mathewhe/aqua_rat huggingface dataset:
Question: Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. The two companies merge, every employee stays with the resulting company, and no new employees are added. If the resulting companyís workforce consists of 25 percent managers, what percent of the workforce originated from Company A?
(A) 10%
(B) 20%
(C) 25%
(D) 50%
(E) 75%
Rationale: Let say Company A has x employes and B has y employees. Now they merge and total no of employees = x+y employees.
Per the question Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. We translate it into equation as follows:
.1x + .3y = .25 (x+y)
=> x + 3y =2.5 (x+y)
=> .5y = 1.5x
=> y=3x.
Now we know total employee = x+y. we need to find %age of x in total (x+y) ie x/(x+y) X100%
=> x/(3x+x) [substitute y=3x] => x/4x X 100%
=> .25 X 100 % => 25%.
ANSWER:C
Answer: (C) 25%
Question: A train 125 m long passes a man, running at 2 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 36
(B) 50
(C) 28
(D) 47
(E) 29
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 2) km/hr. x - 2 = 45 ==> x = 47 km/hr
Answer: D
Answer: (D) 47
Question: The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112
What is the 100th digit of d to the right of decimal point ?
(A) 0
(B) 1
(C) 5
(D) 8
(E) 9
Rationale: Now, let's see first we have those single digit numbers that occupy 9 spaces
Then the next integers from 10 to 19 will be 10 of them that will occupy 2 places each hence 20
The next ones will be from 20 to 29, 10 of them again, 2 places each hence 20 and so on
...
Until we get to 50-59 which will be 10 integers again, 2 places each hence 20 digits.
Now the 100th digit will be in the 50-59 range taking into consideration the first 9 single digit integers.
We also know that the tenth digits is always in an even place while the units digit is in the odd place. Therefore, the 100th digit will be the tenth digit of the given range (50-59) thus 5
Answer is C
Answer: (C) 5
Question: Angelina walked 100 meters from her home to the grocery at a constant speed. She then walked 180 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
(A) 2
(B) 3
(C) 0.5
(D) 6
(E) 12
Rationale: let the speed be X...
so time taken from home to grocery= 100/x..
the speed to gym = 2x..
so time taken = 180/2x=90/x..
its given 100/x-90/x=40..
10/x=40..
x=0.25m/secs..
so grocery to gym=2*0.25=0.5m/s...
Answer : C
Answer: (C) 0.5
Question: The sum of all the integers f such that -26 < f < 24 is
(A) 0
(B) -2
(C) -25
(D) -49
(E) -51
Rationale: Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 f= -49.
D is the answer.
Answer: (D) -49
Question: Tough and Tricky questions: Arithmetic.
(54^2 + 54^2)/18^2 =
(A) 24
(B) 8
(C) 29
(D) 58
(E) 116
Rationale: Ans is 24
my approach was:
(54^2 + 54^2)/18^2 =54(54+54)/18*18
=54*108/18*18=3*6=24
A
Answer: (A) 24
Question: In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, find the number of keepers.
(A) 25
(B) 20
(C) 15
(D) 13
(E) 14
Rationale: Let the number of keepers be x then,
Total number of heads =(50 + 45 + 8 + x)= (103 + x).
Total number of feet = (45 + 8) x 4 + (50 + x) x 2 =(312 +2x).
(312 + 2x)-(103 + x) =224 ==> x =15.
Hence, number of keepers =15.
Answer C.
Answer: (C) 15
Question: Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability Q that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?
(A) 8/28
(B) Q=9/28
(C) Q=10/28
(D) Q=10/18
(E) 11/18
Rationale: (3c2*2c1*3c2)/8c5
=(3*2*3)/(8*7*6/3*2)
=18/56
=9/28
B
Answer: (B) Q=9/28
Question: Express a speed of 63 kmph in meters per second?
(A) 10 mps
(B) 14 mps
(C) 17.5 mps
(D) 19.4 mps
(E) 10.8 mps
Rationale: 63* 5/18 = 17.5 mps
Answer: C
Answer: (C) 17.5 mps
Question: UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
(A) 76%
(B) 58%
(C) 68%
(D) 89%
(E) 49%
Rationale: let total no of Vehicles bought be 100, Toyota 70 and Honda 30, so total number of SUV's bought for Toyota and Honda respectively 70* 70/100=49 and 30* 30/100=9
so total 58 SUV's were bought out of 100 Vehicles bought..so required % is 58%
ANSWER:B
Answer: (B) 58%
Question: A computer store offers employees a 10% discount off the retail price. If the store purchased a computer from the manufacturer for $1200 dollars and marked up the price 10% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (10% off retail price) as opposed to the final retail price.
(A) 122
(B) 132
(C) 142
(D) 152
(E) 162
Rationale: Cost price=1200
Profit=10% =10% of 1200=120
selling price=CP+ Profit
SP=1320
a Discount of 10% to employees means 10% off on 1320
so 10% of 1320= 132
Ans B
Answer: (B) 132
Question: Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time T will the job be finished?
(A) Noon
(B) 12:30 p.m.
(C) 1:00 p.m.
(D) 1:30 p.m.
(E) 2:00 p.m.
Rationale: Ans: C (1:00pm)
From 9:00-11:00c(2 hrs)
A can do 1/8 Job/hr. so in 2 hours he can do 1/4 job.
