RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 100000 and 1000000 ?
A. 10
B. 11
C. 101
D. 1011
Answer: A. 10
Explanation: Binary Divison can provide a quick answer if you are comfortable with it.
as option E is the biggest binary number we try with it first :
100010000/ 10=10000
1000100000/ 101 =100000
so answer is option is A
Question: In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?
A.2:1
B.1:2
C.1:5
D.5:1
Answer: A.2:1
Explanation: 1st variety rs 18 /kg---- 2nd variety rs 24/kg
mix cost 20/kg = (24-20) (20-18)
=4:2 = 2:1
ANSWER A
Question: At Chennai it rained as much on Tuesday as on all the others days of the week combined. If the average rainfall for the whole week was 3 cm. How much did it rain on Tuesday?
A.2.625 cm
B.3 cm
C.10.5 cm
D.15 cm
Answer: C.10.5 cm
Explanation: Total rainfall = 3 x 7 = 21 cm
Hence, rainfall received on Tuesday = 21/2 (as it rained as much on Tuesday as on all the others days of the week combined)
= 10.5 cm.
ANSWER:C
Question: If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 6 is subtracted and divided by 8?
A.4
B.6
C.8
D.5
Answer: B.6
Explanation: Explanation:
Let the number be x. Then,
(x - 5)/7 = 7 => x - 5 = 49
x = 54
.: (x - 6)/8 = (54 - 6)/8 = 6
Answer: Option B
Question: Jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
A.5
B.10
C.22
D.25
Answer: C.22
Explanation: Let's TEST Answer C: 22 seashells...
With 22 seashells, Jamie would have 22(20) =440 cents. This would allow him to buy 8 books for 440 cents total, so this is the correct answer.
C
Question: A sum of money lent out at S.I. amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
A.776
B.267
C.269
D.600
Answer: D.600
Explanation: S.I for 5 years = (1020 - 720)
= Rs. 300.
S.I. for 2 years = 300/5 * 2
= Rs. 120.
Principal = (720 - 120)
= Rs.600.
Answer: D
Question: Which of the following values of x will satisfy the inequality x2 – x – 6 > 0 ?
A.x < – 2 or x > 3
B.–2 < x < 3
C.–3 < x < 2
D.x > – 2 or x < 3
Answer: A.x < – 2 or x > 3
Explanation: x2 – x – 6 > 0
or, x2 – 3x + 2x – 6 > 0
or, x(x – 3) + 2(x – 3) > 0
or, (x – 3)(x + 2) > 0
or, x = 3 or – 2
∴ x < – 2 or x > 3
Answer A
Question: Find the middle one when The sum of three consecutive even numbers is 36?
A.11
B.12
C.15
D.16
Answer: B.12
Explanation: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
A.16
B.17
C.18
D.19
Answer: C.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.
Answer: Option C
Question: What will be the compound interest on a sum of Rs. 20,000 after 3 years at the rate of 12% p.a.?
A.s:8098.56
B.s:10123.29
C.s:10123.20
D.s:10123.28
Answer: A.s:8098.56
Explanation: Amount
= [20000 * (1 + 12/100)3]
= 20000 * 28/25 * 28/25 * 28/25
= Rs. 28098.56
C.I. = (28098.56 - 20000)
= Rs: 8098.56
Answer: A
Question: Find large number from below question The difference of two numbers is 1200. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
A.1437
B.1250
C.1540
D.1600
Answer: A.1437
Explanation: Let the smaller number be x. Then larger number = (x + 1365).
x + 1200 = 6x + 15
5x = 1185
x = 237
Large number = 237+1365 = 1437
A
Question: ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 190 students answered yes only for subject M, how many of the students did not answer yes for either subject?
A.100
B.210
C.300
D.400
Answer: B.210
Explanation: Since 190 students answered yes only for subject M, then the remaining 310 students who answered yes for subject M, also answered yes for subject R. So, 310 students answered yes for both subjects.
If 310 students answered yes for both subjects, then 400-310=90 students answered yes only for subject R.
So, we have that:
200 students answered yes only for subject M;
90 students answered yes only for subject R;
300 students answered yes for both subjects;
Therefore 800-(200+90+300)=210 students did not answer yes for either subject.
Answer: B.
Question: A person purchased a TV set for Rs. 12000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.16.68%
B.87.68%
C.70.68%
D.17.68%
Answer: C.70.68%
Explanation: The total CP = Rs. 12000 + Rs. 6250 = Rs. 18250 and SP
= Rs. 31150
Profit(%) = (31150 - 18250)/18250 * 100
= 70.68%
Answer:C
Question: One years ago,Promila was four times as old as her daughter Sakshi.Six years hence,Promila’s age will excepted her daughter’s age by 9 years.The ratio of the present ages of Promila and her daughter is
A.9 : 2
B.11 : 3
C.12 : 5
D.13 : 4
Answer: D.13 : 4
Explanation: Solution
Let the ages of Promila and Sakshi 1 year ago be 4x and x years respectively.
