 1 cent is the smallest unit?
A.$514.16
B.$514.17
C.$514.18
D.$514.19
Answer: B.$514.17
Explanation: This is equivalent to finding the first number that is divisible by 9 that occurs after 51416.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 51416 = 17 and 18 is divisible by 9.
Hence, we need to add 1 to this number for it to be divisible by 9
Correct Option: B
Question: A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs.­­­­_______ for the horse and Rs.________ for the cart
A.400 & 300
B.400 & 500
C.400 & 200
D.300 & 200
Answer: C.400 & 200
Explanation: let cp of horse be x
and cp of cart be y
then
horse sp=90*x/100=9x/10
cart sp=120*y/100=6y/5
now he say thru these no loss no gain mean cp of both equal to sp of both
=> x+y=(9x/10)+(6y/5)-----(1)
again
horse sp=95*x/100=19x/20
cart sp=105*y/100=21y/20
now at this time he suffer loss of 10 rs mean
cp=sp+10
x+y=19x/20+21y/20+10-----(2)
solving eq 1 and 2 u will get the ans x=400 & y=200
ANSWER:C
Question: Two boys starts from the same place walking at the rate of 4.5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 9.5 km apart?
A.9.5
B.5.5
C.8.5
D.9.6
Answer: A.9.5
Explanation: Explanation:
Relative speed = 5.5 - 4.5 = 1 kmph (because they walk in the same direction)
distance = 9.5 km
time = distance / speed=9.5/1=9.5 hr
Answer :A
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.00 a.m.?
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour
Time duration from 8 am to 9 am = 1 hour
Hence they cross each other 5 times before 9 am
Answer is A
Question: Find the largest number of four digits which is exactly divisible by 27,18,12,21
A.9700
B.9710
C.9828
D.9830
Answer: C.9828
Explanation: Explanation:
LCM of 27-18-12-21 is 756.
After dividing 9999 by 756 we get 171 remainder.
So answer will be 9999-171 = 9828
Option C
Question: A train running at the speed of 52 km/hr crosses a pole in 9 seconds. Find the length of the train?
A.130
B.272
C.278
D.277
Answer: A.130
Explanation: Speed = 52*(5/18) m/sec = 130/9 m/sec
Length of Train (Distance) = Speed * Time
(130/9) * 9
= 130 meter
Answer: A
Question: Every person in a certain group is either a Lakers fan or a Warriors fan, but not both. The ratio of Lakers fans to Warriors fans is 9 to 4. If 40 Lakers fans change teams to become Warriors fans, the ratio of Warriors fans to Lakers fans will be 1 to 1. How many people are in the group?
A.260
B.52
C.182
D.169
Answer: A.260
Explanation: By checking the answer choices:
Since we have an initial ratio of 9:4, the total count should be divisible by 13.
A. 260/13=20, Lakers Fan = 180, Warriors Fan = 100, and 180-40 = 100+40. This is the Correct Answer
B. 52/13=4, Lakers Fan = 36, Warriors Fan = 16, Since 36-40 is not equal to 16+40 this as well can not be the answer.
C. 182/13=14, Lakers Fan = 126, Warriors Fan = 56, Since 126-40 is not equal to 56+40 this as well can not be the answer.
D. 169/13=13, Lakers Fan = 117, Warriors Fan = 52, Since 117-40 is not equal to 52+40 this as well can not be the answer.
E. Out, since not divisible by 13.
A is the correct answer.
Question: If Jesse flips a coin 7 times in a row, what is the probability that the result will be 2 heads and 2 tails at all the times ?
A.21/128
B.29/128
C.35/128
D.1/16
Answer: A.21/128
Explanation: In a flip of a coin seven times in a row, heads and tails 2 each at all times means,
Heads = exact 2 heads
The total outcome of flip is = 2^7 = 128
For any Coins problem write the ask in the shown format.
HHTT
Once you have written in the above mentioned format the answer is pretty straight.
HHTT = [7!]/[5!] [2!]= 21
Sum = 21
Answer = 21/128
Answer - A
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
A.6m
B.9m
C.5m
D.2m
Answer: D.2m
Explanation: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 =2m.
Answer:D
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:1. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?
A.9:8
B.8:9
C.4:9
D.2:3
Answer: C.4:9
Explanation: The ratio of economy to luxury cars is 3:1 --> E:L = 3:1 = 12:4.
The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9.
Thus, L:S = 4:9.
Answer: C.
Question: If a car had increased its average speed for a 210 mile journey by 5 mph, the journey would have been completed in one hour less. What was the original speed of the car for the journey?
