mathewhe/aqua_rat huggingface dataset:
Question: In a Government institute 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash?
(A) A)1000
(B) B)3000
(C) C)3500
(D) D)2500
(E) E)2250
Rationale: For 20 staffs: 300*100*20 = 60000
for driver and cleaning staff: 300*100*2 =6000
From petty Cash : 1000
Answer is A
Answer: (A) A)1000
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $14,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?
(A) 62,000
(B) 85,500
(C) 95,500
(D) 120,500
(E) 100,000
Rationale: Answer equals D in 48 years. I thought by 50th year it would reach 120,500. Options should have been separated more widely for clarity.
Answer: (D) 120,500
Question: Can you find the largest possible number containing any 9 of the 10 digits. considering 0 also as a number that is divisible by 11, without a remainder?
(A) 677652413
(B) 827652413
(C) 997652413
(D) 987652413
(E) 929052413
Rationale: D
987652413
With some trial one will find 987652413 as the highest possible number containg 9 of the 10 digits that is divisible by 11, without a remainder
Answer: (D) 987652413
Question: A volunteer organization is recruiting new members. In the fall they manage to increase their number by 8%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
(A) 16.16%
(B) 15.15%
(C) 14.14%
(D) 13.33%
(E) 12.52%
Rationale: (100%+8%)*(100%-19%) = 1.08*.81 = 0.8748
1-0.8748 = 12.52% lost = -12.52%
The Answer is E
The organization has lost 12.52% of its total volunteers from fall to spring.
Answer: (E) 12.52%
Question: There are 840 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 75
(B) 100
(C) 125
(D) 140
(E) 225
Rationale: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 840.
Hence, we have m+f= 840
Now, we have that half the female participants and one-quarter of the male participants are Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
d = 840/3 = 280
Solving the three equations yields the solution
f = 280,m= 560, and d= 280.
The number of female democratic participants equals half the female participants equals
280/2 = 140.
ANSWER:D
Answer: (D) 140
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 9 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 35 7/8
(B) 36
(C) 34 2/7
(D) 34 5/7
(E) 38 4/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 8 tons of cement, then we'll get 9/7*30 = 38 4/7 tons of mixture.
Answer: E.
Answer: (E) 38 4/7
Question: If a^2bc = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1
(A) I
(B) none
(C) II
(D) III
(E) I&II
Rationale: B
Answer: (B) none
Question: Average age of students of an adult school is 52 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
(A) 1200
(B) 150
(C) 360
(D) 240
(E) None of these
Rationale: Explanation :
Let the original no. of students be x.
According to situation, 52x + 120*32 = (x + 120)36 ⇒ x = 30
So, Required no. of students after joining the new students
= x + 120 = 150
Answer : B
Answer: (B) 150
Question: The arithmetic mean of the set S = {4, K, 3, 9, M, 4} is 5. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5
Rationale: The sum of the numbers is 6*5 = 30
K+M = 30 - 9 - 4 - 4 - 3 = 10
Since K ≠ M, K and M do not equal 5.
Thus one of the two numbers is 4 or less and one is 6 or more.
Then middle two numbers in the set are 4 and 4.
The median is 4.
The answer is C.
Answer: (C) 4
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
(A) Rs. 80
(B) Rs. 96
(C) Rs. 106
(D) Rs. 108
(E) Rs. 128
Rationale: Michel earns Rs 135 by investing Rs1620
To earn Rs 8 how much he have to invest?
=(8*1620)/135=Rs 96
ANSWER:B
Answer: (B) Rs. 96
Question: A man buys a cycle for Rs. 1200 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) s. 1020
(B) s. 1160
(C) s. 1190
(D) s. 1202
(E) s. 1256
Rationale: S.P. = 85% of Rs. 1200 = Rs.85/100x 1200	= Rs. 1020
ANSWER :A
Answer: (A) s. 1020
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
(A) 120 sq m
(B) 150 sq m
(C) 110 sq m
(D) 300 sq m
(E) 330 sq m
Rationale: 1/2 * 20(9 + 6) = 150 cm2
ANSWER:B
Answer: (B) 150 sq m
Question: The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 12, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers?
(A) 16
(B) 18
(C) 19
(D) 20
(E) 22
Rationale: We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r.
The average of the positive integers is 12 which means that in effect, all numbers are equal to 12. If the largest number is 20, it is 8 more than 12. We need r to be maximum so k and m should be as small as possible to get the average of 12. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 11 less than 12 and 2 is 10 less than 12 which means k and m combined are 21 less than the average. 20 is already 8 more than 12 and hence we only have 21 - 8 =13 extra to distribute between r and s. Since s must be greater than r, r can be 12+6 = 18 and s can be 12+7 = 19.
So r is 18.
Answer (D)
Answer: (D) 20
Question: A particular library has 150 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 122 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 40
(B) 60
(C) 80
(D) 100
(E) 120
Rationale: The total number of books is 150.
Let x be the number of books which were loaned out.
65% of books that were loaned out are returned.
35% of books that were loaned out are NOT returned.
Now, there are 122 books, thus the number of un-returned books is 150-122 = 28 books.
0.35x = 28
x = 80
The answer is C.
Answer: (C) 80
Question: Of the 65 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: Neither Car nor Garage
= Total - Garage - (Swim - Common)
= 65 - 50 - (40-35) = 65-55 = 10
Answer A
Answer: (A) 10
Question: Solve: 12.05*5.4+0.6
(A) 108.45
(B) 110.45
(C) 106.45
(D) 109.45
(E) None of them
Rationale: = 12.05*(5.4/0.6) = (12.05*9) = 108.45
Answer is A.
Answer: (A) 108.45
Question: If a cistern has 3 pipes of 1 cm , 4/3 cm and 2 cm thickness ...where the pipe with 2 cm thickness can fill the cistern in 2 hrs and 2 min..then in how much time they can fill the tank?
(A) 53.7min
(B) 54.7min
(C) 55.7min
(D) 56.7min
(E) 57.7min
Rationale: 2cm can fill in 122min
thickness inversly propotional to time
total thickness of the pipe=1+4/3+2=4.3
we know that 2cm can fill in 122min
for 4.3cm time =56.7min
ANSWER:D
Answer: (D) 56.7min
Question: A certain purse contains 30 coins, Each coin is either a nickel or a quarter. If the total value of all coins in the purse is 4.70$, how many nickels does the purse contain?
(A) 12
(B) 14
(C) 16
(D) 20
(E) 22
Rationale: I picked a starting point and then kept ballparking until i hit the right answer
$4.70 - 6 quarters = $3.20. this would be 6 quarters and 64 nickels, WAY more than 30 so we need a lot more quarters
$4.70 - 16 quarters = $0.70 this would be 16 quarters and 14 nickels, 30 coins!
14 nickels! ANS=B
Answer: (B) 14
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 80 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 80% of 50% i.e 40%. so he completed 50 +40 =90 % of total trip.
E
Answer: (E) 90
Question: The length of a room is 10 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
(A) 25650
(B) 25750
(C) 26550
(D) 42750
(E) 55725
Rationale: Area = 10 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 10 × 4.75 × 900
= 10 × 4275 = Rs. 42750
Answer is D.
Answer: (D) 42750
Question: Every ten years, the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri :
Chota Hazri has 4,522 fewer males than MotaHazri.
Mota Hazri has 4,020 more females than males.
Chota klazri has twice as many females as males.
Chota Hazri has 2,910 fewer females than Mota Hazri.
What is the total number of males in Chota Hazri?
(A) 11,264
(B) 14,174
(C) 5,632
(D) 10,154
(E) None
Rationale: Explanation :
Let ‘x’ be the number of males in Mota Hazri.
=> x + 4020 – 2(x – 4522) = 2910 .
=> x = 10154
∴ Number of males in Chota Hazri = 10154 – 4522 = 5632.