Then,[(4x +1)+6]-[(x + 4)+ 4]=64 ⇔ 4x = 48 ⇔ x =12.
∴ Required ratio =(4x +1 ) : (x + 1) : 13 : 4. Answer D
Question: We made a down payment of $80 and borrowed the balance on a new violin which cost $400. The balance with interest was paid in 23 monthly payments of $14 each and a final payment of $22. The amount of interest paid was what percent of the amount borrowed?
A.5.5%
B.6.5%
C.7.5%
D.8.5%
Answer: C.7.5%
Explanation: We borrowed $320.
To pay back this loan, we paid 23*$14 + $22=$344.
The interest was $344-$320=$24.
The percentage was $24/$320=0.075=7.5%.
The answer is C.
Question: Sandy purchased 20 dozen toys at the rate of $144 per dozen. Sandy sold each toy at the rate of $12.60. What was the percentage profit?
A.3%
B.5%
C.7%
D.9%
Answer: B.5%
Explanation: A dozen toys cost $144, so each toy cost $12.
selling price / cost price = 12.60 / 12 = 1.05
The percentage profit is 5%.
The answer is B.
Question: At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using ten colors?
A.21
B.35
C.105
D.120
Answer: D.120
Explanation: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.
As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:
ABC
ACB
BAC
BCA
CAB
CBA
By extension, the first part of your calculation would be the number of possible substances that could be identified with 10 colors: 10c3 = 120 possible substances
D
Question: Find the simple interest on Rs.450 for 8 months at 5 paisa per month?
A.277
B.270
C.180
D.266
Answer: C.180
Explanation: I = (450*8*5)/100 = 180
Answer: C
Question: A solution of 66 litres contains milk and water in the ratio 7:x. If four litres of water is added to the solution, the ratio becomes 3:2, find the value of x?
A.8
B.5
C.3
D.4
Answer: D.4
Explanation: Total new quantity = original sol + water =66+4 =70
New ratio = 3:2, New quantity of milk =3/5*70 = 42 Lit,
New quantity of water = 2/5*70 = 28 Lit
Water present initially = (28-4) = 24 Lit
Ratio = 42/24 =7/4 There for x = 4
ANSWER:D
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
A.11
B.28
C.156
D.44
Answer: B.28
Explanation: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
Answer: B
Question: On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 44 centimeters assuming that 1-inch is 2.54 centimeters?
A.174.2
B.277
C.288.1
D.296
Answer: B.277
Explanation: 1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 44 cm.:
44/(2.54*1.5) = x / 24 ---> x = 24*44/(3.81) = 277
Answer will be B.
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
A.71/9
B.7/15
C.7/18
D.4/17
Answer: B.7/15
Explanation: let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Option B
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
A.5
B.8
C.9
D.2
Answer: B.8
Explanation: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Question: find the number, difference between number and its 3/5 is 60.
A.150
B.153
C.154
D.155
Answer: A.150
Explanation: Explanation:
Let the number = x,
Then, x-(3/5)x = 60,
=> (2/5)x = 60 => 2x = 60*5,
=> x = 150
Answer: Option A
Question: What is the decimal equivalent of (1/4)^1?
A.0.0016
B.0.0625
C.0.16
D.0.25
Answer: D.0.25
Explanation: (1/4)= 0.25
Answer : D
Question: Albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born. What is the difference between the ages of her parents?
A.2
B.4
C.6
D.8
Answer: B.4
Explanation: Mother's age when Albert's brother was born = 46years
Father's age when Albert's brother was born = 48+2 = 50years
Required difference = 50-46 = 4 years
Answer is B
Question: The contents of a certain box consist of 20 apples and 30 oranges. How many oranges must be added to the box so that exactly 20% of the pieces of fruit in the box will be apples?
A.50
B.55
C.75
D.85
Answer: A.50
Explanation: apple = (apple + orange + x)*0.2
20 = (30 + 20 + x)*0.2
x = 50
Answer: A
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
A.8%
B.5%
C.2%
D.3%
Answer: B.5%
Explanation: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer: B
Question: A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?
A.22
B.38
C.62
D.122
Answer: D.122
Explanation: Same logic but with application of factorials.
2*4*6*8*...*n = 2(1*2*3*4*...n/2) = 2*(n/2)!
