mathewhe/aqua_rat huggingface dataset:
Question: A, B and C started a business by investing Rs. 45000, Rs. 55000 and Rs. 60000 respectively. At the end of a year, they got a total profit of Rs. 11200. Find how much B gets more than A in the profit?
(A) Rs. 700
(B) Rs. 750
(C) Rs. 710
(D) Rs. 780
(E) None of these
Rationale: Explanation:
Ratio of shares of A, B and C = 45000 : 55000 : 60000
= 9 : 11 : 12
A's Share = Rs.[(9/32) × 11200] = Rs. 3150
B's Share = Rs. [(11/32) × 11200] = Rs. 3850
.: B's share is more than A by Rs.(3850 - 3150) = Rs. 700
Answer: Option A
Answer: (A) Rs. 700
Question: The length of a rectangle is two - seventh of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 5929 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 25 units?
(A) 660 sq.units
(B) 440 sq.units
(C) 770 sq.units
(D) 550 sq.units
(E) 220 sq.units
Rationale: Given that the area of the square = 5929 sq.units
=> Side of square = âˆš5929 =77 units
The radius of the circle = side of the square = 77 units
Length of the rectangle = 2/7* 77 = 22 units
Given that breadth = 25 units
Area of the rectangle = lb = 22*25 = 550sq.units
Answer:D
Answer: (D) 550 sq.units
Question: A box contains four cent coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
D
Answer: (D) 4/5
Question: A boat goes 100 km downstream in 10 hours, and 60 km upstream in 30 hours. The speed of the stream is?
(A) 5km/h
(B) 2km/h
(C) 3km/h
(D) (1/2) km/h
(E) E)4
Rationale: 100 --- 10 DS = 10
? ---- 1
60 ---- 30 US = 2
? ----- 1 S = (10 - 2)/2
= 4 kmph
ANSWER:E
Answer: (E) E)4
Question: A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 9)%. In terms of x, how many species of bacteria will the group be able to model?
(A) x*x – 5x
(B) (x)(105 – x)
(C) (100)(105 – x)
(D) (x)*(109 - x)
(E) (x-5)/100
Rationale: Initial: (x/100)*10000 = 100x (bacterial species)
After reduce BY (x - 9)%, the percentage of bacterial species = 1 - (x - 9)% = 1 - (x - 9)/100 = (109 - x)/100
Note: Difference between reduce to[means: the remain] and reduce by[means: the remain = 1 -reduce by]
So, the number of bacterial species after reducing: 100x*(109 - x)/100 = (x)*(109 - x)
Ans is D.
Answer: (D) (x)*(109 - x)
Question: The ratio of red boxes to blue boxes in a certain warehouse is 15 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
(A) 37
(B) 74
(C) 111
(D) 148
(E) 80
Rationale: Ratio = R/B = 15/25 or R = 15/25 B -----------(1)
2R/B+150 = 15/25*1/2 = 3/10 or we can say that 20R=3B+450 -------------(2)
solving (1) and (2) we get
B=50 and R = 30
so total boxes is B + R = 50+30=80
Hence E. 80 is the correct answer
Answer: (E) 80
Question: What is the probability of getting a sum 9 from two throws of a dice?
(A) 1/9
(B) 1/6
(C) 1/8
(D) 1/4
(E) 1/12
Rationale: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)=4/36=1/9.
hence:A
Answer: (A) 1/9
Question: Two members of a certain club are selected to speak at the next club meeting. If there are 66 different possible selections of the 2 club members, how many members does the club have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 12
Rationale: Method-1
Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]
i.e. If total member = n
then nC2 = n! / [(2!)(n-2)!] = 66
i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 66
i.e. n*(n-1) = 132
(for Positive Values of n)
therefore, n*(n-1) = 132
i.e. n= 12
Answer: Option E
Answer: (E) 12
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R = 1/24
Rate of machine S = 1/12
Rate of R+S = 1/8
To finish the work in 2 hrs, the combined rate needs to be 1/2.
x * 1/8 = 1/2
x = 4
The answer is B.
Answer: (B) 4
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 88
(B) 98
(C) 106
(D) 108
(E) 111
Rationale: Explanation:
The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways
D)
Answer: (D) 108
Question: Express 15 mps in kmph?
(A) 54
(B) 88
(C) 90
(D) 27
(E) 21
Rationale: 15 * 18/5 = 54 kmph
Answer:A
Answer: (A) 54
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 2 students left over. What is the sum of the two smallest possible values of n?
(A) 33
(B) 46
(C) 49
(D) 54
(E) 86
Rationale: n = 4k+1 = 5j+2
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 5j+2.
1, 5, 9, 13, 17 = 5(3)+2
The next such number is 17 + 4*5 = 37.
17+37 = 54
The answer is D.
Answer: (D) 54
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) 45%
(B) 45(5/11)%
(C) 54(6/11)%
(D) 55%
(E) 65%
Rationale: Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50.
Required percentage = (50/110 x 100)% =45(5/11)%
ANSWER IS B
Answer: (B) 45(5/11)%
Question: If 60/x is an integer and 6/x is an integer, which of the following must be true? I. 6/x is an integer II. 12/x is an integer III. 15/x is an integer
(A) II only
(B) I only
(C) III only
(D) I, II only
(E) II, III only
Rationale: The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 6, GCD of 60 and 6, and if x=6 then ONLY I is true.
Answer: B
Answer: (B) I only
Question: Due to construction, the speed limit along an 7-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A)  4.37
(B)  8
(C)  10
(D)  15
(E)  24
Rationale: Old time in minutes to cross 7 miles stretch = 7*60/55 = 7*12/11 = 7.63
New time in minutes to cross 7 miles stretch = 7*60/35 = 7*12/7 = 12
Time difference = 4.37
Ans:A
Answer: (A)  4.37
Question: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y. Which of the following could be the difference of X and Y ?
(A) 73
(B) 44
(C) 36
(D) 29
(E) 8
Rationale: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y:
X = 10a + b
Y = 10a + b
X - Y = (10a + b) - (10a + b) = 9(a - b). As you can see the difference must be a multiple of 9. Only option C is a multiple of 9.
Answer: C.
Answer: (C) 36
Question: Jane covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
(A) 2 hours 30 minutes
(B) 3 hours
(C) 2 hours
(D) 1 hour 45 minutes
(E) None of these
Rationale: Explanatory Answer
Let Jane travel 'x' at 60 miles per hour.
As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.
Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles.
Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x miles.
Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.
Therefore, total distance = 60x + 400 - 80x.
Total distance travelled = 340 miles.
Therefore, 340 = 60x + 400 - 80x
20x = 60 or x = 3 hours.
Choice B is the correct answer.
Answer: (B) 3 hours
Question: If 100<x<199 and 20<y<100, then the product xy CANNOT be equal to:
(A) 1900
(B) 19,303
(C) 19,356.732
(D) 19,502
(E) 19,909
Rationale: Correct Answer: (A)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 20. The largest value must be less than 199 * 100. This means that 2000 < xy < 19,900. (A) is outside of this range, so it is not a possible product of xy.
Answer: (A) 1900
Question: 26 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
(A) 30
(B) 39
(C) 60
(D) Data inadequate
(E) None of these
Rationale: Capacity of the tank = 26 Ã— 13.5= 351 litres
When the capacity of each bucket = 9 litres, then the required no. of buckets
= 351â„9 = 39
Answer B
Answer: (B) 39
Question: A train of length 250 m crosses a bridge of length 120m in 20 seconds. What is the speed of train?
(A) 33
(B) 27
(C) 66.6
(D) 22
(E) 72
Rationale: Sol : (length of train+ length of bridge) = speed of train x Time
(250+120) = 20 x Speed
Speed = 370/20= 18.5 m/s =66.6 km/h
ANSWER=C
Answer: (C) 66.6
Question: Two parallel sides of a trapezium are 4 cm and 5 cm respectively. The perpendicular distance between the parallel sides is 6 cm. Find the area of the trapezium.
(A) 24cm2
(B) 25cm2
(C) 26cm2
(D) 27cm2
(E) 28cm2
Rationale: Area of trapezium when height and two parallel sides are given = 1/2×h×(a+b)= 1/2x 6 x (4 + 5) = 27cm2
Answer D
Answer: (D) 27cm2
Question: In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 60 and a standard deviation of 12, which of the following is exactly 1.95 standard deviations more than the mean?
(A) a) 48
(B) b) 60
(C) c) 72
(D) d) 77.5
(E) e) 83.4
Rationale: Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 60
2) The standard deviation of the group is 12
If you go 1 SDupfrom the average, you hit.....60+12 = 72
If you go 1 SDdownfrom the average, you hit.....60-12 = 48
If you go 2 SDsupfrom the average, you hit.....60+2(12) = 84
If you go 2 SDsdownfrom the average, you hit.....60-2(12) = 36
Etc.
Here, we're asked for the number that is EXACTLY 1.95 SDs above the mean....
1.95 SDsupwould be.....60 + 1.95(12) = 83.4
E
Answer: (E) e) 83.4
Question: For how many values n is 2^x = x^2 ?
(A) Three
(B) One
(C) Two
(D) None
(E) More than Three
Rationale: draw a graph with x^2 and 2^x, you'll see 3 intercepts between the 2 curves and the answer is A
Answer: (A) Three
Question: In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 91% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
(A) 3%
(B) 5%
(C) 2.5%
(D) 4.2%
(E) 6%
Rationale: Explanation :
Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.
Products from M1 = 40, from M2 = 30 and from M3 = 30.
Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.09 x 30 = 2.7
Therefore, total number of defective products = 4.2.
Answer : D
Answer: (D) 4.2%
Question: Last week John spent 30 percent of his wages on recreation. This week, his wages are 25 percent less than last weekʼs wages and he spent 20 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week?
(A) 60%
(B) 70%
(C) 80%
(D) 90%
(E) 50%
Rationale: Say John's wages last week were $100, so he spent 0.30*100=$30 on recreation;
This week's wages is 0.75*100=$75, so he spends 0.2*75=$15 on recreation;
15/30=0.50, hence the amount he spends on recreation this week is 50% of the amount he spent on recreation last week: 30*0.5=15
Answer: E
Answer: (E) 50%
Question: What number times (1⁄6)^2 will give the value of 6^3?
(A) 6
(B) 36
(C) 216
(D) 1296
(E) 7776
Rationale: x*(1/6)^2 = 6^3
x = 6^2*6^3 = 6^5 = 7776
The answer is E.
Answer: (E) 7776
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes. Find the amount of his profit or loss?
(A) lost 10 cents
(B) lost 4 cents
(C) broke even
(D) gained 4 cents
(E) gained 10 cents
Rationale: 20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer is C.
Answer: (C) broke even
Question: Find the area of a parallelogram with base 12 cm and height 10 cm?
(A) 297 cm2
(B) 384 cm2
(C) 120 cm2
(D) 267 cm2
(E) 186 cm2
Rationale: Area of a parallelogram
= base * height
= 12 * 10
= 120 cm2
Answer: C
Answer: (C) 120 cm2
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 5 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/900
Rationale: If it takes 5 minutes to inspect one vehicle, the # of vehicles that can be inspected in 3 hours (180 minutes) = 180/5 = 36. Hence, for calculating the probability that the police will find the transmitter within three hours, the favorable cases = 36. Now, we need to figure out the total # of cases.
The total # of cases = Total # of such cars possible. The details given about the car is that it starts with 79, which leaves 2 more digits, both of which can be filled by all 10 numbers (0-9). In addition, we have 3 letters, each of which can be filled by any from the set {A,B,C}. Hence the total # of such cars possible = 10*10*3*3 = 900
So, the probability that the police will find the transmitter within three hours = 36/900 = 1/25. Option C
Answer: (C) 1/25
Question: Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 1/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?
(A) 9/29
(B) 8/23
(C) 9/25
(D) 17/29
(E) 3/4
Rationale: Suppose Q can drain in 1 hr. So, rQ = 1/1 = 1
So, rP = 1/[(3/4)rQ] = 4/3
Also, rP = rR/(1/3) => 4/3 = rR/(1/3) => rR = 4/9
Let H is the time it takes to drain by running all 3 pipes simultaneously
So combined rate = rC = 1/H = 1 + 4/3 + 4/9 = 25/9 = 1/(9/25)
Thus running simultaneously, Pipe Q will drain 9/25 of the liquid.
Thus answer = C.
Answer: (C) 9/25
Question: In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 8P pots?
(A) 60/M
(B) 8M
(C) 2M/15
(D) 480M
(E) M/60
Rationale: The time it takes to wash 8P pots is 8M minutes which is 8M / 60 = 2M/15 hours.
The answer is C.
Answer: (C) 2M/15
Question: The fourth proportional to 12, 16 and 18 is?
(A) 21
(B) 24
(C) 88
(D) 99
(E) 26
Rationale: (16*18)/12 = 24
Answer: B
Answer: (B) 24
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 76 cm2
(B) 15 cm2
(C) 76 cm2
(D) 17 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 28/2
= 35 cm2
Answer: E
Answer: (E) 35 cm2
Question: The sum of three numbers is 136. If the ratio between first and second be 2 : 3 and that between second and third is 5 : 3, then the second number is
(A) 38
(B) 27
(C) 99
(D) 60
(E) 82
Rationale: Explanation:
A : B = 2 : 3 and B : C = 5 : 3
=>A : B : C = = 10 : 15 : 9.
Second number = = 60.
Answer: D) 60
Answer: (D) 60
Question: sunil start from home at 4 pm and reaches school everyday at 5pm to pick up his children.on saturday the school got over ai 4 pm and children started walking towards home.sunil met them on the way and returned home 15min early.if speed of sunil is 35km/hr then for how many min did children walk? what is speed of children???
(A) 4 km/hr
(B) 5 km/hr
(C) 6 km/hr
(D) 7 km/hr
(E) 8 km/hr
Rationale: sunil reach 15 min early. it is time save at both for going to school and coming to home.
so, sunil meet children befor 15/2= 7.5 min.
speed of sunil is 35km/hr i.e. 583.33 m/min.
remaining distance to cover by sunil or else we can say total distance cover by children is 7.5*583.33=4375 m
Sunil meet children after 52.5 min i.e. (1hr-7.5min).
so 4375 is distance cover by children in 52.5min.
so, speed of children is 4375/52.5=83.33m/min=5 km/hr.