Answer : C
Answer: (C) 5,632
Question: A and B start a business with Rs.7000 and Rs.9000 respectively. Hoe should they share their profits at the end of one year?
(A) 7:9
(B) 9:7
(C) 3:9
(D) 3:1
(E) 3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
7000 : 9000 => 7:9,Answer: A
Answer: (A) 7:9
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length?
(A) 16.5
(B) 16.0
(C) 15
(D) 16.8
(E) 16.1
Rationale: D = 110 + 140 = 250 m
S = 60 * 5/18 = 50/3
T = 250 * 3/50 = 15 sec
Answer: C
Answer: (C) 15
Question: In a series of football matches, the probability that Team P wins a match against Team Q is 1/5 and the probability that the match ends in a draw is 1/2. If the two teams play five matches, what is the probability that all five matches end in a draw?
(A) 1/64
(B) 1/32
(C) 1/16
(D) 1/8
(E) 1/4
Rationale: P(5 draws)=(1/2)^5=1/32
The answer is B.
Answer: (B) 1/32
Question: What is the 2532nd position of the number in the sequence
1,2,2,3,3,3,4,4,4,4,1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,…..
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 10,20,30,40...
10(1+2+3----+22)=2530
That mean upto 22 th pos total numbers are 2530
2532 th numner must be 1..
ANSWER:A
Answer: (A) 1
Question: If 4^(2x + 2) = 16^(3x − 1), what is the value of x ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 2^(4x+4) = 2^(12x-4)
4x+4=12x−4
x=1
Answer B
Answer: (B) 1
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/467
(C) 1/427
(D) 1/419
(E) 1/417
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= ³C₃/¹⁵C₃
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: (A) 1/455
Question: If q is a positive integer, then 3^q + 3^(q +1) =
(A) 4^a
(B) 3^a − 1
(C) 3^(2a) + 1
(D) 3^a*(a − 1)
(E) 4(3^q)
Rationale: 3^q + 3^(q +1)
= 3^q + (3^q * 3^1)
= 3^q (1 + 3)
= 3^q(4)
Ans. E) 4(3^q)
Answer: (E) 4(3^q)
Question: In a building there are 5 rooms.Each having a equal area .The length of the room is 4m and breadht is 5 m.The height of the rooms are 2m. If 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room ?
(A) 320
(B) 340
(C) 300
(D) 330
(E) 360
Rationale: Explanation :
Area of the floor = 4m x 5m = 20 m2
17 bricks are needed to make 1 m2 area.
So to make 20 m2 no of bricks needed = 17 x 20 = 340
Answer : B
Answer: (B) 340
Question: Working alone, machine X can manufacture 1,000 nails in 10 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
(A) 3 9/17
(B) 5 1/3
(C) 10
(D) 11 1/5
(E) 18 4/7
Rationale: rate of machine x = 1000/10
(1000/10 + y)5=1000
y=100
100 * t = 1000
t=10
C.
Answer: (C) 10
Question: Two good train each 250 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
(A) 12 sec
(B) 24 sec
(C) 48 sec
(D) 60 sec
(E) None
Rationale: Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (250 + 250) m = 1000 m.
Required time = (500 x 6 / 125) sec = 24 sec.
Answer B
Answer: (B) 24 sec
Question: A train 360 m long is running at a speed of 36 km/hr. In what time will it pass a bridge 140 m long?
(A) 50 sec
(B) 29 sec
(C) 26 sec
(D) 27 sec
(E) 34 sec
Rationale: Speed = 36 * 5/18 = 10 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/10
= 50 sec
Answer: A
Answer: (A) 50 sec
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 648
(B) 849
(C) 600
(D) 849
(E) 940
Rationale: Explanation:
D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km
Answer: Option C
Answer: (C) 600
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 45% took a marketing class last semester, and 50% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
(A) 60%
(B) 50%
(C) 20%
(D) 15%
(E) 10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 45 - {both} + 50
{both} = 20%.
The answer is C.
Answer: (C) 20%
Question: 10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range U of the 10 numbers?
(A) 25
(B) 27
(C) 30
(D) 52
(E) 55
Rationale: Positions: 1 2 3 4 5 6 7 8 9 10
Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b
y - x = 25
Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.
b - a = 30 --> b = 30 + a
In order to increase the range, we have to maximize the value of 'b'.
'b' can be maximized by taking the max value of 'a'.
From the assumed values, maximum value of 'a' can be 22.
Therefore, b = 30 + 22 = 52
Range U= 52 - 0 = 52
Answer: D
Answer: (D) 52
Question: Sequence F consists of 16 consecutive integers. If -6 is the least integer in sequence F, what is the range of the positive integers in sequence F?
(A)  16
(B)  15
(C)  9
(D)  8
(E)  7
Rationale: Since set F consists of 16 consecutive integers and -6 is the least integer then set F is consecutive integers from -6 to 9, inclusive: 9-(-6)+1=16.
The range of positive integers in sequence F is 9-1=8.
Answer: D.
Answer: (D)  8
Question: A tourist purchased a total of $1,500 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was three more or three less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,230
(B) $1,310
(C) $1,290
(D) $1,270
(E) $1,150
Rationale: Let the number of $10 checks cashed beT
Let the number of $50 checks cashed beF
7 checks cashed;
T+F=7
Now; T can be F+3 OR T can be F-3
Let's check both conditions;
T=F+3
T+F=7
F+3+F=7
2F=4
F=2
T=5
Value cashed = 2*50+5*10=$150
Let's check the other condition as well;
T=F-3
T+F=7
F-3+F=7
2F=10
F=5
T=2
Value cashed = 5*50+2*10=$270
The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.
Value cashed = $270
Value lost = 1500-270 = $1230
Ans:A
Answer: (A) $1,230
Question: A man buys 100 lts of liquid which contains 25% of the liquid and the rest is water. He then mixes it with 90 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
(A) 81
(B) 75
(C) 72.63
(D) 73
(E) 76
Rationale: 25% in 100 lts is 25. So water = 100-25 = 75 lts. 30% of 90 lts = 27. So water in 2nd mixture = 90-27 = 63 lts. Now total quantity = 100 + 90 = 190 lts. Total water in it will be 75 + 63 = 138 lts. % of water = (100*138)/190 = 72.63
ANSWER:C
Answer: (C) 72.63
Question: What will be the next sequence in this series?
10,24,130,336,1342,_____?
(A) 2174
(B) 2184
(C) 2284
(D) 2884
(E) 2984
Rationale: 2^3 + 2 = 10
3^3 - 3 = 24
5^3 + 5 = 130
7^3 - 7 = 336
11^3 + 11 = 1342
2,3,5,7,11,13,... prime no.s
next is ( 13^3 - 13 ) = 2184
ANSWER:B
Answer: (B) 2184
Question: A grocer has a sale of Rs. 6345, Rs. 6927, Rs.6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 3000
(B) Rs. 4991
(C) Rs. 5991
(D) Rs. 6001
(E) NOne
Rationale: Sol.
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562)
= Rs. 34009.
∴ Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer B
Answer: (B) Rs. 4991
Question: The youngest of 4 children has siblings who are 3, 6, and 7 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 30, what is the age of the youngest sibling?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: x + (x+3) + (x+6) + (x+7) = 120
4x + 16 = 120
4x = 104
x = 26
The answer is E.
Answer: (E) 26
Question: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, white and yellow. This pattern continues (red, green, blue, white and yellow) until it ends with a white shirt. If there are more than 5 people in line, which of the following cannot be the number of people in the line?
(A) 29
(B) 39
(C) 54
(D) 64
(E) 75
Rationale: The correct answer should not take the form: 5x + 4. Hence, it is E
Answer: (E) 75
Question: What is the CP of Rs 100 stock at 9 discount, with 1/5% brokerage?