Now we have: 2*(n/2)!/2013=2*(n/2)!/(3×11×61)
For the expression 2*(n/2)! To be divisible by 2013 min value of n/2 should be 61.
So n/2=61 => n=122
Answer D.
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.650 in 2 years?
A.221
B.287
C.400
D.589
Answer: D.589
Explanation: Explanation:
650 = P(21/20)2
P = 589.56
Answer:D
Question: In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 90π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
A.360π
B.400π
C.450π
D.500π
Answer: A.360π
Explanation: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.
4(90π) = 360π
The answer is A.
Question: Given that 0.0010010 x 10^q > 10^3, and q is an integer, which of the following is the smallest possible value of q?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: 0.0010010 x 10^q > 10^3, and q is an integer
This will be true only when LHS will be 1001
so the smallest possible value of q to make LHS > 10^3 is q=6
ANSWER:D
Question: The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides?
A.3
B.6
C.5
D.9
Answer: C.5
Explanation: S = (1 + 2 + 7)/2= 5 Answer:C
Question: 0.6 of a number equals 0.09 of another number. The ratio of the number is:
A.2:3
B.1:15
C.20:3
D.3:20
Answer: D.3:20
Explanation: Explanation :
Let 0.6 of x be equal to 0.09 of y:
i.e. 0.6x = 0.09y
=> x/y = 0.09/0.6 = 3/20
Answer : D
Question: If Rs. 782 be divided into three parts, proportional to 1/2: 2/3: 3/4, then the first part is:
A.202
B.203
C.204
D.205
Answer: D.205
Explanation: (1/2+2/3+3/4)x=782
x=782*12/23=408
fist part is: (1/2)x=408/2=204
ANSWER:D
Question: The average marks of a class of 24 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
A.52.2
B.59.5
C.52.8
D.53.5
Answer: D.53.5
Explanation: Sum of the marks for the class of 24 students = 24 * 40 = 960
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 74 students =
960 + 3000 = 3960
Average marks of all the students = 3960/74
= 53.5
Answer:D
Question: If in a certain sequence of consecutive multiples of 50, the median is 725, and the greatest term is 950, how many terms that are smaller than 725 are there in the sequence?
A.6
B.5
C.8
D.12
Answer: B.5
Explanation: Since the median is 725 we know there must be a even number of integers because 50 is not a multiple of 725.
So the list around 725 must go. 600 650 700(725) 750 800 850 900 950
Since we know there are 5 numbers greater than 725 then there must be 5 numbers less then 725.
answer:B
Question: What will be the day of the week 15th August, 2010?
A.Tuesday
B.Saturday
C.Monday
D.Sunday
Answer: D.Sunday
Explanation: 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.
Given day is Sunday
Answer is D.
Question: Find the area of the square, one of whose diagonals is 3.8 m long ?
A.7.22m^2
B.3.86m^2
C.8.96m^2
D.2.68m^2
Answer: A.7.22m^2
Explanation: Area of the square= 1/2(diagonal)^2
=(1/2*3.8*3.8)m^2
= 7.22m^2
Answer (A)
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 5
III. 7
A.I only
B.II only
C.III only
D.I,III only
Answer: B.II only
Explanation: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 5, 6, 7,8,9 and 10, then the sum = 45.
45 is divisible by 5
45 is NOT divisible by 6
45 is NOT divisible by 7
There's only one answer that 'fits' with these facts. Answer : B
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3647
A.3647
B.9654
C.5945
D.7963
Answer: A.3647
Explanation: The product of first two digits in a number equals the last two digits, except in 3647. Hence, it is the odd one.
The answer is 3647.
ANSWER:A
Question: A train 490 m long, running with a speed of 63 km/hr will pass a tree in?
A.25
B.26
C.27
D.28
Answer: D.28
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 490 * 2/35 = 28 sec
Answer: Option D
Question: In a race of length Lmetres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
A.L(L-N) / L-M
B.(N-M)*L/(L-M)
C.L-N
D.M-N
Answer: B.(N-M)*L/(L-M)
Explanation: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 100
M = 10
N =20.
So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect
Out of which, i choose B.
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 38 years. What is Deepak present age?
A.22
B.24
C.77
D.266
Answer: B.24
Explanation: Present age is 4x and 3x,
=> 4x + 6 = 38 => x = 8
So Deepak age is = 3(8) = 24
Answer: B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A.s.4529
B.s.4586
C.s.4597
D.s.6342
Answer: D.s.6342
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 7
=Rs.6342
Answer: D
Question: A man is 27 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
A.11
B.25
C.27
D.22
Answer: B.25
Explanation: Let the son's present age be x years.
