mathewhe/aqua_rat huggingface dataset:
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
(A) 564/123
(B) 646/458
(C) 456/847
(D) 175/256
(E) 256/175
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans: D
Answer: (D) 175/256
Question: In a certain zoo, the ratio of horses to penguins is 5 to 11. If there are 80 more penguins than horses at the zoo, how many horses are there?
(A) 24
(B) 36
(C) 66
(D) 72
(E) 132
Rationale: 5/11 = x / x+80
5*80 = 6x
x=66
C. 66
Answer: (C) 66
Question: A watch was sold at a loss of 10%. If it was sold for Rs.190 more, there would have been a gain of 4%. What is the cost price?
(A) s.1000
(B) s.1009
(C) s.1007
(D) s.1357.1
(E) s.1002
Rationale: Explanation:
90%
104%
--------
14% ---- 190
100% ---- ? => Rs.1357.1
Answer:D
Answer: (D) s.1357.1
Question: The C.P of 10 pens is equal to the S.P of 20 pens. Find his gain % or loss%?
(A) loss 16 2/8%
(B) loss 50%
(C) loss 16 2/3%
(D) loss 18 2/3%
(E) loss 16 25%
Rationale: 10 CP = 20 SP
20 --- 10 CP loss
100 --- ? => 50% loss
Answer:B
Answer: (B) loss 50%
Question: A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 30
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: Answer : A
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 160
16x = 160
x = 10.
Hence, total number of notes = 3x = 30.
Answer: (A) 30
Question: Sarah is driving to the airport. After driving at 50 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 100 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
(A) 140
(B) 175
(C) 200
(D) 245
(E) 280
Rationale: After driving at 50 miles per hourfor one hour, this distance left to cover is d-50. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 50 miles per hour and 100 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/50 - x/100 = 3/2 --> 2x/100 - x/100 = 3/2 --> x/100 = 3/2 --> x = 150
Total distance = x + 50 = 200 miles.
Answer: C.
Answer: (C) 200
Question: If v equals the sum of the odd integers from 5 to 505, inclusive, and q equals the sum of the odd integers from 3 to 303, inclusive, what is the value of v - q?
(A) 1616
(B) 153007
(C) 40902
(D) 1147612
(E) 50503
Rationale: Use following formulae for such problems:
Sum of evenly spaced integers = (# of integers)*(mean of integers)
# of integers = [(last - first)/2] + 1
Mean of integers = (last + first)/2
In above problem:
# of integers = [(505 - 5)/2] + 1= 251 and [(303-3)/2]+ 1 = 151
Mean of integers = (505 + 5)/2 = 255 and (303 + 3)/2 = 153
Sum of integers = (251*255) = 64005 and (151*153) = 23103
Thus their difference (v - q) = 40902
ANSWER:C
Answer: (C) 40902
Question: The compound ratio of 5:7, 3:2 and 4:5?
(A) 1:7
(B) 6:5
(C) 6:7
(D) 4:7
(E) 6:9
Rationale: 5/7 * 3/2 * 4/5 = 6/7
6:7
ANSWER:C
Answer: (C) 6:7
Question: A computer wholesaler sells eight different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
(A) 15/56
(B) 3/28
(C) 1/28
(D) 1/56
(E) 1/168
Rationale: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 6 avilable. so 6C1 is the numerator.
Total no of ways we can choose 3 from 8 is 8c3, which is the denominator.
So, the probability: 6c1/8c3= 3/28 ans is B.
Answer: (B) 3/28
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 150
(B) 180
(C) 200
(D) 310
(E) 250
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen
Required number of ways = 6C3*5C2 = 200
Answer is C
Answer: (C) 200
Question: Jerry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Jerry a third of her cards. Jerry plays next, and Michelle follows. Then the game ends. Jerry ended up with 28 more cards than Michelle. How many cards did each player have originally?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 56
Rationale: GameMichelle Jerry
Initially 54 54 assume
After game 1 36 72
After game 2 60 48
After game 3 40 68
Now Merry has 28 cards more than Michelle. This option gives us exactly what number of cards they had initially.
So the answer is D
Answer: (D) 54
Question: Find the value o f 72519 x 9999 = m?
(A) 434539873
(B) 355797990
(C) 435453490
(D) m=725117481
(E) 873430134
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) m=725117481
Question: If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?
(A) 4
(B) 6
(C) 15
(D) 20
(E) 24
Rationale: If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?
let the certain number be 60, which is both divisible by 12 and 10.
60/24 = 5/2
ANSWER:E
Answer: (E) 24
Question: Each Machine of type X has 3 steel parts and 2 chrome parts. Each machine of type Y has 4 steel parts and 7 chrome parts. If a certain group of type X and type Y machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group
(A) 2
(B) 3
(C) 6
(D) 8
(E) 9
Rationale: Look at the below representation of the problem:
Steel Chrome total
X 3 2 20 >>no. of type X machines=20/5=4
Y 4 7 22 >>no. of type Y machines=22/11=2
So the answer is 6 i.e C.
Answer: (C) 6
Question: The average age of students in section A of 115 students is 15 years and the average age of students in section B of 120 students is 22 years. Find the average age of students in both sections taken together?
(A) 26 years
(B) 30years
(C) 18years
(D) 25years
(E) 20years
Rationale: The required average = (115*15+120*22)/115+120 = 18 years
Answer is C
Answer: (C) 18years
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 29
(B) 8
(C) 16
(D) 99
(E) 12
Rationale: 10 * 15 + 36 – 26 = 160/10
= 16
Answer: C
Answer: (C) 16
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
(A) 1/20
(B) 1/21
(C) 1/45
(D) 1/43
(E) 1/23
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
A
Answer: (A) 1/20
Question: A man desired to get into his work building, however he had forgotten his code.
However, he did recollect five pieces of information
-> Sum of 5th number and 3rd number is 14.
-> Difference of 4th and 2nd number is 1.
-> The 1st number is one less than twice the 2nd number.
->The 2nd number and the 3rd number equals 10.
->The sum of all digits is 30.
Crack the code ?
(A) 54658
(B) 74658
(C) 84658
(D) 14658
(E) 34658
Rationale: B
74658
* 8 + 6 =14
* 5 - 4 = 1
* 7 = 2*4 - 1
* 4 + 6 = 10
* 7+4+6+5+8 = 30
Answer: (B) 74658
Question: In how many ways can the letters of the word, ‘KEYBOARD’ be arranged in such a way that the vowels always come together?
(A) 4250
(B) 4520
(C) 4320
(D) 4230
(E) 4530
Rationale: In the word ‘KEYBOARD’ we treat the vowels EOA as one letter. Thus, we have KYBRD (EOA).
Thus we have 6 letters can be arranged in 6! = 720 ways
The vowels (EOA) can be arranged among themselves in 3! = 6 ways
Therefore, Required number of ways= (720*6)= 4320
ANSWER:C
Answer: (C) 4320
Question: If a certain sample of data has a mean of 21.0 and the value 42.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
(A) 8.3
(B) 7.3
(C) 7.5
(D) 6.5
(E) 6.2
Rationale: 42.0 is more than 2.5 standard deviations from 21 --> 42 > 21 + 2.5*{SD} --> 2.5*{SD} < 21 --> {SD} < 8.4. Only option A offers the standard deviation less than 8.4.
Answer: A
Answer: (A) 8.3
Question: There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ?
(A) 120ways
(B) 220ways
(C) 420ways
(D) 720ways
(E) 520ways
Rationale: By kept 3boys together(1) and arranging 4 girls with them
5! = 5*4*3*2*1 = 120ways. (i.e., 4+1 =5)
Possible arrangements of 3 boys in following ways
3! = 3*2*1 = 6ways
Now, arrange all with the boys together
120*6 = 720ways
ANSWER:D
Answer: (D) 720ways
Question: Five machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days?
(A) 4
(B) 6
(C) 8
(D) 5
(E) 10
Rationale: Rate of one machine = 1 job / (20*5) days
let X = number of machines needed to complete the job in 10 days
1/(5*20) * 10 * X = 1 job
X = 10
10-5= 5
ANSWER: D
Answer: (D) 5
Question: Jeya decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Jeya's savings by the end of the year from these monthly savings were two times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 5/7
(B) 6/7
(C) 9/7
(D) 5/7
(E) 4/7
Rationale: Let Jeya's monthly savings = S
Jeya's monthly pay = P
Jeya's monthly expenditure = P-S
Jeya's savings by the end of the year from these monthly savings were two times the amount she spent per month
12S = 2*(P-S)
=>6S = P-S
=> P = 7S
Jeya's monthly expenditure = P-S = 7S-S = 6S
fraction of her salary that Jeya spent each month = 6S / 7S=P-S/P = 6/7. Answer is B
Answer: (B) 6/7
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270 m
(B) 280 m
(C) 279 m
(D) 282 m
(E) 279 m
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec
= 27 * 10 = 270 m.
The length of the faster train
= 270 m.
Answer: A
Answer: (A) 270 m
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
(A) 2888
(B) 27798
(C) 27766
(D) 29971
(E) 10500
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7
= Rs. 10500
Answer: E
Answer: (E) 10500
Question: 7 people average age is 30. youngest person age is 5. find average of the people when youngest was born.
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: average age of people =30
so have total age =210
before 7 years we have to deduct each person age by seven years 210-35=161
so average age would be 175/7=25
ANSWER:C
Answer: (C) 25
Question: Cars M and N are approaching each other on the same highway. Car M is moving at 45 mph northbound and Car N is moving at 55 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart?
(A)  3:30 pm
(B)  3:45 pm
(C)  4:00 pm
(D)  4:15 pm
(E)  4:30 pm
Rationale: Total distance, which should be covered by both cars is 190+35=225 miles.
Let t be the time so the equation will be 45t+55t=225 thus,
t=2.25 hours
Answer: D
Answer: (D)  4:15 pm
Question: 4 years ago, Paula was 4 times as old as Karl. In 4 years, Paula will be twice as old as Karl. What is the sum of their ages now?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: P-4 = 4(K-4) and so P = 4K-12
P+4 = 2(K+4)
(4K-12)+4 = 2K+8
K = 8
P = 20
P+K = 28
The answer is D.
Answer: (D) 28
Question: A train 800 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 180 sec. The speed of the train is?
(A) 5 km/hr
(B) 1 km/hr
(C) 2 km/hr
(D) 3 km/hr
(E) 4 km/hr
Rationale: Speed of the train relative to man = 800/180 = 40/9 m/sec.
= 40/9 * 18/5 = 16 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 15 = 16 => x = 1 km/hr.
Answer: B
Answer: (B) 1 km/hr
Question: Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 8 inches on a side and costs $10, and a large pizza that measures 12 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?
(A) 5 square inches
(B) 10 square inches
(C) 16 square inches
(D) 25 square inches
(E) 350 square inches
Rationale: In the first case each can buy one pizza of $10 and one pizza of $20.
In square inches that would be (8*8=64) for the small pizza and (12*12=144) for the large pizza. In total sq inches that would be (64+144)*2= 416 sq inches.
In the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be 3*144= 432 sq inches.
Hence, the difference is 16 square inches more (432-416).
The correct answer is C
Answer: (C) 16 square inches
Question: At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended $35 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
(A) 291.67
(B) 105
(C) 301.05
(D) 288
(E) 249.55
Rationale: System of Equations
a = (36/100) c
(1/3) a = 35 --> a = 105
Substitution
105 = (36/100) c
c = (100/36) 105
- You can do the ugly calculation 105/36 * 100
The Correct Answer is A.
The correct answer is 291.67
Answer: (A) 291.67
Question: George baked a total of 50 pizzas for 5 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: 3/5 of the 50 pizzas cooked on Saturday = 30 pizzas
3/5 of the remaining pizzas on Sunday = 12 pizzas
We're left with (50-30-12) =8 pizzas for the remaining 3 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W
5 2 1 =8
W=1
E
Answer: (E) 1
Question: Excluding stoppages, the average speed of a bus is 50 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
(A) 12 min
(B) 18 min
(C) 16 min
(D) 20 min
(E) 26 min
Rationale: In 1hr, the bus covers 50 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (50 - 40) km i.e 10 km at 50 km/hr.
stoppage time = 10/50 hrs
= 12 min
Answer: A
Answer: (A) 12 min
Question: When x is divided by y, the quotient is z with remainder a. Which of the following is equal to a?
(A) yz – x
(B) y/x−z
(C) x – y – z
(D) x – yz
(E) zx – y
Rationale: (x/y)=z(+a)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Answer: (D) x – yz
Question: If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x?
(A) 308
(B) 154
(C) 70
(D) 44
(E) 20
Rationale: If x is divisible by 2,14 and 11,then x must be a multiple of 2,7 and 11.
Hence,the least multiple of x will be 2*7*11=154.
ANSWER:B
Answer: (B) 154
Question: Six years ago, the ratio of ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's age at present?
(A) 16 years
(B) 18 years
(C) 20 years
(D) Cannot be determined
(E) None of these
Rationale: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then, [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10
10(6x + 10) = 11(5x + 10) => x = 2
Sagar's present age = (5x + 6) = 16 years.
ANSWER:A
Answer: (A) 16 years
Question: We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 20, and the difference between the total number of strawberries and the total number of blueberries would increase by 80. Each blue box contains how many blueberries?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Let x be the number of blueberries in each blue box.
Then there are x+20 strawberries in each red box.
x+(x+20)=80
x = 30
The answer is B.
Answer: (B) 30
Question: 210 university students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
(A) 25
(B) 40
(C) 50
(D) 60
(E) 75
Rationale: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: (B) 40
Question: A and B can do a piece of work in 4 2/3 days and 5 days respectively. They work together for 1 days and then A leaves. In how many days after that B will complete the work alone.
(A) 3.92 days
(B) 1.92 days
(C) 2.12 days
(D) 2.02 days
(E) 2.92 days
Rationale: 3/14 * 1 + (1 + x)/5 = 1
x = 2.92 days
ANSWER:E
Answer: (E) 2.92 days
Question: A person covers a distance in 9 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
(A) 18 m/s
(B) 4 m/s
(C) 15 m/s
(D) 10 m/s
(E) 6 m/s
Rationale: Explanation:
T = 9 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
9 x (10/3) = 5x
x = 6 m/s
Answer: Option E
Answer: (E) 6 m/s
Question: Find k if 16 / k = 4.
(A) 6
(B) 7
(C) 8
(D) 4
(E) 3
Rationale: Since 16 /k = 4 and 16 / 4 = 4, then
k = 4 correct answer D
Answer: (D) 4
Question: Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 6 more than the average expenditure of all the nine. The total money spent by all of them was
(A) 26
(B) 40
(C) 33.75
(D) 27
(E) None of the above
Rationale: Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 6 = 9x
⇒ x = 3.75
∴ Total money spent = 9x = 9 × 3.75 = 33.75
Answer C
Answer: (C) 33.75
Question: 60 boys can complete a work in 24 days.how many men need to complete twice the work in 20 days
(A) 144
(B) 170
(C) 180
(D) 190
(E) 200
Rationale: one man can complete the work in 24*60=1440 days = one time work
to Complete the work twice it will be completed in
let M be the no. of worker assign for this therefore the eqn becomes
M*20=2*1440
M=144 workers
ANSWER:A
Answer: (A) 144
Question: 10,17,31,59,115, (...)
(A) 142
(B) 123
(C) 446
(D) 84
(E) 227
Rationale: 10
10Ã— 2 - 3 =17
17 Ã— 2 - 3= 31
31 Ã— 2 - 3 = 59
59Ã— 2 - 3 = 115
115Ã— 2 - 3 = 227
Answer is E
Answer: (E) 227
Question: Mixture of milk & water has been kept in two separate bowl. Ratio of milk to water in one of the bowls is 5 : 1 and that in the other bowl 7 : 2. In what ratio the mixtures of these 2 bowl should be added together so that the quantity of milk in the new mixture may become 80%?
(A) 2:3
(B) 3:5
(C) 4:5
(D) 4:7
(E) 5:9
Rationale: Lett. mixtures of the two containers be added together in the ratio of x
= = [ixoox l00%
Since the percentage quantity ofmilk in the new mixture is SO% — so% (45x + 42y) x 5 4 x 54(x y) 225x 210y 216.3E+216y
9x=6y
x:y=2:3
A
Answer: (A) 2:3
Question: Ram professes to sell his goods at the cost price but he made use of 970 grms instead of a kg, what is the gain percent?
(A) 11 1/7%
(B) 3.09%
(C) 11 1/9%
(D) 71 1/9%
(E) 11 1/2%
Rationale: 970 --- 30
100 --- ? => 3.09%
Answer:B
Answer: (B) 3.09%
Question: If x^2=2x+1, then x^3= ?
(A) 5x+2
(B) 3x-2
(C) 2x+1
(D) 4x-3
(E) 3x+4
Rationale: x^2 = 2x+1
x^3 = x*x^2 = x*(2x+1) = 2x^2 + x = 2(2x+1)+x = 5x+2
The answer is A.
Answer: (A) 5x+2
Question: The end of a blade on an airplane propeller is 5 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
(A) 200π
(B) 240π
(C) 300π
(D) 480π
(E) 150π
Rationale: Distance traveled in 1 revolution = 2πr= 2π5/5280
Revolutions in one second= 1320
Revolutions in 60 seconds (one minute)= 1320*60
Total distance traveled= total revolutions *distance traveled in one revolution
1320*60 *2π5/5280= 150π
E is the answer
Answer: (E) 150π
Question: Is 2 a prime number or a composite number?
(A) prime number
(B) composite number
(C) both prime composite number
(D) Not prime composite number
(E) Don't Know
Rationale: A Prime Number can be divided evenly only by 1 or itself
So 2 is prime number
Answer: (A) prime number
Question: Each of three different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
(A) 1/8
(B) 1/6
(C) 1/9
(D) 3/8
(E) 1/2
Rationale: I was just going over probability questions.
can some one explain me what's wrong in my approach here.
Probability of choosing one right key out of 3 is 1/3.
Probablity of choosing another right key is 1/3.
since the question is asking for 2 right keys , probability is multiplication of both = 1/3 * 1/3 = 1/9.
Ans C
Answer: (C) 1/9
Question: A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
(A) 2
(B) 4
(C) 6
(D) 5
(E) 3
Rationale: Speed downstream = (13 + 4) km/hr = 17 km/hr.
Time taken to travel 68 km downstream = 68/17
= 4 hrs
Ans - B
Answer: (B) 4
Question: A board 8ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
(A) 5ft. 7 inches
(B) 2ft. 11 inches
(C) 4ft. 7 inches
(D) 2ft. 7 inches
(E) 1ft. 7 inches
Rationale: Length of board=8ft. 9 inches=(8*12+9)inches=105 inches.
Therefore, Length of each part = (105/3) inches = 35 inches = 2ft. 11 inches
Answer is B.
Answer: (B) 2ft. 11 inches
Question: nd the area of trapezium whose parallel sides are 20 cm and 16 cm long, and the distance between them is 15 cm?
(A) 270cm2
(B) 275cm2
(C) 280cm2
(D) 285cm2
(E) 290cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 16) * (15)
= 270 cm2
Answer:A
Answer: (A) 270cm2
Question: The area of a side of a box is 120 sq cm. The area of the other side of the box is 72 sq cm. If the area of the upper surface of the box is 60 sq cm then find the volume of the box.
(A) 259200 cm3
(B) 86400 cm3
(C) 720 cm3
(D) Cannot be determined
(E) None of these
Rationale: Volume of the box = √120×72×60 = 720 cm3
Answer C
Answer: (C) 720 cm3