(A) 96.9
(B) 96.3
(C) 91.2
(D) 96.7
(E) 96.21
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-9+1/5
91.2
Thus the CP is Rs 91.2.
ANSWER: C
Answer: (C) 91.2
Question: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
(A) 20 kmph
(B) 15 kmph
(C) 17 kmph
(D) 16 kmph
(E) 19 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km
He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x
=20 kmph.
Answer: A
Answer: (A) 20 kmph
Question: If s, t, and p are consecutive integers such that s > t > p and the sum of s, t, and p is a multiple of 10, which of the following could be the value of s?
(A) 0
(B) 1
(C) 9
(D) 10
(E) 12
Rationale: We're given a very specific set of restrictions in this prompt:
1) S, T and P are CONSECUTIVE INTEGERS
2) S > T > P
3) S+T+P = a multiple of 10
We're asked which of the 5 answer COULD be the value of S given these restrictions. Rather than staring at the screen or doing layered math, we canbrute forcethe answers until we find one that fits these restrictions..
Answer A: S = 0
In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.
Answer B: S = 1
In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.
Final Answer:
B
Answer: (B) 1
Question: Divide Rs.32000 in the ratio 1:9?
(A) 12000, 20000
(B) 12000, 200098
(C) 12000, 20007
(D) 3200, 28800
(E) 12000, 20001
Rationale: 1/10 * 32000 = 3200
9/10 * 32000 = 28800
Answer: D
Answer: (D) 3200, 28800
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a even. You pick a card from a full playing-card deck, and success would be picking a ten with red color card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 9/104
(B) 51/104
(C) 25/52
(D) 1/52
(E) 51/52
Rationale: Event(1): Probability of getting head in a flip of coin = 1/2
Event(2): Probability of getting even in a roll of dice = 3/6 = 1/2
Event(3): Probability of getting ten with red color in a pack of card = 2/52 = 1/26
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*1/2*25/26 +1/2*1/2*25/26 +1/2*1/2*1/26
=25/104 + 25/104 +1/104
=51/104
Answer :B
Answer: (B) 51/104
Question: When tossing two coins once, what is the probability of heads on both the coins?
(A) 1/4
(B) 1/2
(C) 3/4
(D) None of these
(E) 2/5
Rationale: Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 × 2 = 4
(∵ Here, S = {HH, HT, TH, TT})
E = event of getting heads on both the coins = {HH}
Hence, n(E) = 1
P(E) = n(E)n(S)=1/4
Answer is A
Answer: (A) 1/4
Question: One night 20 percent of the female officers on a police force were on duty. If 100 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
(A) 90
(B) 180
(C) 250
(D) 500
(E) 1,000
Rationale: Let total number of female officers in the police force = F
Total number of officers on duty on that night = 100
Number of female officers on duty on that night = 100/2 = 50
(20/100)*F =50
=>F = 250
Answer C
Answer: (C) 250
Question: What is the greater of the two numbers whose product is 2496, given that the sum of the two numbers exceeds their difference by 64?
(A) A)96
(B) B)108
(C) C)110
(D) D)78
(E) of these
Rationale: Let the greater and the smaller number be g and s respectively.
gs = 2496
g + s exceeds g - s by 64 i.e., g + s - (g - s) = 64
i.e., 2s = 64 => s = 32.
g = 2496/s = 78.
ANSWER:D
Answer: (D) D)78
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Tuesday
(B) Monday
(C) Sunday
(D) Wednesday
(E) Friday
Rationale: The year 2004 is a leap year. It has 2 odd days.
The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday.
Answer: Option C
Answer: (C) Sunday
Question: The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is prime, then f(p) =
(A) P-1
(B) P-2
(C) (P+1)/2
(D) (P-1)/2
(E) 2
Rationale: This question is wordy and confused me at first. If P is prime it's only factors are P and 1. So no number below it will have a common factor with it except 1. Therefore answer should just be P-1.
ANS = A
Answer: (A) P-1