Then, man's present age = (x + 27) years.
(x + 27) + 2 = 2(x + 2) x + 29 = 2x + 4 => x = 25.
Answer: B
Question: In how many different ways can the letters of the word â€˜EVERâ€™ be arranged?
A.12
B.280
C.300
D.310
Answer: A.12
Explanation: Number of ways = 4!/2! = 4X3X2X1/2X1 = 12
A
Question: The average of numbers 0.54204, 0.54203, 0.54202 and 0.54201 is ?
A.0.54202
B.0.54204
C.0.542022
D.0.542025
Answer: D.0.542025
Explanation: Answer
Average = (0.54204 + 0.54203 + 0.54202 + 0.54201)/ 4
=2.1681/ 4
=0.542025
Correct Option: D
Question: Jill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 18 songs, what are the chances that the third song he hears will be his favorite?
A.1/18
B.1/12
C.1/11
D.3/14
Answer: A.1/18
Explanation: The player plays the songs on the album at random, so there are 18 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.
Total outcomes ==> 18
Total positive outcomes ==> 1
Correct answer is A) 1/18
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 4 cups of tea are prepared, 2 in one way and 2 in other. Find the different possible ways of presenting these 4 cups to the expert.
A.25
B.24
C.30
D.34
Answer: B.24
Explanation: Solution:
Since, there are 2 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[4!/(2!x2!)]= 24
Answer: Option B
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be A's share in the total profit of Rs.26,000 earned at the end of 2 years from the starting of the business?
A.Rs.7500
B.Rs.9000
C.Rs.9500
D.Rs.10,400
Answer: D.Rs.10,400
Explanation: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
A's share	=Rs.(26000×4/10)
= Rs.10400.
Answer D
Question: What is the probability of rolling a nine with two, fair, six-sided dice?
A.1/6
B.1/9
C.2/13
D.1/12
Answer: B.1/9
Explanation: There are 4 ways to roll a nine: 3 and 6, 6 and 3, 4 and 5, 5 and 4 with two six-sided dice. There are 6 times 6 = 36 ways to roll two dice. The probability of rolling a 9 is thus 4/36 = 1/9. B
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
A.54.3 kg
B.55.5 kg
C.66.5 kg
D.67.8 kg
Answer: D.67.8 kg
Explanation: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Question: If a + b + c = 13, then find the ab + bc + ca :
A.22
B.99
C.50
D.29
Answer: C.50
Explanation: Answer: C) 50
Question: In order to complete a reading assignment on time, Terry planned to read 100 pages per day. However, she read only 75 pages per day at first, leaving 625 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
A.8
B.7
C.9
D.10
Answer: B.7
Explanation: D=100*X - according to the plan, assignment to be completed on time reading 100 pages per day for next X days. But, Terry's plans changed so she read as follow:
75 pages for first Y days and 625 pages for last 6 days, we get these equations:
75*Y+625=100*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 75 pages per day and 6 leftover days used to complete a lump 625 pages
From above we find that X=Y+6 and 75Y+625=100Y+600 or 25Y=25 --->>>>> Y=1, hence X=7
Answer : B
Question: If a*b*c=130, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ?
A.1/2
B.1/4
C.3/4
D.2/3
Answer: A.1/2
Explanation: Explanation :
a∗b∗c/b∗c∗d= 130/65 => a/d = 2
d∗e∗f/c∗d∗e= 250/1000 => f/c = 14
a/d* f/c = 2 * 1/4 = 1/2
Answer : A
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 12 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
A. 18/79
B. 16/900
C. 1/25
D. 1/50
Answer: B. 16/900
Explanation: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/12 = 16
P = 16/900
Ans:B
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $54 of gas?
A.236
B.354
C.432
D.512
Answer: C.432
Explanation: 54/4 = 13.5 gallons
13.5*32 = 432 miles
The answer is C.
Question: Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fifth widget, starting with the fifth, and Steven inspects every third, starting with the third, how many of the 95 widgets produced in the first hour of operation are not inspected by either inspector?
A.50
B.43
C.45
D.55
Answer: A.50
Explanation: Widgets inspected by Lauren: ((95-5)/5)+1=18+1=19
Widgets inspected by Steven: ((93-3)/3)+1 =31+1 =32
Widgets inspected by both: ((90/15)+1 =6
Total : 19+32 -6=45
hence, widgets not inspected: 95-45=50
Option A
Question: Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
A.(a + y) / t
B.2(a + t) / ay
C.2ayt / (a + y)
D.2(a + y + t) / ay
Answer: C.2ayt / (a + y)
Explanation: If we choose for d (distance): 10 miles, for a 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits.