mathewhe/aqua_rat huggingface dataset:
Question: The greatest number by which the product of two consecutive multiples of 3 is always divisible is
(A) 54
(B) 76
(C) 18
(D) 162
(E) None of these
Rationale: Solution
Required number	= Product of first three multiplies of 3
= (3 Ã— 6)= 18.
Answer C
Answer: (C) 18
Question: Seven female friendsseven male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?
(A) 50803200
(B) 1680
(C) 1152
(D) 576
(E) 70
Rationale: now any of the alternate 8 places can be filled by 7 male or female in 7!
similarily,
other 7 alternate places can be filled in 7!
hence required probability= 2*7!*7!=5,08,03,200
hence A
Answer: (A) 50803200
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 14,7
(B) 64,4
(C) 18,4
(D) 14, 4
(E) 12,4
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x
= 14, y = 4.
Answer:D
Answer: (D) 14, 4
Question: What will be the cost of building to paint which area equal to 196 sq ft, if the price per foot of building is Rs. 15?
(A) 120
(B) 240
(C) 360
(D) 380
(E) 840
Rationale: Let the side of the square plot be a ft.
a2 = 196 => a = 14
Length of the fence = Perimeter of the plot = 4a = 56 ft.
Cost of building the fence = 56 * 15
= Rs.840.
Answer: E
Answer: (E) 840
Question: A batsman makes a score of 85 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
(A) 19
(B) 29
(C) 37
(D) 49
(E) 59
Rationale: let the average after 17th inning =x
Then average after 16th inning=(x-3)
Therefore 16(x-3)+85=17x
Therefore x=37
ANSWER:C
Answer: (C) 37
Question: The length of rectangle is thrice its breadth and its perimeter is 64 m, find the area of the rectangle?
(A) 432
(B) 376
(C) 299
(D) 276
(E) 288
Rationale: 2(3x + x) = 64
l = 36 b = 8
lb = 36 * 8
= 288
E
Answer: (E) 288
Question: The ratio of the arithmetic mean of two numbers to one of the numbers is 5:9. What is the ratio of the smaller number to the larger number?
(A) 1:5
(B) 1:6
(C) 1:7
(D) 1:8
(E) 1:9
Rationale: For two numbers, the arithmetic mean is the middle of the two numbers.
The ratio of the mean to the larger number is 5:9, thus the smaller number must have a ratio of 1.
The ratio of the smaller number to the larger number is 1:9.
The answer is E.
Answer: (E) 1:9
Question: When x is multiplied by 3, the result is 20 more than the result of subtracting x from 20. What is the value of x?
(A) 10
(B) -2
(C) 11
(D) 13
(E) 22
Rationale: The equation that can be formed is:
3x-20=20-x
or, 4x=40
or, x=10.
Answer : A
Answer: (A) 10
Question: $366 is divided amongst A,B and C so that A may get 1/2 as much as B and C together, B may get 2/3 as much as A and C together, then the share of A is
(A) $122
(B) $150
(C) $176
(D) $200
(E) $250
Rationale: A:(B+C) = 1:2
A's share = 366*1/3 = $122
Answer is A
Answer: (A) $122
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 3 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 3 minute mark.)
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 3 minutes is 180 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
180/24=7 plus remainder.
In the time period, Lamp A and Lamp B will flash together 7 times.
Lamp A and Lamp C will flash together every 30 seconds.
180/30=6.
In the time period, Lamp A and Lamp C will flash together 6 times.
Lamp B and Lamp C will flash together every 40 seconds.
180/40=4 plus remainder.
In the time period, Lamp B and Lamp C will flash together 4 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
180/120=1 plus remainder.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 7+6+4-3=14 times.
The answer is A.
Answer: (A) 14
Question: Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 90 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
(A) 46
(B) 42
(C) 56
(D) 32
(E) 40
Rationale: I'm going in on this one.
So let's say that we have the following
So we know that L1 = 90 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 90 = 110. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 60 = 40.
