RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If it is true that x< 8 and 2x> -4, which of the following must be true?
A. -8 < x< 4
B. x> 2
C. x> -8
D. x< 4
Answer: C. x> -8
Explanation: Two points:
1) x< 8
2) 2x> -4 or x> -2
From 1 and 2: -2 < x< 8
(A) is not true because x could be > 4.
(B) is not true because x could be < 2.
(C) is true because x value is always > -8.
(D) is not true because x could be >4.
(E) is not true because C is true.
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
A.10.39
B.10.37
C.10.3
D.10.31
Answer: C.10.3
Explanation: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.Answer:C
Question: John found that the average of 15 numbers is 40. If 14 is added to each number then the mean of number is?
A.54
B.45
C.65
D.78
Answer: A.54
Explanation: (x+x1+...x14)/15 = 40
54
Option A
Question: Given a spinner with four sections of equal size labeled R, B, C, and D, what is the probability of NOT getting an R after spinning the spinner two times?
A.15/16
B.9/16
C.1/2
D.1/4
Answer: B.9/16
Explanation: The probability of NOT getting an R after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Question: On a 26 question test, five points were deducted for each wrong answer and eight points were added for each correct answer. If all the questions were answered, how many were correct, if the score was zero ?
A.10
B.12
C.11
D.13
Answer: A.10
Explanation: Explanation :
Let the correct answer be : x
Therefore wrong answers = (26 - x)
Total socre = 8x - 5(26-x) = 0
or, 13x = 130
Therefore x = 10
Answer : A
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $46 of gas?
A.124
B.256
C.368
D.424
Answer: C.368
Explanation: 46/4 = 11.5 gallons
11.5*32 = 368 miles
The answer is C.
Question: R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
A. None
B. Two
C. Four
D. Five
Answer: D. Five
Explanation: R is the set of positive even integers less than 101, 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, 36, 64, and 100 are even integers (less than 101) that are in both sets.
Solution: Five
Answer: D
Question: If Z is a positive integer greater than 1, what is the sum of the multiples of Z from Z to Z^2, inclusive?
A. Z(Z + 1)(Z-1)
B. Z^2(Z + 1)/2
C. Z^2(Z-1)
D. (x^3 + 2x)/2
Answer: B. Z^2(Z + 1)/2
Explanation: Ans :- B=Z^2(Z + 1)/2
I substituted 3 in all answer choices.
Option B and C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
Only B option satisfied.
Question: Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
A.864
B.863
C.865
D.1728
Answer: D.1728
Explanation: Solution:
Required number of ways, = 3C2 *4! *4! = 1728.
Answer: Option D
Question: A 14% stock yields 8%.The market value of the stock is :
A.Rs. 175
B.Rs. 92
C.Rs. 112.50
D.Rs. 116.50
Answer: A.Rs. 175
Explanation: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 14, investment = Rs.(100/8X14)= Rs. 175
∴ Market value of Rs. 100 stock = Rs.175
Answer A
Question: If the digits 27 in the decimal 0.00027 repeat indefinitely, what is the value of (10^5-10^3)(0.00027)?
A.0.27
B.0.027
C.27
D.0.0027
Answer: C.27
Explanation: 99*0.27=26.73 approx. 27
Answer : C
Question: In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
A.145 m
B.176 m
C.268 m
D.129 m
Answer: A.145 m
Explanation: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
Answer:A
Question: If a 4-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?
A.6
B.15
C.20
D.60
Answer: B.15
Explanation: Another way:
1st member can be selected in 6 ways
2nd can be selected in 5 ways
3rd can be selected in 4 ways
4th can be selected in 3 ways
So total ways : 360
But to avoid the similar scenarios 360/4!=15
B
Question: In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 5 boys when a boy gets any no. of prizes?
A.48
B.50
C.625
D.602
Answer: C.625
Explanation: Ans.(C)
Sol. In this case, repetitions are allowed, so all the four prizes can be given in 5 ways, i.e. (5*5*5*5) ways = 54 ways = 625 ways Or nr ways = 54 ways = 625 ways
Question: If an object travels 90 feet in 3 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
A.17.36
B.20.45
C.23.87
D.26.92
Answer: B.20.45
Explanation: 90 feet/3 seconds = 30 feet/second
(30 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 20.45 miles/hour (approximately)
The answer is B.
