mathewhe/aqua_rat huggingface dataset:
Question: What is the 10th digit of (5!*4!*4! - 5!*4!*3!)/2880?
(A) 4
(B) 1
(C) 6
(D) 7
(E) 8
Rationale: (5!*4!*4! - 5!*4!*3!)/2880?
=5!*4!(4! -3!)/4!*5!
=4!-3!
=18
Sum of digits =1
Answer B
Answer: (B) 1
Question: How many trailing zeroes would be found in 4617!, upon expansion?
(A) 1150
(B) 1151
(C) 1152
(D) 1153
(E) 1154
Rationale: for no of trailing zeros we have to find the no of 5 in 4617!,because 4617!=1*2*3*4*5*.........4616*4617.
no of 5 in 4617!= (4617/5^1)+(4617/5^2)+(4617/5^3)+(4617/5^4)+(4617/5^5)+... up to 5^n 4617.
now no of 5 =4617/5 + 4617/25 + 4617/125 + 4617/625 +4617/3125
=923 + 184 + 36 + 7 + 1 ( only take the integer value )
=1151
so the no of zeros at the end of 4617! is 1151.
ANSWER:B
Answer: (B) 1151
Question: A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 2 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
(A) 1/7
(B) 1/12
(C) 1/14
(D) 1/18
(E) 1/21
Rationale: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 2 bottles of apple juice is 6C2*4C4 = 15*1 = 15
P(selling 2 bottles of apple juice) = 15/210 = 5/70 = 1/14
The answer is C.
Answer: (C) 1/14
Question: fill in ht blank:(a) the point with coordinates (0,0) is called ____ of a rectangular ____ system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___
(A) (a) the point with coordinates (0,0) is called origin of a rectangular xyz system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y
(B) (a) the point with coordinates (0,0) is called end of a rectangular line system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y
(C) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let y equal 0 and solve for z ; to find x- intercept , we let x equal 0 and solve for y
(D) (a) the point with coordinates (0,0) is called end of a rectangular end system, (b) to find the y-intercept of a line, we let z equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
(E) none of the above
Rationale: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer (E)
Answer: (E) none of the above
Question: At what time between 2 and 3 o'clock will the hands of a clock be together?
(A) 10x10/11
(B) 10x11/10
(C) 11x10/11
(D) 12x10/11
(E) None
Rationale: At 2 o'clock, the hour is at 2 and the minute hand is at 12,i.e. they are 10 min. Spaces apart. To be together, the minute hand must gain 10 minutes over the hour hand. Now,55 minutes will be gained in 60 min. 10 minutes spaces will be gained in (60/55 x10) min. = 10x10/11 min. The hands will coincide at 10x10/11 min.past 2.
Answer A
Answer: (A) 10x10/11
Question: Goldenrod and No Hope are in a horse race with 6 contestants. How many different W arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
(A)  720
(B)  360
(C)  120
(D)  24
(E)  21
Rationale: no hope finishing before goldenrod= 1/2 of the times
therefore the different arrangements W are 1/2* 6! = 360 = B
Answer: (B)  360
Question: Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?
(A) 33
(B) 40
(C) 99
(D) 277
(E) 28
Rationale: We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2 = 40.
Answer:B
Answer: (B) 40
Question: In a stack of boards at a lumber yard, the 25th board counting from the top of the stack is immediately below the 15th board counting from the bottom of the stack. how many boards are in the stack?
(A) 38
(B) 36
(C) 35
(D) 34
(E) 32
Rationale: 1 2 3 ... 14 15 16 ...................
..............25 24 ................. 1
So the number of boards = 25+13 =38
Option: A
Answer: (A) 38
Question: The wages earned by Robin is 20% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
(A) 18.75%
(B) 33%
(C) 30%
(D) 50%
(E) 100%
Rationale: Let wage of Erica = 10
Wage of Robin = 1.2*10 = 12
Wage of Charles = 1.6 *10 = 16
Percentage by which wage earned by Charles is more than that earned by Robin = (16-12)/12 * 100%
= 4/12 * 100%
=33%
Answer B
Answer: (B) 33%
Question: Johnny travels a total of one hour to and from school. On the way there he jogs at 6 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?
(A) 2 miles
(B) 4 miles
(C) 4.8 miles
(D) 9.2 miles
(E) 10 miles
Rationale: Answer: D) 9.2 miles.
Average speed for round trip = 2*a*b/(a+b), where a,b are speeds
so, average speed was = 2*6*20/(6+20) = 9.2m/hr
the distance between schoolhome should be half of that. ie. 9.2 miles
Answer D
Answer: (D) 9.2 miles
Question: An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
(A) 16
(B) 36
(C) 49
(D) 144
(E) 196
Rationale: 49 = 7^2 so it can not be the square of an even number multiplied by an odd number.
The answer is C.
Answer: (C) 49
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
(A) 19
(B) 88
(C) 77
(D) 14
(E) 17
Rationale: Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs.Answer:D
Answer: (D) 14
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
(A) 277
(B) 268
(C) 287
(D) 480
(E) 281
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer:D
Answer: (D) 480
Question: A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 4 specified cars. In how many ways cars can be arranged?
(A) 1210
(B) 650
(C) 576
(D) 1640
(E) 1440
Rationale: we arranged 2 specified cars in 4 slots = 4!
remaining 4 cars in 4 slots = 4!
number of ways = 4!*4! = 576
correct option is C
Answer: (C) 576
Question: A train 150 m long crosses a platform 100 m long in 10 sec; find the speed of the train?
(A) 100
(B) 70
(C) 95
(D) 90
(E) 85
Rationale: D = 150 + 100 = 250
T = 10
S = 250/10 * 18/5 = 90 kmph.
Answer: D
Answer: (D) 90
Question: Tom drives from town T to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between T and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
(A) 12
(B) 20
(C) 24
(D) 30
(E) 36
Rationale: Let's assume that it takes 4 hours to go from point T to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
Answer: (B) 20
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 337
(B) 267
(C) 176
(D) 100
(E) 981
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100
Question: In a hostel there were 100 students. To accommodate 30 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) A)Rs.5800
(B) B)Rs.5480
(C) C)Rs.5400
(D) D)Rs.5900
(E) E)Rs.3900
Rationale: 100x + 400
= 130(x – 5)
x = 35
100 *35 + 400
= 3900
Answer:E
Answer: (E) E)Rs.3900
Question: If two men starting from same point, walking in the opposite directions with 9km/hr and 11km/hr as average speeds respectively. Then the distance between them after 8 hours is?
(A) 106
(B) 160
(C) 610
(D) 155
(E) 165
Rationale: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (9Ã— 8) + (11Ã— 8)
= 72+ 88
= 160 Km
Answer:B
Answer: (B) 160
Question: The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is?
(A) 22
(B) 27
(C) 18
(D) 19
(E) 11
Rationale: Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :
Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice
(20-x)/(x-15) = 2/3 60 - 3x = 2x - 30
5x = 90 x = 18.
Answer: C
Answer: (C) 18
Question: 5,6,8,11,?,20,26,33
(A) 10
(B) 13
(C) 15
(D) 8
(E) 19
Rationale: The Pattern is + 1, + 2, +3, ...
11+4=15
Answer :C
Answer: (C) 15
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs.6850
(B) Rs.7268
(C) Rs.6871
(D) Rs.6150
(E) Rs.6381
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs. 6150.
Answer:D
Answer: (D) Rs.6150
Question: 20 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
(A) 10
(B) 6
(C) 4
(D) 7
(E) 5
Rationale: Required number of machines = 20*10/40 = 5
Answer is E
Answer: (E) 5
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 31
(B) 35
(C) 32
(D) 38
(E) 40
Rationale: A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.
ANSWER A
Answer: (A) 31
Question: If |x|/6 < 1, which of the following must be true?
(A) x>6
(B) x<6
(C) x=6
(D) x=12
(E) x=-12
Rationale: if x <6, then If |x|/6 < 1
Like x=2
Then |2|/6 < 1
1/3<1
ANSWER B x<6
Answer: (B) x<6
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 140?
(A) 3
(B) 6
(C) 28
(D) 42
(E) 70
Rationale: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)
140 = 4*5*7
The GCF could be 4 or 28
The answer is C.
Answer: (C) 28
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
(A) 11 min
(B) 56 min
(C) 13 min
(D) 20 min
(E) 19 min
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio
= 4:51 -------- 5 4 --------- ? è 20
Answer:D
Answer: (D) 20 min
Question: A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But
whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11
mornings and 12 afternoons. How many days did they stay there totally?
(A) 16
(B) 18
(C) 20
(D) 13
(E) 14
Rationale: Explanation :
Clearly 11 mornings and 12 afternoons = 23 half days
=> Since 13 days raining means 13 half days.
=> So 23-13 =10 halfdays ( not effecetd by rain )
=> So 10 halfdays =5 fulldays
Hence ,
Total no. of days = 13+5 =18 days
Answer : B
Answer: (B) 18
Question: Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
(A) 1.5
(B) 1.7
(C) 2.3
(D) 2.5
(E) 3.0
Rationale: Ratio of A to B in the final mixture = 50-30 : 30-15 = 4:3
Gallons of A used = 4/7*4 = 2.28
ANSWER:C
Answer: (C) 2.3
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
(A) 32 6/7%
(B) 22 6/7%
(C) 72 6/7%
(D) 42 6/7%
(E) 12 6/7%
Rationale: Explanation:
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: (D) 42 6/7%
Question: If the remainder is 8 when positive integer n is divided by 12, what is the remainder when n is divided by 6?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Assume x is quotient here,
n=12x+8 ----------(1)
and n=6x+ ?