Thus E is the correct answer choice
Answer: (E) 40
Question: A set consist of 2p-1 element. What is the number of subsets of this set which contain at most p-1 elements?
(A) 2^(2p-2)
(B) 2^(2p) - 2
(C) 2^(2p) -1
(D) 2^(2p)
(E) 2^(2p-1)
Rationale: I used p=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
Avoid 2 since you will get 1 arrangement (p-1) and may be risky since 1 is a number with certain unique properties
Answer: (A) 2^(2p-2)
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
(A) 7:6
(B) 7:3
(C) 7:9
(D) 7:1
(E) 7:8
Rationale: Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
Answer: E
Answer: (E) 7:8
Question: Distance between A and B is 36 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 2 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 1 mph, in the second hour it was 1.25 mph, in the third hour it was 1.5 mph, and so on. When will they meet each other?
(A)  12 miles away from A
(B)  12 miles away from B
(C)  after 6 hours from start
(D)  after 9 hours from start
(E)  after 12 hours from start
Rationale: Since the question is asking when A and B will meet each other, the answer will be one involving time elapsed.
In such questions, look for the symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of A (assuming guy who starts from A is A) is 2 mph and distance is 36 miles. So this means that A would take a total of 36/2 = 18 hours to cover the distance from A to B. So, if B's speed were also 2, both A and B would travel for 9 hours to meet in the middle.
B has uniform speed per hour so its average will be the simple average of all speeds: 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5...
and 2 is actually right in the middle of the 9 speeds, implying both A and B have the same average speed.
Since 2 is actually right in the middle of the 9 speeds, this implies both A and B will have the same average speed.
So the correct answer is (D): A and B will meet after 9 hours (midway between A and B.)
Had it been determined that B's average speed was more than 2 then that would indicate A and B would meet closer to point A and will take less than 9 hours and so on...
The correct answer is (D).
Answer: (D)  after 9 hours from start
Question: At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
(A) 11 points
(B) 12 points
(C) 15 points
(D) 10 points
(E) 12 points
Rationale: "A can give 15 points to B in 60".
=> In a game of 60, A starts with 0 points where B starts with 15 points
"A can give 20 points to C in 60".
=> In a game of 60, A starts with 0 points where C starts with 20 points
ie, in a game of 60-15-45, B can give C 20-15=5 points
=> ie, in a game of 90, B can give C 5×2=10 points
Answer is D
Answer: (D) 10 points
Question: If 4x = 8^y, which of the following expresses x in terms of y?
(A) 2^(y-2)
(B) 2^(y-1)
(C) 2^(3y-2)
(D) 2^(2y-3)
(E) 2^y
Rationale: By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C
Answer: (C) 2^(3y-2)
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $58 of gas?
(A) 242
(B) 353
(C) 464
(D) 575
(E) 686
Rationale: 58/4 = 14.5 gallons
14.5*32 = 464 miles
The answer is C.
Answer: (C) 464
Question: Present ages of X and Y are in the ratio 6:8 respectively. Ten years hence this ratio will become 8:10 respectively. What is X's present age in years?
(A) 35
(B) 36
(C) 37
(D) 39
(E) 30
Rationale: Let the present ages of X and Y be 6x and 8x years respectively.
Then, (6x + 10)/(8x + 10) = 8/10
10(6x + 10) = 8(8x + 10) => 60x+100 = 64x+80 => 4x =20 => x =5
X's present age = 6x = 6*5 = 30
ANSWER: E
Answer: (E) 30
Question: The number of arrangements that can be made with the letters of the word MOTHER so that the vowels occupy the even places?
(A) 48
(B) 25
(C) 21
(D) 3
(E) 13
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 2 = 48.
Answer:A
Answer: (A) 48
Question: A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 10 %
(B) 9/2 %
(C) 8/4 %
(D) 6/12 %
(E) 45 5/11 %
Rationale: Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50.