Question: On a ranch, a rancher can place a loop of rope, called a lasso, once in every 3 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 3 attempts?
A.1/3
B.5/9
C.7/9
D.19/27
Answer: D.19/27
Explanation: P(missing all 3)=(2/3)^3=8/27
P(success on at least one attempt)=1-8/27=19/27
The answer is D.
Question: If the price has fallen by 14% what percent of its consumption be: increased so that the expenditure may be the same as before?
A.11 1/8%
B.11 1/5%
C.16 12/43%
D.17 7/9%
Answer: C.16 12/43%
Explanation: 100 â€“ 14 = 86
86------14
100------? => 16 12/43%
Answer: C
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ?
A.Equal to 3
B.Less than 3
C.More than 10
D.Less than 10
Answer: C.More than 10
Explanation: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10
ANSWER:C
Question: A train 345 m long passed a pole in 15 sec. How long will it take to pass a platform 760 m long?
A.76 sec
B.43 sec
C.45 sec
D.15 sec
Answer: B.43 sec
Explanation: Speed = 345/15 = 23 m/sec.
Required time = (345 + 760)/23
= 48 sec.
Answer:B
Question: In a series of four football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 4 draws in the series?
A.24/576
B.125/864
C.1/25
D.1/256
Answer: D.1/256
Explanation: Since the probability of a draw is 1/4, then the probability of 4 draws in 4 matches is (1/4)^4=1/256.
Answer: D.
Question: A flight takes off at 2.00 a.m. from a place at 18N 10E and landed 10 hours later at a place with co-ordinates 36N 70W. What is the local time when the plane landed?
A.6.00 a.m.
B.6.40 a.m.
C.7.00 a.m.
D.7.40 a.m.
Answer: B.6.40 a.m.
Explanation: Time difference between places will be 4*(70+10) minutes = 320 min =
5 hrs 20 min
as change of 1 degree in longitude cause change of 4 minutes in time.
and that change is 80 degrees here.
so when plane land. time will be = 2.00 + 10.00 -5.20 = 6.40 a.m.
ANSWER:B
Question: If log 27 = 1.401, then the value of log 9 is:
A.0.934
B.0.945
C.0.954
D.0.958
Answer: A.0.934
Explanation: log 27 = 1.401
log (3cube ) = 1.401
3 log 3 = 1.401
log 3 = 0.467
log 9 = log(3square ) = 2 log 3 = (2 x 0.467) = 0.934.
Answer: Option A
Question: 95 80 85 65 50 85 35 ? ?
A.25 15
B.25 85
C.20 85
D.85 35
Answer: C.20 85
Explanation: 95-15=80
again 85
80-15=65
65-15=50
again 85
50-15=35
35-15=20
again 85
then answer is 20 ,85
ANSWER:C
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
A.14700
B.15700
C.16700
D.18700
Answer: A.14700
Explanation: Total amount invested = 50000
Assume that investment of C = x.
Then investment of B = 5000 + x ,
Investment of A = 4000+5000+x = 9000+x
x + 5000+x + 9000+x = 50000
=> 3x + 14000 = 50000
=> 3x = 50000 – 14000 = 36000
=> x = 36000/3 = 12000
=> Investment of C = x = 12000 ,
Investment of B = 5000 + x = 17000,
Investment of A = 9000+x = 21000
Ratio of the investment of A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
Share of A = Total Profit * 21/50 = 35000 * 21/50 = 700*21 = 14700
Answer is A
Question: Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and
f(x) = x2nd for xε2 (0,1). Compute f(-3/2) + f(1).
A.-1
B.-1/2
C.-1/4
D.1/4
Answer: D.1/4
Explanation: Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1/4. Because f
is odd, we know that f(1) = -f(-1), but because f is periodic, f(1) = f(-1). Therefore,
f(1) = 0 and the answer is 1/4.
correct answer D
Question: Six men and six women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
A.5!*6!
B.6!*6!
C.5!*7!
D.6!*7!
Answer: A.5!*6!