We can also write equation (1) as:
n=(12x+6)+2.
ie 6(2x+1)+2 ie the first term is perfectly divisible by 6.
So,the remainder left is 2.
So,answer (C) is right choice.
Answer: (C) 2
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 175 m
(B) 180 m
(C) 185 m
(D) 170 m
(E) 190 m
Rationale: Explanation:
Length of the train be â€˜Xâ€™
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
ANSWER IS B
Answer: (B) 180 m
Question: A and B start a business with Rs.5000 and Rs.7000 respectively. How should they share their profits at the end of one year?
(A) 3:5
(B) 3:4
(C) 5:7
(D) 3:2
(E) 3:9
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
5000 : 7000 => 5:7
Answer:C
Answer: (C) 5:7
Question: In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots?
(A) -12
(B) -6
(C) 12
(D) 6
(E) 24
Rationale: Explanation:
The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12.
we get, sum of the roots = 1 / a = 1
a = 1
Product of the roots = -12 / 1 =-12
ANSWER: A
Answer: (A) -12
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 5. What are the coordinates of P?
(A) (5/2, 5/2)
(B) (7/2, 7/2)
(C) (9/2, 9/2)
(D) (11/2, 11/2)
(E) (15/2, 15/2)
Rationale: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
The x, y coordinates are 5/6 of the distance from 3 to 6.
x = 3 + (6-3)*(5/6) = 3 + 5/2 = 11/2 = y
The answer is D.
Answer: (D) (11/2, 11/2)
Question: Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company M last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 5/22
(B) 4/22
(C) 3/22
(D) 9/22
(E) 7/22
Rationale: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22
E
Answer: (E) 7/22
Question: A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 1243 toys
(B) 1375 toys
(C) 1543 toys
(D) 1212 toys
(E) 1598 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
5500 * 4 = 1375 toys
correct answer B
Answer: (B) 1375 toys
Question: A 6 litre sol is 40% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
(A) A.0.6
(B) B.1.2
(C) C.2.1
(D) D.3
(E) E.5.4
Rationale: 40% of 6 = 2.4
50% of 6 = 3
shortage is 0.6
so we need to have 0.6/50% to get 50% alcohol content.
= 1.2 B
Answer: (B) B.1.2
Question: The average age of 44 students in a group is 12 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
(A) cannot be determined
(B) None of these
(C) 55
(D) 56
(E) 57
Rationale: Age of the teacher = (45 × 13 – 44 × 12) years
= 57 years.
Answer E
Answer: (E) 57
Question: The fourth proportional to 5, 8, 15 is:
(A) 24
(B) 20
(C) 23
(D) 16
(E) None
Rationale: Answer: Option A
Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
5x = (8 x 15)
x =	(8 x 15) /5 = 24
Answer: (A) 24
Question: The greatest common factor of positive integers m and n is 15. What is the greatest common factor of (2m^2, 2n^2)?
(A) 15
(B) 30
(C) 150
(D) 450
(E) 900
Rationale: m = 15j and n = 15k, where the greatest common factor of j and k is 1.
2m^2 = 2*15*15*j^2 and 2n^2 = 2*15*15*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*15*15 = 450
The answer is D.
Answer: (D) 450
Question: What number has a 5:1 ratio to the number 10?
(A) 11
(B) 50
(C) 17
(D) 12
(E) 18
Rationale: 5:1 = x: 10
x = 50
Answer: B
Answer: (B) 50
Question: In a dairy farm, 34 cows eat 34 bags of husk in 34 days. In how many days one cow will eat one bag of husk ?
(A) 34 days
(B) 40 days
(C) 46 days
(D) 50 days
(E) None of these
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 34
Bags 34 1]::34:x
=>x∗34∗1=34∗1∗34
=>x=34
Option A
Answer: (A) 34 days
Question: It costs $2 for the first 1/5 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 2 hours and 15 minutes, how much will it cost him?
(A) $25.
(B) $26.
(C) $29.
(D) $30.
(E) $31.
Rationale: 2 hrs 15 min = 135 min
First 12 min ------> $2
Time left is 135 min...
Now, 60 min costs $ 12
1 min costs $ 12/60
135 min costs $ 12/60*135 => $ 27
So, Total cost will be $27 + $2 => $ 29
Hence answer will be C
Answer: (C) $29.
Question: x, y, and z are all unique numbers. If x is chosen randomly from the set {10, 11} and y and z are chosen randomly from the set {20, 21, 22, 23}, what is the probability that x and y are prime and z is not?