Required percentage =(50/110*100)%=45 5/11 %
Answer: E
Answer: (E) 45 5/11 %
Question: Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.6%, what fraction of the products was checked by worker y?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 3/7
Rationale: x: 0.5% is 0.1%-points from 0.6%.
y: 0.8% is 0.2%-points from 0.6%.
Therefore the ratio of products checked by y:x is 1:2.
Thus, worker y checked 1/3 of the products.
The answer is C.
Answer: (C) 1/3
Question: There are 5 identical pens and 7 identical books. In how many different ways can a person select at least one object from this set?
(A) 11
(B) 12
(C) 39
(D) 47
(E) 56
Rationale: We can select from 0 to 5 pens and from 0 to 7 books.
Thus the total possible ways to select objects is 6*8 = 48
We must subtract 1 for the case with 0 pens and 0 books.
The answer is D.
Answer: (D) 47
Question: If m^(-1) = -1/5 then m^(-2) is equal to
(A) -9
(B) -3
(C) -1/9
(D) 1/25
(E) 9
Rationale: You made a mistake here.
You're right till
m^-2 = 1/m^2 and m^-1 = 1/m^1 = 1/m
given m^-1 = -(1/5) so, 1/m = -(1/5) solving this, m = -5
Now, m^-2 = 1/m^2 = 1/(-5)^2 = 1/25 ANS D
Answer: (D) 1/25
Question: The average of first 15 natural numbers is?
(A) 5.2
(B) 5.5
(C) 8
(D) 9
(E) 10
Rationale: Sum of 15 natural no. = 240/2 = 120
Average =120/15 = 8
Answer:C
Answer: (C) 8
Question: A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
(A) 81 km/hr
(B) 88 km/hr
(C) 62 km/hr
(D) 46 km/hr
(E) 56 km/hr
Rationale: Let x is the length of the train in meter and y is its speed in kmph
x/8.4 = (y - 4.5)(10/36) ---(1)
x/8.5 = (y - 5.4)(10/36) ---(2)
Dividing 1 by 2
8.5/8.4 = (y - 4.5)/ (y - 5.4)
=> 8.4y - 8.4 × 4.5 = 8.5y - 8.5 × 5.4
0.1y = 8.5 × 5.4 - 8.4 × 4.5
=> .1y = 45.9 - 37.8 = 8.1
=> y = 81 km/hr
ANSWER:A
Answer: (A) 81 km/hr
Question: A man has an investment of $3000 which yields a fixed 305 for every $500 invested. if the man takes out $12.6 for every $500 how long will it take for him to double his investment assuming no compounding of interest.
(A) 4
(B) 33.8
(C) 10
(D) 30
(E) 37.3
Rationale: Annual increase is (500 + 30.5 - 12.6)*6=3107.4
Hence every year there is an increase of 107.4
for his saving to double he needs additional $4000
therefore $4000/107.4=37.3
correct option is E)37.3
Answer: (E) 37.3
Question: Two representatives must be selected from each of two groups of students. One group consists of three men and one woman, and the other group consists of two women and two man. What is the probability that 2 men and 2 women will be selected ?
(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 5/12
Rationale: Group 1: 3 Men and 1 Woman
Group 2: 2 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*1*2*2 = 12 ways
Total Favorable cases = 3+12 = 15
Total Possible ways of selecting students 2 from each group = 4C2*4C2 = 6*6 = 36
Probability = 15/36 = 5/12
Answer : Option E
Answer: (E) 5/12
Question: A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied.
Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?
(A) 1/8
(B) 2/9
(C) 2/7
(D) 3/8
(E) 3/9
Rationale: Explanation :
Total names in the lottery,
=3×100+2×150+200
=800.
Number of Year-III's names,
=3×100
=300.
The required probability,
=300/800.
=3/8.