Explanation: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 6 men in a circle can be arranged in (6-1)! ways and if we place 6 women in empty slots between them then no two women will be together. The # of arrangement of these 6 women will be 6! and not 5! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 5!*6!.
A
Question: A man saves Rs 250 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
A.Rs 827.53
B.Rs 862.01
C.Rs 822.02
D.Rs 862.03
Answer: A.Rs 827.53
Explanation: Explanation:
=[250(21/20Ã—21/20Ã—21/20)+250(21/20Ã—21/20)+250(21/20)]=827.53
Option A
Question: A certain candy manufacturer reduced the weight of Candy Bar M by 40 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?
A.66.66
B.62.5
C.58
D.60
Answer: A.66.66
Explanation: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.6 oz
new price of candy = 1/0.6 =1.6666
price increase 66.66 %
A
Question: What are the maximum value and minimum values of f(x) = |2sin(2x - pi/3) - 5| + 3
A.max10-min6
B.max11-min7
C.max12-min8
D.max13-min9
Answer: A.max10-min6
Explanation: -1 <= sin(2x - pi/3) <= 1 : range of a sine function
-2 <= 2sin(2x - pi/3) <= 2 : mulitply all terms of the double inequality by 2
-2 - 5 <= 2sin(2x - pi/3) - 5 <= 2 - 5 : add -5 to all terms of the inequality.
-7 <= 2sin(2x - pi/3) - 5 <= -3
3 <= |2sin(2x - pi/3) - 5| <= 7 : change the above using absolute value.
3 + 3 <= |2sin(2x - pi/3) - 5| + 3 <= 7 + 3 : add 3 to all terms of the double inequality.
The maximum value of f(x) is equal to 10 and the minimum value of f(x) is equal to 6.
correct answer is A)max10-min6
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A.53
B.50
C.99
D.288
Answer: A.53
Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8 = 45 ==> x = 53 km/hr.Answer: A
Question: Of the 5 numbers, whose average is 100, the first is one-fourth of the sum of the last 4. The first number is?
A.83.3
B.80
C.78.63
D.56.98
Answer: A.83.3
Explanation: Let the first number be x
sum of the 5 numbers = x+5x = 6x
6x/5 = 100
x = 100*5/6 = 83.3
Answer is A
Question: In how many different number of ways 4 men and 3 women can sit on a bench such that girls always sit together.
A.720
B.740
C.750
D.770
Answer: A.720
Explanation: 720
A)
Question: A division of a company consists of four men and six women. If two of these ten employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
A.1/6
B.1/5
C.1/4
D.1/3
Answer: D.1/3
Explanation: The total number of ways to choose two representatives is 10C2=45.
The number of ways to choose two females is 6C2=15.
P(choosing two female representatives)=15/45=1/3
The answer is D.
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by L percent, which of the following expressions represents the final price of the item?
A.(10,000z + 100z(x – y) – xyz)/10,000
B.(10,000z + 100z(y – x) – xyz)/10,000
C.(100z(x – y) – xyz)/10000
D.(100z(y – x) – xyz)/10000
Answer: C.(100z(x – y) – xyz)/10000
Explanation: value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by L% on Total L/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - L/100 ( A +Ax/100)
C
Question: The sum of the non-prime numbers between 40 and 50, non-inclusive, is
A.131
B.176
C.274
D.405
Answer: C.274
Explanation: The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}.
6 times 40 something is approx north of 240
Hence the answer is (C) 274
Question: If 75 percent of a class answered the first question on a certain test correctly, 35 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
A.10%
B.(8) 20%
C.30%
D.50%
Answer: C.30%
Explanation: I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
20% appeared in the exam; however did not answer Question AQuestion B correctly
So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.
Now,
100 - [(75 - x) + x + (35 - x)] = 20 .......... values are in percent
x = 20 - 100 + 110
x = 30
Ans: C
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?
A.4
B.6
C.12
D.16
Answer: C.12
Explanation: The four digits available are 1,2,3 and 6
as the extensions can only be even numbers, the last digit has to be either 2 or 6
If it is 2...it leaves 1,3 and 6 for the first three digits...these can be arranged in 3! ways
If the last digit is 6...it leaves 1,2 and 3 for the first three digits...these can be arranged in 3! ways
Thus answer is 2*3! = 12 C
Question: We have 10 people and 3 chairs. In how many ways chairs can be occupy?
