mathewhe/aqua_rat huggingface dataset:
Question: A farmer had d animals, all of which the farmer bought for the same price. The farmer decided to sell the animals. 20 of the animals were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, the farmer made neither a profit nor a loss. Which of the following is equal to d?
(A) 24
(B) 26
(C) 28
(D) 30
(E) 36
Rationale: Let P be the price the farmer paid for each animal.
The total profit on the 20 animals is 20*0.1*P.
The total loss on the other (d-20) animals is (d-20)*0.2*P.
(d-20)*0.2*P = 20*0.1*P
0.2*d = 2 + 4
d = 30
The answer is D.
Answer: (D) 30
Question: A batsman in his 12th innings makes a score of 65 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’?
(A) 32
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 3) + 65
∴ x = 32
Answer A
Answer: (A) 32
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 6.22
(C) 6.29
(D) 6.39
(E) 6.13
Rationale: Required run rate
= [282 - (3.2 * 10)]/40
= 250/40
= 6.25
Answer: A
Answer: (A) 6.25
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
(A) 2
(B) 7
(C) 5
(D) 6
(E) 8
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Answer: (C) 5
Question: There were two candidates in an election. Winner candidate received 55% of votes and won the election by 100 votes. Find the number of votes casted to the winning candidate?
(A) 550
(B) 744
(C) 255
(D) 199
(E) 231
Rationale: W = 55% L = 45%
55% - 45% = 10%
10% -------- 100
55% -------- ? => 550
Answer:A
Answer: (A) 550
Question: A person invested in all 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is:
(A) 200
(B) 600
(C) 800
(D) 1200
(E) None of these
Rationale: Let the parts be x, y and [2600 – (x + y)].Then,
x×4×1/100=y×6×1/100=[2600−(x+y)]×8×1/100
∴ y⁄x = 4⁄6 = 2⁄3 or y = 2⁄3x.
So, x×4×1100=[2600−53x]×8100x×4×1100=[2600−53x]×8100
⇒ 4x = (7800−5x)×8/3⇒52x=(7800×8)
⇒ x = (7800×8/52)=1200.
∴ Money invested at 4% = 1200.
Answer D
Answer: (D) 1200
Question: There are 23 students in a class. In how many different ways can a committee of 3 students be formed?
(A) 1254
(B) 1482
(C) 1771
(D) 1875
(E) 1923
Rationale: 23C3 = 23*22*21 / 6 = 1771
The answer is C.
Answer: (C) 1771
Question: What will come in place of the x in the following Number series? 2, 4, 8, x , 22
(A) 33
(B) 16
(C) 12
(D) 14
(E) 43
Rationale: (D)
The pattern is + 2, + 4, + 6, +8 â€¦â€¦â€¦..
So the missing term is = 8 + 6= 14
Answer: (D) 14
Question: A pair of articles was bought for $50 at a discount of 20%. What must be the marked price of each of the article?
(A) $25
(B) $31.25
(C) $29.65
(D) $35.95
(E) $45.62
Rationale: S.P. of each of the article = 50/2 = $25
Let M.P = $x
80% of x = 25
x = 25*100/80 =$31.25
Answer is B
Answer: (B) $31.25
Question: The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg. What is the weight of the new person?
(A) 75 kg
(B) 85 kg
(C) 95 kg
(D) 65 kg
(E) 55 kg
Rationale: The total weight increase = (8 x 2.5) kg = 20 kg
weight of new person = (35 + 20) kg = 55 kg
The answer is E.
Answer: (E) 55 kg
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) 227
(B) 887
(C) 585
(D) 2679
(E) 27
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer:C
Answer: (C) 585
Question: In how many different ways can 3 boys and 3 girls sit on a bench such that the girls always sit together?
(A) 96
(B) 108
(C) 120
(D) 132
(E) 144
Rationale: We can think of the girls as one unit.
The number of ways to arrange 4 units in order is 4!
The girls can have different arrangements, so we multiply this by 3!
The number of ways to sit is 4!*3!=144
The answer is E.