Answer : D
Answer: (D) 3/8
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
(A) 25/42
(B) 25/45
(C) 25/29
(D) 25/87
(E) 25/26
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer: A
Answer: (A) 25/42
Question: Four hundred students at College Q study a foreign language. Of these, 110 of those students study French, and 170 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from
(A) 10 to 40
(B) 40 to 100
(C) 60 to 100
(D) 60 to 110
(E) 60 to 200
Rationale: 110 students study French
290 students do not study French
170 students study Spanish
230 students do not study Spanish
90 students study neither French nor Spanish
290-230=60
290-90=200
E. 60 to 200
Answer: (E) 60 to 200
Question: A room is 12 meters long, 10 meters wide 8 meters in height. The longest possible rod which can be placed in the room is
(A) 16.95 meters
(B) 16.80 meters
(C) 16.75 meters
(D) 16.55 meters
(E) 17.55 meters
Rationale: Square root of 12^2+10^2+8^2...(Diognal) which is square root of 308 that lies 17<√308<18. Hence the answer should be E
Answer: (E) 17.55 meters
Question: If x is an integer, which of the following must be an even integer?
(A) x^2-x-1
(B) x^2-4x+6
(C) x^2-5x+5
(D) x^2+3x+8
(E) x^2+2x+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: x^2-x-1 = -1 { If x = 1 }
B: x^2-4x+6 = 3 { If x = 1 }
C: x^2-5x+5 = 1 { If x = 1 }
D: x^2+3x+8 = 12 { If x = 1 } & x^2+3x+8 = 18 { If x = 2 }
E: x^2+2x+10 = 13 { If x = 1 }
Thus the only possible answer is (D)
Answer: (D) x^2+3x+8
Question: If Rs. 595 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?
(A) s.420
(B) s.360
(C) s.389
(D) s.368
(E) s.323
Rationale: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 595 * 2/17 = Rs. 70
B's share = 595 * 3/17 = Rs. 105
C's share = 595 * 12/17 =Rs.420.
Answer:A
Answer: (A) s.420
Question: Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
(A) 17 kmph
(B) 13 kmph
(C) 12 kmph
(D) 18 kmph
(E) 97 kmph
Rationale: Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer: C
Answer: (C) 12 kmph
Question: Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,20,000 earned at the end of 3 years from the start of the business in 1999?
(A) Rs.40,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.75,000
(E) none
Rationale: Solution
Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's share	=Rs.(120000×2/6)
= Rs.40000.
Answer A
Answer: (A) Rs.40,000
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 14%, then the cost price of the article is:
(A) 500
(B) 540
(C) 555
(D) 664
(E) 5598
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/114 = Rs. 540
Answer: Option B
Answer: (B) 540
Question: If x+y=2 and x2y3 + y2x3=32, what is the value of xy?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: xy=4
As x+y=2
x2y3+y2x3=32
x2y2(y+x)=32
Substituting x+y
x2y2=16
xy=4
ANSWER:D
Answer: (D) 4
Question: A work can be finished in 17 days by twenty eight women. The same work can be finished in seven days by seventeen men. The ratio between the capacity of a man and a woman is
(A) 4:3
(B) 1:4
(C) 2:3
(D) 3:2
(E) 4:5
Rationale: Work done by 28 women in 1 day = 1/17
Work done by 1 woman in 1 day = 1/(17Ã—28)
Work done by 17 men in 1 day = 1/17
Work done by 1 man in 7 day = 1/(17Ã—7)
Ratio of the capacity of a man and woman =1/(17Ã—7) : 1/(17Ã—28) = 1/7 : 1/28
= 1/1 :1/4 = 1:4
Answer is B.
Answer: (B) 1:4
Question: A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ?
(A) 30 days
(B) 15 days
(C) 45 days
(D) 24 days
(E) None of these
Rationale: Let C completes the work in x days.
Work done by (A + B) in 1 day = 1⁄10
Work done by (B + C) in 1 day = 1⁄18
A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’work = 1
or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1
or 5⁄10 + 5⁄18 + 10⁄x = 1 or x = 45 days
Answer C
Answer: (C) 45 days
Question: Find compound interest on Rs. 5000 at 12% per annum for 1 year, compounded half-yearly.