A.20 mph
B.10 mph
C.30 mph
D.40 mph
Answer: C.30 mph
Explanation: C
30 mph
Question: A recycling facility is staffed by 10 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/10 of all wages paid at the facility, what is the value of n?
A.5/4
B.10/9
C.3/2
D.5/3
Answer: B.10/9
Explanation: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 10x+xn and we are told that it equals to 10xn:
10x+xn=10xn --> reduce by x:10+n=10n -->9n= 10
n = 10/9
Answer: B
Question: If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 44 kmh, what was the average speed of the car for the entire trip?
A.39 kmh
B.40 kmh
C.42 kmh
D.44 kmh
Answer: A.39 kmh
Explanation: Assume D/3 = 2640 (this number is convenient because it is divisible by 80, 24 and 44)
So:
2640 = 80*T1 = 33 hrs
2640 = 24*T2 = 110 hrs
2640 = 44*T3 = 60 hrs
T = T1 + T2 + T3 = 203 hrs
D = RT
(2640*3) = R*203
R = 39
ANSWER: A
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum z of all the even integers between 99 and 301?
A.10,100
B.20,200
C.22,650
D.40,200
Answer: B.20,200
Explanation: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum z= Average*total count = 200*101 = 20,200
Answer is B
Question: Jhon's average (arithmetic mean) test score on 5 tests is 87. What must be the Jhon's score on a 6th test for the Jhon's average score on the 6 tests to be 85?
A.65
B.75
C.85
D.95
Answer: B.75
Explanation: (5*87+x)/6=85
x=(6*85)-(5*87)
x= 510 - 435
total score required 510 - 435=75
Correct answer is B
Question: A parking garage rents parking spaces for $10 per week or $42 per month. How much does a person save in a year by renting by the month rather than by the week?
A. $14
B. $16
C. $22
D. $24
Answer: B. $16
Explanation: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 42 = 504$
520 - 504 = 16
Ans B
Question: In how many different ways can the letters of the word FLUTE be arranged in such a way that the vowels occupy only the even positions?
A.8
B.12
C.18
D.24
Answer: B.12
Explanation: The 2 vowels can be arranged in even places in 2! ways.
The 3 consonants can be arranged in three odd places in 3! ways.
The number of arrangements with vowels in even positions = 2! Ã— 3! = 2 Ã— 6 = 12
The answer is B.
Question: N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N?
A.3/2
B.5/3
C.1+1/3
D.1 1/2
Answer: C.1+1/3
Explanation: N is such that when multiplied by 0.75 gives 1" is written mathematically as
N * 0.75 = 1
Solve for N
N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3
correct answer C
Question: The integer Q has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of Q and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: Let Q be 67 and y be a8. Then the product of Q and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.
So the answer is (C).
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
A.11%
B.20%
C.12%
D.19%
Answer: B.20%
Explanation: P = (P*5*R)/100
R = 20%
Answer:B
Question: Pat, kate and mark charged a total of 144 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
A.18
B.36
C.80
D.90
Answer: C.80
Explanation: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 144 -total hours charged for,
x= 16.
Mat charged 6x-x or 5x for more hours than kate, or for 80 hours .
C is correct
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 2 if a 1 was the value of the first coin flip ?
A.1/8.
B.1/4.
C.1/5.
D.3/8.
Answer: B.1/4.
Explanation: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
If 1 was the first flip you can only have (1,0,0) (1,1,1)(1,0,1) (1,1,0) only two of these have a value of 2
So answer will be 2/8 OR 1/4. Option B.
Question: A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: Let n=3q+1 and let q= 2p+1. Then, n= 3(2p+1)+1= 6p+4
Therefore, the number when divided by 6, we get remainder= 4
ANSWER:C
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
A.Rs.4082.20
B.Rs.4062.40
C.Rs.4042.40
D.Rs.4082.40
Answer: D.Rs.4082.40
Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04)
= 4095 - 12.6
= Rs.4082.40
Answer:D
Question: The length of a rectangular floor is more thanits breadth by 200%. If Rs.324 is requiredto paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
A.14
B.18
C.19
D.22
Answer: B.18
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
B
Question: There are 21 balls in a box: 8 balls are green, 8 are blue and 5 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?
A.1/13
B.4/13
C.3/13
D.5/19
Answer: D.5/19
Explanation: If 1 green and 1 blue ball are taken from the box, then there are 7 green, 7 blue and 5 white balls, a total of 19 balls. If one ball is selected at random, the probability that it is white is given by
5/19
Answer : D
Question: A batch of cookies was divided amomg 3 tins: 3/4 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin
A.15/2
B.9/4
C.5/9
D.3/5
Answer: D.3/5
Explanation: This will help reduce the number of variables you have to deal with:
G + B = 3/4
R = 1/3
B = 1/4
We can solve for G which is 1/2
What fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin?