A.650
B.720
C.810
D.790
Answer: B.720
Explanation: no. of ways they can be occupy = 10*9*8 = 720
Answer is B
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 80 different models of televisions, what is the minimum number of letters that must be used to make the codes?
A.6
B.7
C.9
D.8
Answer: C.9
Explanation: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥80. The smallest n which fulfills this condition is n = 9.
Answer C
Question: X, Y, and Z are different prime numbers. The product X^2*Y^2*Z^2 is divisible by how many different positive numbers?
A.9
B.18
C.27
D.36
Answer: C.27
Explanation: The exponents of X^2*Y^2*Z^2 are 2, 2, and 2.
The number of factors is (2+1)(2+1)(2+1) = 27
The answer is C.
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 20% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
A.25%
B.30%
C.50%
D.55%
Answer: C.50%
Explanation: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.2N
x = 0.5N
The percentage of rooms which permit smoking is 1 - 0.5 = 50%
The answer is C.
Question: Right triangle ABC is the base of the prism in the figure above. If AB=AC=âˆš10 and the height of the prism is 4, what is the volume of the prism?
A.40
B.85
C.20
D.60
Answer: C.20
Explanation: Volume of prism = Area of base * height = 1/2* (square root of 10) * (square root of 10)*4= 20
Answer: C
Question: Jacob bought a scooter for a certain sum of money.He spent 10% of the cost on repairs and sold the scooter for a profit of Rs.1100. How much did he spend on repairs if he made a profit of 20% ?
A.Rs.400
B.Rs.440
C.Rs.500
D.Rs.550
Answer: C.Rs.500
Explanation: Total Profit = Rs. 1100.
%Profit = 20.
20% = 1100,
So,
100% = 5500.
Rs. 5500 would be the cost price for Jacob.
He spends 10% on repairing. So,
Initial Cost + Repair Cost = 5500.
Let Initial Cost was X. then
X + 10% of X = 5500
1.1X = 5500
X = 5500/1.1
X = 5000.
The initial cost price was Rs. 5000. Thus, he spends Rs. 500 on repairing.
ANSWER : OPTION C
Question: Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds. The ratio of their speeds is:
A.3 : 1
B.3 : 2
C.3 : 8
D.2 : 5
Answer: D.2 : 5
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 25 x meters, and length of the second train = 18 y meters. (25 x + 18 y) / (x + y) = 20 ==>
25 x + 18 y = 20 x + 20 y ==> 5 x = 2 y ==> x/y = 2/5
Answer: Option D
Question: A man invests Rs. 4,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
A.Rs. 1200
B.Rs. 1300
C.Rs. 1500
D.Rs. 2000
Answer: D.Rs. 2000
Explanation: Explanation :
Interest on Rs.4000 at 5% per annum = ( 4000 × 5 × 1) / 100 = Rs. 200
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (4000 + x) × 6 × 1/100.
=> 200 + 2x/25 = (4000 + x) × 6 × 1/100.
=> 20000 + 8x = (4000 + x) × 6.
=> 20000 + 8x = 24000 + 6x.
=> 2x=4000.
=> x=2000.
Answer : D
Question: 96% of 5/8 =
A.0.2
B.0.5
C.0.6
D.0.75
Answer: C.0.6
Explanation: Should be simple.
0.96*5/8 = 4.8/8 = 0.6
Correct Option : C
Question: A man travelled from the village to the post office at the rate of 10kmph and walked backed at the rate of 5 kmph. If the whole journey took 3hours, find the distance of the post office from the village?