ANSWER:B
Answer: (B) 5 km/hr
Question: A train 75 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
(A) 11 s
(B) 5 s
(C) 7 s
(D) 12 s
(E) None of these
Rationale: We know from the formula Time = Distance/ Speed
Thus, Time = 75/ 54 x 5/18
or, Time = 5 sec.
ANSWER:B
Answer: (B) 5 s
Question: A man purchases 2 watches for $ 560. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 260 and $ 300
(B) $210 and $ 350
(C) $224 and $336
(D) $560 and $560
(E) $224 and $ 350
Rationale: x + y = 560 --- (1)
1.15x + 0.9y = 560 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*112)/(3*112) = 224/336
Answer: C
Answer: (C) $224 and $336
Question: A car travels 25km an hour faster than a bus for a journey of 500km. If the bus takes 10 hours more than the car, then the speeds of the bus and the car are
(A) 25km/hr and 40km/hr respectively
(B) 25km/hr and 60 km/hr respectively
(C) 25km/hr and 50km/hr respectively
(D) None of these
(E) Cannot be determined
Rationale: Let the speeds of bus and car be x and y. Here, y = x +25
As per the question, 500/x - 500/x+25 =10
⇒ 500(x + 25) − 500(x) =10x(x+25) ⇒ x = 25, y = 50.
Answer: C.
Answer: (C) 25km/hr and 50km/hr respectively
Question: A recycling facility is staffed by 7 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/7 of all wages paid at the facility, what is the value of n?
(A) 3/7
(B) 4/5
(C) 7/5
(D) 7/6
(E) 7/4
Rationale: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 7x+xn and we are told that it equals to 7xn:
7x+xn=7xn --> reduce by x: 7+n=7n -->6n= 7
n = 7/6
Answer: D
Answer: (D) 7/6
Question: The difference between the squares of two consecutive numbers is 37. Find the numbers.
(A) 14-15
(B) 20-23
(C) 11-12
(D) 18-19
(E) 13-14
Rationale: If the difference between the squares of two consecutive numbers is x, then the numbers are (x-1)/2 and (x+1)/2
(37-1)/2 and (37+1)/2
36/2 and 38/2
Therefore the required answer = 18 and 19.
Answer: (D) 18-19
Question: A sells a bicycle to B at a profit of 75% and B sells it to C at a loss of 40%. Find the resultant profit or loss.
(A) -4%
(B) 5%
(C) -5%
(D) 6%
(E) -7%
Rationale: The resultant profit or loss = 75 - 40 - (75*40)/100 = 5%
Profit = 5%
Answer is B
Answer: (B) 5%
Question: When 7 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
(A) 1
(B) 3
(C) 8
(D) 32
(E) 30
Rationale: Total outcome is 2^7 = 128
Favourable cases = H_ _ _ _ _ H
The second, to sixth places can be occupied by either H or T
There are 2^5 =32 ways that can be done.
Hence, the correct option is D
Answer: (D) 32
Question: Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.
(A) 27/34
(B) 25/34
(C) 19/34
(D) 21/34
(E) 21/53
Rationale: Explanation :
The probability that no girl is selected is :-
=>8C2/17C2.
=>28/136.
=>7/34.
Hence, the probability that atleast one girl is selected is :-
=>1- 7/34.
=>27/34.
Answer : A
Answer: (A) 27/34
Question: A certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 70
(C) 140
(D) 135
(E) 315
Rationale: 1 of 3 will be chosen for the math
2 of 10 will be chosen for the computer
None of the 3 chosen people can be in more than one departments.
We can choose any of the 3 candidates for the math dep., which gives as 3 selections.
We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.
So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:
10! /2!*8!= (9*10) / 2 = 90 / 2 = 45.
We are multiplying our individual selections: 3*45 = 135
In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.
Ans D
Answer: (D) 135
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 220 meter
(B) 225 meter
(C) 230 meter
(D) 235 meter
(E) 240 meter
Rationale: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+270/9=500/9
=>x+270=500=>x=230 So the length of the train is 230 meters
ANSWER IS C
Answer: (C) 230 meter
Question: How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg ?
(A) 83 Kg
(B) 65 Kg
(C) 13 Kg
(D) 63 Kg
(E) 23 Kg
Rationale: By the rule of alligation:
C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.
Answer: D
Answer: (D) 63 Kg
Question: 22.32 + 583.122 + 42.42 = ?
(A) 622.441
(B) 647.862
(C) 622.233
(D) 622.443
(E) None of these
Rationale: Explanation :
22.32 + 583.122 + 42.42 = 647.862. Answer : Option B
Answer: (B) 647.862