(A) Rs. 600
(B) Rs. 618
(C) Rs. 525
(D) Rs. 620
(E) None
Rationale: Principal = Rs.5000, Rate=6% per half year Time = 1 year = 2 half-years Amount = Rs. {5000 x ( 1 + 6/100)2] = Rs. [ 5000 x 53/50 x 53/50 ] = Rs. 5618 C.I. = Rs. (5618 – 5000) = Rs. 618
Answer B
Answer: (B) Rs. 618
Question: What is 10-8+6-4+...+(-16)?
(A)  8
(B)  10
(C)  12
(D)  14
(E)  16
Rationale: The expression considers all even numbers between 10 and -16 with alternate addition and subtraction of the numbers.
The numbers to be used are: 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, and -16.
Now, the first term is positive and the next term is subtracted. So, the required expression becomes,
10 - 8 + 6 - 4 + 2 - 0 + (-2) - (-4) + (-6) - (-8) + (-10) - (-12) + (-14) - (-16)
= 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16
= 58 - 44
= 14
Hence the correct answer choice is D.
Answer: (D)  14
Question: Martha has the unique talent of being able to guess other people’s height and weight. For every six people that Martha meets, she consistently guesses the people’s correct height five times, and for every eight people that she meets, she consistently guesses the people’s correct weight six times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?
(A) 8/27
(B) 2/5
(C) 485/512
(D) 98/125
(E) 625/952
Rationale: Probability that she guesses the height correctly P(h)=5/6
Probability that she guesses the weight correctlyP(w)=6/8
Probability that she guesses both weight and height correctly(P(h)*P(w))=5/6 * 6/8= 30/48
Now the Q asks about the probability of this happening atleast once.
We calculate it by finding the probability of not being able to guess in any of the three occasions.
Probability of not being able to guess any no. of times =1-30/48=18/48=3/8
For all three occasions P(A)=3/8 * 3/8 * 3/8=27/512
Probability of the event happening atleast once=1- P(A)=1-27/512=485/512
Ans should be C
Answer: (C) 485/512
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 50 kmph
(B) 62 kmph
(C) 54 kmph
(D) 74 kmph
(E) 55 kmph
Rationale: B
54 kmph
S = 240/16 * 18/5 = 54 kmph
Answer: (B) 62 kmph
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:5
(B) 4:3
(C) 4:4
(D) 4:8
(E) 4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9
= 4:3
Answer: B
Answer: (B) 4:3
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
(A) 153
(B) 150
(C) 137
(D) 135
(E) 89
Rationale: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Only 135 satisfies these two conditions.
The answer is D.
Answer: (D) 135
Question: The third proportional to 1 and 2 is?
(A) 8
(B) 7
(C) 4
(D) 5
(E) 3
Rationale: (2*2)/1 = 4
Answer:C
Answer: (C) 4
Question: (A% of 6B + B% of A) is equal to ?
(A) A% of B
(B) B% of A
(C) 7% of AB
(D) AB% of 3
(E) None
Rationale: Answer
A% of 6B + B% of A =6AB/100 + AB/100
= 7AB/100 = 7% of AB
Correct Option: C
Answer: (C) 7% of AB
Question: If k is the sum of the digits of integer m, and m=10n, where n is an integer, which of the following must be true?
(A) k is not divisible by 9
(B) The sum of the digits of k is divisible by 3
(C) m is a multiple of 10k
(D) k is a multiple of 9
(E) k is a multiple of 6
Rationale: m= 10n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =10,20,30,40 or -10 ,-20 ,-30 ,-40 then k 1,2, 3,4 or -(1+0) , -(2+0) , -(3+0) ,-(4+0) .
ans(C)
Answer: (C) m is a multiple of 10k
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?
(A) 29 ½ days
(B) 22 ½ days
(C) 92 ½ days
(D) 28 ½ days
(E) 92 ½ days
Rationale: 1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 ¼ *2
=22 ½ days
Answer:B
Answer: (B) 22 ½ days
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
(A) 6
(B) 7
(C) 5
(D) 4
(E) 3
Rationale: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
Answer:C
Answer: (C) 5