Answer: (E) 144
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) 2
(B) 8
(C) 9
(D) 6
(E) 4
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: (B) 8
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/45 hours
(B) 30/14 hours
(C) 37/13 hours
(D) 30/13 hours
(E) 30/19 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26
= 30/13 hours.
Answer: D
Answer: (D) 30/13 hours
Question: Beth received 2/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 2/3 of the votes cast?
(A) 1/5
(B) 2/7
(C) 3/10
(D) 7/20
(E) 4/9
Rationale: Let the total votes be 100. Beth received 40 votes, other votes 100-40=60. In order to have received 1/2 of the votes she needed 200/3 votes so 80/3 more, which is 4/9 of the other votes.
Answer: E.
Answer: (E) 4/9
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 2 4/2 hours
(B) 2 1/2 hours
(C) 2 1/6 hours
(D) 2 1/1 hours
(E) 2 1/2 hours
Rationale: Required time
= (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer:E
Answer: (E) 2 1/2 hours
Question: A 300 meter long train crosses a platform in 30 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 287m
(B) 278m
(C) 350m
(D) 200m
(E) 282m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 30
= 50/3
3(x + 300)
= 1500 è x
= 200m.
Answer:D
Answer: (D) 200m
Question: Find the least number of complete years in which a sum of money put out at 15% compound interest will be more than double of itself?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 5 years
Answer: A
Answer: (A) 5
Question: A baker filled with a measuring cup with 2/5 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 21/40 cup
(D) 1/2 cup
(E) 7/8 cup
Rationale: 2/5 is the original water in cup .half in batter.So left is 1/5 out which 1/8 is spilled out.So again left with 3/40.
so 50% more than what he started was =2/5+1/2*(2/5)=3/5
Amount of water needed to add = 3/5 - 3/40=21/40
C
Answer: (C) 21/40 cup
Question: A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 2.62
(B) 2.56
(C) 2.5
(D) 2.8
(E) 3.2
Rationale: Required time = (5 1/4)/3 + (5 1/4)/6 = 2.625 hours.
Answer:A
Answer: (A) 2.62
Question: do you know how many 2's are there between the terms 112 to 375?
(A) A)156
(B) B)157
(C) C)158
(D) D)159
(E) E)160
Rationale: Let us calculate total 2's in the units place. (122, 132, 142 ... 192), (201, 212, 222, ... 292), (302, 312, ... 372) = 8 + 10 + 8 = 26
Total 2's in tenth's place, (120, 121, 122, ..., 129) + (220, 221, ..., 229) + (320, 321, ..., 329) = 30
Total 2's in hundred's place = (200, 201, ... 299) = 100.
Total 2's between 112 and 375 = 26 + 30 + 100 = 156
Answer:A
Answer: (A) A)156
Question: The ratio between the present ages of P and Q is 5 : 8. After four years, the ratio between their ages will be 2 : 3. What is Q’s age at present?
(A) 36 years
(B) 20 years
(C) 24 years
(D) Data inadequate
(E) None of these
Rationale: P⁄Q = 5⁄8 or P = 5Q⁄8 .....(i)
P+4/Q+4=23
or, 3P + 12 = 2Q + 8 or, 2Q – 3P = 4... (ii)
Putting value of P from eq. (i),
2Q – 3 × 5⁄8Q = 4 ⇒ Q = 32
Answer E
Answer: (E) None of these
Question: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Five years ago Jim was 5 times as old as Sam. How old is Jim now?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24
Rationale: We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) Five years ago, Jim was 5 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
5 years ago, Jim was 15 and Sam was 3, so Jim WAS 5 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D
Answer: (D) 20
Question: A shopkeeper sold an article offering a discount of 10% and earned a profit of 25%. What would have been the percentage of profit earned if no discount was offered?
(A) 39%
(B) 52%
(C) 15%
(D) 21%
(E) 28%
Rationale: Let C.P. be $100.
Then, S.P. = $ 125
Let marked price be $ x. Then, 90/100 * x = 125
x = 12500/90 = $ 139
Now, S.P. = $ 139, C.P. = Rs. 100
Profit % = 39%.