So..
X*(G+R)=G
X*(1/2 + 1/3) = 1/2
X = 3/5
ANSWER: D
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.90 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
A.$255
B.$275
C.$459
D.$1,250
Answer: C.$459
Explanation: Total no. Of boxes = 3060000/(20×20×15) = 510
Total cost = 510×$0.9=$459
Answer C
Question: 162 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x?
A.120
B.150
C.180
D.250
Answer: C.180
Explanation: Let B be the number of boys in the school.
162 = xB/100
B = 0.5x
16200=0.5x^2
x^2 = 32400
x = 180
The answer is C.
Question: A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
A.33/7
B.43/7
C.24/7
D.19/7
Answer: C.24/7
Explanation: If A can do a piece of work in n days, then A's 1 day's work = 1/n
(A + B + C)'s 1 day's work =1/24+1/6+1/12=7/24
So, all the three together will complete the job in = 24/7 days
Answer: C
Question: At what time between 4 and 5 o’clock will the hands of a watch point in opposite directions?
A.54 6/11 min. past 4
B.50 min. past 4
C.45 min past 4
D.40 min past 4
Answer: A.54 6/11 min. past 4
Explanation: Sol.
At 4 o’clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
∴ Minute hand will have to gain 50 min. spaces.
55 min. spaces are gined in 60 min.
50 min. spaces are gained in [60/55 * 50] min. or 54 6/11 min.
∴ Required time = 54 6/11 min. past 4
Answer A
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 55 percent of those who attended the meeting were stockholders and 61 percent were employees, what percent were stockholders who were not employees?
A.37
B.38
C.39
D.40
Answer: C.39
Explanation: 55+61=116 so 16% were both stockholders and employees.
The percent who were stockholders but not employees is 55-16=39%
The answer is C.
Question: In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.2.8 sec
C.5 sec
D.2.2 sec
Answer: C.5 sec
Explanation: Speed = 144 * 5/18
= 40 m/sec
Time taken = 200/40
= 5 sec.
Answer:C
Question: Machine P and Machine Q are each used to manufacture 550 sprockets. It takes Machine P 10 hours longer to produce 550 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
A.5
B.15
C.55
D.95
Answer: A.5
Explanation: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
550/x = 550/1.1x + 10
1.1(550) = 550 + 11x
11x = 55
x = 5
The answer is A.
Question: A car drives 40 miles on local roads at 20 mph, and 180 miles on the highway at 60 mph, what is the average speed of the entire trip?
A.36 mph
B.40 mph
C.44 mph
D.52 mph
Answer: C.44 mph
Explanation: Explanations
1) In phase #1 of the trip, the car traveled 40 mi at 20 mph. That time of this phase was:
time = distance/rate = (40 mi)/(20 mph) = 2 hr
In phase #2 of the trip, the car traveled 180 mi at 60 mph. That time of this phase was:
time = distance/rate = (180 mi)/(60 mph) = 3 hr
The total distance of the trip = 40 mi + 180 mi = 220 mi
The total time of the trip = 2 hr + 3 hr = 5 hr
The average speed of trip is given by
speed = distance/time = (220 mi)/(5 hr) = 44 mph
Answer: C.
Question: Tim and Jim enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Tim received $800 more than Jim did, what was the profit made by their business in that year?
A.4565
B.3000
C.4654
D.353464
Answer: B.3000
Explanation: Say the profit was $x.
Tim share = x/6 (half of the third) + (x-x/3)*0.7
Jim share = x/6 (half of the third) + (x-x/3)*0.3
Thus (x-x/3)*0.7-(x-x/3)*0.3=800 --> x=3000.
answer is B
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation g of the mean, what percent of the distribution is less than m+g?
A. 16%
B. 32%
C. 48%
D. 84%
Answer: D. 84%
Explanation: 16%
________________________________________________ m+g
34%
________________________________________________ m
34%
________________________________________________ m-g
16%
since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-g and 16% lie above m+g
now below m+g = 16+34+34 = 84%
hence D
Question: What is 92% of 4/5?
A.6.9
B.69.0
C.0.736
D.0.6859
Answer: C.0.736
Explanation: 92%*(4/5)=0.92*0.8=0.736
Answer :C
Question: If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 20, what is the value of r-p?
A.20
B.10
C.30
D.40
Answer: A.20
Explanation: Arithmetic mean expression for p and q:
(p+q)/2=10 ; p+q=20 ----eq1
Arithmetic mean expression for q and r:
(q+r)/2=20 ; q+r=40 ----eq2
Subtracting eq1 from eq2 we get: r-p=20
Hence, the correct answer is A