(A) 1/5
(B) 3/20
(C) 1/8
(D) 3/10
(E) 1/10
Rationale: P(x is prime) = 1/2
P(y is prime) = 1/4
If y is prime, then z is not prime since y and z are unique.
Then the probability is 1/2*1/4 = 1/8
The answer is C.
Answer: (C) 1/8
Question: Debini normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Debini averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
(A) 135
(B) 105
(C) 95
(D) 75
(E) 45
Rationale: Debini normally drives to work in 45 minutes at an average speed of 40 miles per hour.
Use formula D = RT
Car:
T1: 45 min
R1: 40 mph
D1: [(40*45)/60] = 30 miles
Bike:
T1:?
R2: 12 - 16 mph
D2: 08*D1 = 24 miles
T1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)
Therefore, Deb has to leave 120 min - 45 min = 75 min early
ANSWER: D
Answer: (D) 75
Question: In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?
(A) 10.7%
(B) 20%
(C) 25%
(D) 33 1/3
(E) 58 1/3
Rationale: No of bank customers in 1985 = 60 x .45 = 27
No of bank customers in 1987 = 144 x .25 = 36
increase in % = 100 X 9/27 = 100/3 or 33 1/3
D is the correct answer
Answer: (D) 33 1/3
Question: A sum fetched total simple interest of 4016.25 at the rate of 12 p.c.p.a. in 5 years. What is the sum?
(A) 6693.75
(B) 8032.5
(C) 4462.5
(D) 8900
(E) None of these
Rationale: Let the sums be P.
Now, 60% of P = 4016.25
or, P = 6693.75
Answer A
Answer: (A) 6693.75
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 121km
(B) 242km
(C) 224km
(D) 112km
(E) 115km
Rationale: Explanation:
Average Speed =2Ã—21Ã—24/21+24=22.4 km/hr
Total distance =22.4Ã—10=224 km
ANSWER IS C
Answer: (C) 224km
Question: A train 70 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 4 sec
(B) 16 sec
(C) 6 sec
(D) 20 sec
(E) 8 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 70 * 2/35 = 16 sec
ANSWER: A
Answer: (A) 4 sec
Question: A man buys an article for $100. and sells it for $130. Find the gain percent?
(A) 10%
(B) 15%
(C) 25%
(D) 20%
(E) 30%
Rationale: C.P. = $100
S.P. = $130
Gain = $30
Gain% = 30/100 *100 = 30%
Answer is E
Answer: (E) 30%
Question: There are 8 books in a shelf that consist of 3 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 65
Rationale: 8C4 [Select any four] - 6C4 [Select all hard backs] =65.
E
Answer: (E) 65
Question: Simplify the following equation
[(p - q)2 - (p + q)2] / 4p = b/a
(A) a b = q
(B) q b = a
(C) a q = b
(D) a q = -b
(E) None of these
Rationale: [(p - q)2 - (p + q)2] / 4p = b/a
=> [p2 + q2 - 2pq - (p2 + q2 + 2pq)] / 4p = b/a
=> - 4pq/4p = b/a
=> q = - b/a
=> a q = -b
ANSWER:D
Answer: (D) a q = -b
Question: A bag contains 12 white and 18 black balls. Two balls are drawn in succession without replacement. What is the probability that first is white and second is black?
(A) 20/145
(B) 18/145
(C) 35/120
(D) 36/145
(E) 40/145
Rationale: The probability that first ball is white:
=12C1/30C1
12/30
=>2/5
Since, the ball is not replaced; => the number of balls left in bag- 29.
the probability the second ball - BLACK
18C1/29C1 = 18/29
req = 2/5 * 18/29 = 36/145
ANSWER D
Answer: (D) 36/145
Question: The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $62,500, how much profit did the business make?
(A) $100,000
(B) $125,000
(C) $150,000
(D) $200,000
(E) $250,000
Rationale: Majority owner + two partners = 0.25*P + 2*(0.25)*(0.75)*P = 0.25*P + (0.5)*(0.75)*P = 0.25*P + (0.375)*P = (0.625)*P
This equals $62,500.
(0.625)*P = 62,500 ----- divide both sides by 625
(0.001)*P = 100 ------ multiply by 1000
P = 100,000
Answer = A
Answer: (A) $100,000
Question: A thief steals at a car at 3.00 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
(A) 1 p.m
(B) 3 p.m
(C) 4 p.m
(D) 5.30 p.m
(E) 6 p.m
Rationale: D
5.30 p.m
Suppose the thief is overtaken x hrs after 3.00 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 5.30 p.m.
Answer: (D) 5.30 p.m
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
(A) 1/6
(B) 1/9
(C) 1/5
(D) 1/1
(E) 1/3
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability
= 3!4!/6! = 1/5
Answer:C
Answer: (C) 1/5