Answer: A
Answer: (A) 39%
Question: A man purchased some fruits for Rs. 1000. He sold fruits worth 400 at 10% profit. At what profit per cent, must he sell the rest in order to gain 20% on the whole?
(A) 26(2/3)%
(B) 25%
(C) 30%
(D) 33(1/3)%
(E) None
Rationale: Solution: To get 20 % profit on whole,
1000(CP)==20%(gain)==>1200(SP).
Total Profit = 1200 - 1000 = Rs. 200.
400 ==10%(gain)==>440.
He gets Rs. 40 profit on 400 hundred. Rest Profit = 200 - 40 = 160.
Then he must get Rs. 160 as profit on Rs. 600;
Hence, % profit = 160*100/600 = 26.66%.
Answer: Option A
Answer: (A) 26(2/3)%
Question: Find the volume , curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm.
(A) 952cm^2
(B) 957cm^2
(C) 954cm^2
(D) 958cm^2
(E) None of them
Rationale: Volume = ∏r2 h = ((22/7)x(7/2)x(7/2)x40) = 1540 cm^3. .
Curved surface area = 2∏rh = (2x(22/7)x(7/2)x40)= 880 cm^2 .
Total surface area = 2∏rh + 2∏r2 = 2∏r (h + r)
= (2 x (22/7) x (7/2) x (40+3.5)) cm2
= 957 cm^2
Answer is B
Answer: (B) 957cm^2
Question: A thief is noticed by a policeman from a distance of 250 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100
(B) 277
(C) 2987
(D) 150
(E) 271
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 250 - 100 = 150 m.
Answer: D
Answer: (D) 150
Question: Working simultaneously and independently at an identical constant rate, 20 machines of a certain type can produce a total of x units of product P in 4 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 8 days?
(A) 30
(B) 32
(C) 35
(D) 38
(E) 40
Rationale: The rate of 20 machines is rate=job/time=x/4 units per day --> the rate of 1 machine 1/20*(x/4)=x/80 units per day;
Now, again as {time}*{combined rate}={job done}
then 8*(m*x/80)=3x --> m=30.
Answer: A.
Answer: (A) 30
Question: (6+√3+√5)^2-(√3+√5)^2=?
(A) 1+2√3+2√5
(B) 36+12√3+12√5
(C) 1-√3+√5
(D) 1+√3-√5
(E) √3+√5
Rationale: (6+√3+√5)^2-(√3+√5)^2
(6+√3)^2 + 5 +2 (6+√3) (√5) - ( 3 +5 + 2√3√5)
36+ 3+ 12√3 +5 +12 √5 + 2 √15 - 3-5 -2√15
36+12√3+12√5
B is the answer
Answer: (B) 36+12√3+12√5
Question: Two unbiased coins are tossed. Find the probability of getting two heads?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 2/3
(E) 3/5
Rationale: S = {HH,HT,TH,TT}
E = Event of getting two heads
E = {TT}
P(E) = 1/4
Answer is C
Answer: (C) 1/4
Question: Find the odd man out. 742, 743, 633, 853, 871, 990, 532
(A) 532
(B) 990
(C) 633
(D) 742
(E) 871
Rationale: Explanation :
In all numbers except 742, the difference of third and first digit is the middle digit.
Answer : Option D
Answer: (D) 742
Question: The average monthly salary of 18 employees in an organisation is Rs. 2000. If the manager's salary is added, then the average salary increases by Rs. 200. What is the manager's monthly salary?
(A) Rs.5800
(B) Rs.3618
(C) Rs.3600
(D) Rs.3619
(E) Rs.3610
Rationale: Manager's monthly salary
= Rs. (2200 * 19 - 2000 * 18)
=Rs.5800 Answer:A
Answer: (A) Rs.5800
Question: The area of a square is equal to nine times the area of a rectangle of dimensions 121 cm * 144 cm. What is the perimeter of the square?
(A) 1500 cm
(B) 1800 cm
(C) 1584 cm
(D) 1718 cm
(E) 1086 cm
Rationale: Area of the square = s * s = 9(121 * 144)
=> s = 3* 11 * 12 = 396 cm
Perimeter of the square = 4 * 396 = 1584 cm.