A.10km
B.15km
C.20km
D.25km
Answer: A.10km
Explanation: Average speed = 2xy/x+y = 2*10*5/10+5 = 20/3km/hr
Distance travelled in 3hours = 20/3 * 3 = 20km
Distance of the post office from the village = 20/2 =10km
Answer is A
Question: In two triangle, the ratio of the areas is 4:3 and that of their heights is 3:4 the ratio of their bases is
A.16:9
B.9:16
C.9:12
D.16:12
Answer: A.16:9
Explanation: Explanation:
Given a1/a2 =4/3, h1/h2=3/4
also, we know that
a1/a2=(1/2×b1×h1)/(1/2×b2×h2)
on substituting in above equation, we get
b1/b2= 16/9
therefore b1:b2= 16:9
Answer: Option A
Question: seven friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $530. If one of the friends had a coupon for 32% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
A.$90
B.$70
C.$51
D.$37
Answer: C.$51
Explanation: 530 * 0,32 = 169
530 - 169 = 361
361 / 7 = 51
Answer C
Question: If a traveller was offered 5 city in asia and 11 city in europe and asked to chose atleast 3 city in asia and overall a 11 city. How many ways can he travel
A.2854
B.2958
C.3156
D.3762
Answer: D.3762
Explanation: 5c3*11c8+5c4*11c7+5c5*11c6=3762 ways
ANSWER:D
Question: An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. What is the rate of the plane in still air?
A.344 km/hr
B.767 km/hr
C.807 km/hr
D.908 km/hr
Answer: C.807 km/hr
Explanation: Let the speed of the air plane in still air be x km/hr
And the speed of the wind be y km/hr.
Then speed of the airplane going with the wind = (x + y) km/hr
and speed of the airplane going against the wind = (x - y) km/hr.
We know that,
Distance = Speed ? Time
or, Speed = Distance
Time
According to the problem,
An airplane travels 4362 km against the wind in 6 hours
x - y = 4362/6
or, x - y = 727 ----------- (1)
Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours
x + y = 5322/6
or, x + y = 887 ----------- (2)
Now add (1) and (2) we get,
x - y = 727
x + y = 887
2x = 1614
or, 2x/2 = 1614/2, (Divide both sides by 2)
or, x = 807
Now substitute the value of value of x = 807 in equation (2) we get,
807 + y = 887
-807 -807, (Subtract 407 from both sides)
y = 80
Answer: Rate of the plane in still air = 807 km/hr
correct answer C
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 33 kmph. Of how many minutes does the train stop per hour?
A.73
B.83
C.16
D.83
Answer: C.16
Explanation: Explanation:
T = 12/45 * 60 = 16
Answer: Option C
Question: Kelly and Jody packed boxes with books. If Jody packed 80% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?
A.1 to 6
B.1 to 4
C.2 to 5
D.3 to 5
Answer: B.1 to 4
Explanation: Explanation:
If Jody packed 80% of the boxes then Kelly packed 20%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 20%/80%=1/4
Answer: Option B
Question: 65% of x = 20% of 552.50. Find the value of x?
A.100
B.170
C.150
D.180
Answer: B.170
Explanation: 65% of x = 20% of 552.50
Then, 65/100 * x = 20/100 * 5525/10
x = 170
Answer is B
Question: Jim’s Taxi Service charges an initial fee of $2.05 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
A.$5.20
B.$4.45
C.$4.80
D.$5.05
Answer: A.$5.20
Explanation: Let the fixed charge of Jim’s Taxi Service = 2.05 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.05 + (3.6/.4) * .35
= 2.05 + 9*.35
= 5.2 $
Answer A
Question: A person travels first 100km at 40km/hr and the next 100km at 60km/hr. The average speed for the first 200km of the tour is?
A.36km/hr
B.50km/hr
C.48km/hr
D.60km/hr
Answer: C.48km/hr
Explanation: Total time taken = 100/40 + 100/60 = 25/6 hrs
Average speed = 200*6/25 = 48km/hr
Answer is C
Question: The area of the largest circle that can be drawn inside a square of side 56 Cm in length is:
A.2464
B.2052
C.3201
D.4202
Answer: A.2464
Explanation: Radius of required circle = 28 Cm
its area = 22/7 × 28 × 28
88 × 28 = 2464 Cm(power)2
Answer is A.
Question: Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number D is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+D is odd?
A. 1/2
B. 2/3
C. 3/4
D. 4/7
Answer: D. 4/7
Explanation: All primes except 2 are odd, thus N must be odd. For N + D = odd + D to be odd, D must be even.
There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.
Therefore the probability that N + D is odd is 4/7.
Answer: D.