Answer: C
Answer: (C) 1584 cm
Question: (.24 x .35 ) / (.14 x .15 x .02) is equal to ?
(A) 2
(B) 20
(C) 200
(D) 2000
(E) None of these
Rationale: Answer
(.24 x .35) / (.14 x .15 x .02)
= (24 x 35 x 100 ) / (14 x 15 x 2)
=200
Correct Option: C
Answer: (C) 200
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 50 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 21
(B) 88
(C) 45
(D) 99
(E) 22
Rationale: Relative speed = 50 + 30 = 80 km/hr.
80 * 5/18 = 200/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 9/200 = 45 sec
Answer: C
Answer: (C) 45
Question: A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 424. What is the sum of the last 8 of the even integers?
(A) 488
(B) 540
(C) 552
(D) 568
(E) 584
Rationale: Sum of n even consecutive integers = n(n+1)
Sum of 8 consecutive even integers that start at some point after n = (n+8)(n+9)
Given => (n+8)(n+9) - n(n+1) = 424
16n +72 = 424 - General equation for sum of consecutive 8 digits where n is where counting starts
Solving we get n = 22 (Where the count starts)
Sum of 8 consecutive integers after n = 22 will be count starting at n1 = 22+8 = 30
So Answer = 16*30 +72 = 552
ANSWER:C
Answer: (C) 552
Question: In an election, candidate A got 70% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
(A) 330000
(B) 340000
(C) 347000
(D) 333200
(E) 357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 70 %
Therefore, the number of valid votes polled in favour of candidate A = 70 % of 476000
= 70/100 × 476000
= 33320000/100
= 333200
D)
Answer: (D) 333200
Question: If 80 percent of a class answered the first question on a certain test correctly, 55 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%
(E) 55%
Rationale: 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 - [(80 - x) + x + (55 - x)] = 20 .......... values are in percent
x = 20 - 100 + 135
x = 55
Ans: E
Answer: (E) 55%
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 2835 what is the least possible value of k?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: 2835 = 3*3*3*3*5*7
Thus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 (that is: 3, 6, and 9=3*3).
The answer is C.
Answer: (C) 9
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent E of thatbeforeJuly 1 last year?
(A) 90%
(B) 99%
(C) 100%
(D) 101%
(E) 110%
Rationale: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before E = [0.9n (1.1x)]/xn= 0.99 or 99%=B
Answer: (B) 99%
Question: An exam paper consists of 5 problems, each problem having 3 internal choices. In how many ways can a candidate attempt one or more problems?
(A) 1020
(B) 1023
(C) 1030
(D) 1054
(E) 1060
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
B
Answer: (B) 1023
Question: A 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 286 m
(B) 350 m
(C) 277 m
(D) 400 m
(E) 267 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/42 = 50/3
x = 400 m.
Answer:D
Answer: (D) 400 m
Question: If a 9 ton whale is divided into 2 equal large pieces and 3 equal small pieces, how much does a small piece weigh if all of the small pieces put together weigh as much as one of the large pieces?
(A) 1 ton
(B) 1 1/2 tons
(C) 2 tons
(D) 2 1/2 tons
(E) 3 tons
Rationale: A. Each large piece is a third of the whale. Each small piece is a third of the remaining third of the whale. One third of one third is one ninth. One ninth of nine tons is one ton, so the answer is A
Answer: (A) 1 ton
Question: W, S, Q, M, ?
(A) M
(B) K
(C) H
(D) Y
(E) S
Rationale: Explanation:
No explanation is available for this question!
ANSWER: B
Answer: (B) K
Question: The sum of digits of a two digit number is 12,The difference between the digits is 6. Find the number
(A) 85
(B) 93
(C) 83
(D) 72
(E) None
Rationale: Description :
=> x+y=12, x-y=6
Adding these 2x =18
=> x=9, y=3.
Thus the number is 93
Answer B
Answer: (B) 93
Question: The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 11.5 cm
(C) 91.8 cm
(D) 92.5 cm
(E) 152.5 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 35) + 2(35)
= 49.5 + 70
= 152.5 cm
Answer:E
Answer: (E) 152.5 cm
Question: ax ± b = c. All problems like the following lead eventually to an equation in that simple form.
Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?
(A) 28
(B) 26
(C) 24
(D) 22
(E) 20
Rationale: Every word problem has an unknown number. In this problem, it is the price of the blouse. Always let x represent the unknown number. That is, let x answer the question.
Let x, then, be how much she spent for the blouse. The problem states that "This" -- that is, $42 -- was $14 less than two times x.
Here is the equation:
2x − 14 = 42.
2x=42+14
=56.
x=56/2
= 28
The blouse cost $28.
Answer is A.
Answer: (A) 28
Question: The probability of two events A and B are0.25 and 0.30 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________
(A) 0.45
(B) 0.4
(C) 0.5
(D) 0.05
(E) 0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.25+.30-.15
=.40
but the probability of neither A nor B=1-.40
=0.60
ANSWER:E
Answer: (E) 0.6
Question: The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 5 unit of standard deviation above the mean?
(A) -35.6 degrees Celsius
(B) -20.0 degrees Celsius
(C) -30.4 degrees Celsius
(D) -27.8 degrees Celsius
(E) -25.2 degrees Celsius
Rationale: Let us suppose mean = M and SD = d.
So, we are given M - 2d = -38.2
and M + 4d = -22.6
solving both the equations, we will get M = -33 an d = 2.6
So, we need to find out M + 5d = -33 +5* 2.6 = -20. Hence, B
Answer: (B) -20.0 degrees Celsius
Question: How long will a car take to run round a circular field of radius 2/π metres. If car runs at the rate of 8km/hr ?
(A) 2.5 sec.
(B) 10 sec.
(C) 3 sec
(D) 2 sec
(E) 1.8 sec
Rationale: Speed = 8 km/hr = 8*5/18 = 20/9 m/sec
distance = 2πr=2π*2/π=4 m
time taken = 4*9/20 = 1.8 sec.
Answer E
Answer: (E) 1.8 sec
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 15 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/75
(C) 1/25
(D) 1/50
(E) 1/900
Rationale: If it takes 15 minutes to inspect one vehicle, the # of vehicles that can be inspected in 3 hours (180 minutes) = 180/15 = 12. Hence, for calculating the probability that the police will find the transmitter within three hours, the favorable cases = 12. Now, we need to figure out the total # of cases.
The total # of cases = Total # of such cars possible. The details given about the car is that it starts with 79, which leaves 2 more digits, both of which can be filled by all 10 numbers (0-9). In addition, we have 3 letters, each of which can be filled by any from the set {A,B,C}. Hence the total # of such cars possible = 10*10*3*3 = 900
So, the probability that the police will find the transmitter within three hours = 12/900 = 1/75. Option B
Answer: (B) 1/75
Question: Let y = 2g + x^2 and g = 4x + 1.
If g^2 = 289, then which of the following can be a value of 2y + 3g?
(A) 100
(B) 130
(C) 141
(D) 151
(E) 160
Rationale: 800score Official Solution:
First note that g can either be 17 or -17. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 17 and then g = -17. If g = 17, then x = 4. If g = -17, then x = -18/4. Since all of our solutions are whole numbers, we can dismiss -18/4. We use g = 17 and x = 4 to determine the value of y: y = 2(17) + 16 =50. Finally, we substitute the values for y and g into the last expression to determine its value : 2(50) + 3(17) = 100 + 51 = 151;the correct answer is (D).
Answer: (D) 151
Question: For any number y, y* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.2 – 6.2*?
(A) 0.2
(B) 1.2
(C) 1.8
(D) 2.2
(E) 4.0
Rationale: Since y* is defined as the greatest positive even integer less than or equal to y, then 6.2* = 4 (the greatest positive even integer less than or equal to 6.2 is 4).
Hence, 6.2 – 6.2* = 6.2 - 4 = 2.2
Answer: D.
Answer: (D) 2.2