B can do 1/10 job/hr so in 2 hrs. he can do 1/5 Job.
C can do 1/12 job/hr so in 2 hours he can do 1/6 job.
Total = 1/4+1/5+1/6 = 37/60 Job
Now balance work needs to be done by B and C.
Balance Work= 23/60 Job
Combined rate of B and C = 1/10+1/12 = 11/60 job/hr.
So they will do 22/60 work in 2 hrs (approx. to the balance work of 23/60)
Hence the Job will be completed 2hrs. after 11:00 i.e. @ 1:00pm=T
Ans: C (1:00pm)
Answer: (C) 1:00 p.m.
Question: If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 4?
I. x^2
II. y^2
III. xy
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: 4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is D
Answer: (D) I and II only
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
(A) 2.21%
(B) 2.07%
(C) 2.08%
(D) 2.01%
(E) 2.11%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer:D
Answer: (D) 2.01%
Question: Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?
(A) 22 km/hr
(B) 70 km/hr
(C) 77 km/hr
(D) 66 km/hr
(E) 44 km/hr
Rationale: Let their speed be x km/hr and y km/he respectively.
Then, 120/(x + y) = 1 => x + y = 120 --- (i)
Now, when they move in same direction:
(Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km
6x - 6y = 120 => x - y = 20 --- (ii)
Sloving (i) and (ii), we get x = 70, y = 50
P's speed = 70 km/hr.
Answer:B
Answer: (B) 70 km/hr
Question: A certain collage has total of 420 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
(A) 100
(B) 80
(C) 75
(D) 60
(E) 50
Rationale: Answer is A.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 420 seniors.
So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 100.
A
Answer: (A) 100
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 100%
(B) 75%
(C) 60%
(D) 25%
(E) 50%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: D
Answer: (D) 25%
Question: What is the average of xx,2x2x,and 66?
(A) x+2
(B) x+2x
(C) x+2x+2
(D) 2x+2
(E) x+2x-2
Rationale: By the definition of an average, we get:
x+2x+63=3x+63x+2x+63=3x+63
=3(x+2)3=x+2.=3(x+2)3=x+2.
Hence, the answer is x+2x+2 or Option C
Answer: (C) x+2x+2
Question: ?% of 360 = 93.6
(A) 277
(B) 36
(C) 26
(D) 72
(E) None of these
Rationale: ?% of 360 = 93.6
or, ? = 93.6×100/360=26
Answer C
Answer: (C) 26
Question: How many ways can 5 friends be arranged around a circular dinner table?
(A) 24
(B) 56
(C) 108
(D) 120
(E) 132
Rationale: The number of ways to order 5 people is 5!
However, around a circular table, each pattern would be repeated 5 times.
So the number of ways to seat 5 friends around a circular table is 4! = 24
The answer is A.
Answer: (A) 24
Question: Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 19 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
(A)  60
(B)  70
(C)  100
(D)  120
(E)  140
Rationale: 30% of the members have passed the test, thus 70% have not passed the test.
We also know that 30+19=49 members have not passed the test, thus 0.7*Total=49 --> Total=70.
Answer: B.
Answer: (B)  70
Question: How much 60% of 50 is greater than 42% of 30?
(A) 18
(B) 91
(C) 11
(D) 17.4
(E) 12
Rationale: (60/100) * 50 – (42/100) * 30
30 - 12.6 = 17.4
Answer: D
Answer: (D) 17.4
Question: The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 388
(B) 267
(C) 225
(D) 288
(E) 261
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X = 225 m.
Answer: C
Answer: (C) 225
Question: Sarah, Fatima, Salma, and Lina all got tips during their waitressing shift. The average of Sarah, Fatima, and Salma's tips was $100. The average of Fatima, Salma, and Lina's tips was $90. If Lina earned $85, what did Sarah earn?
(A) 105
(B) 108
(C) 110
(D) 113
(E) 115
Rationale: To solve:
Average tips for Sarah, Fatima and Sarah = $100
Total tips = 3*100 = 300
Average tips for Fatima, Salma, and Lina = $90
Total tips = 3*90 = 270
Lina's tips = $85
Now,
(Sarah+Fatima+Salma) - (Fatima+Salma+Lina) = 300-270 = 30
Sarah-Lina = 30
Sarah = Lina +30 = $115
Answer: Option E
Answer: (E) 115
Question: mixture contains alcohol and water in the ratio 4 : 3. If 6.5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
(A) 10
(B) 99
(C) 27
(D) 22
(E) 5.6
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
26x = 4(3x+5)
14x = 20
x = 1.4
Quantity of alcohol = (4 x 1.4) litres = 5.6 litres.
Answer: E
Answer: (E) 5.6
Question: Which of the following expressions CANNOT be equal to 0 when x^2 − 2x = 3?
(A) x^2 − 6x + 9
(B) x^2 − 4x + 3
(C) x^2 − x − 2
(D) x^2 − 7x + 6
(E) x^2 − 9
Rationale: E. Can x^2 − 9 = 0?
Factor to get (x + 3)(x - 3) = 0
So, (x + 3) = 0 or (x - 3) = 0
ELIMINATE E
D. Can x^2 − 7x + 6 = 0
Factor to get (x - 1)(x - 6) = 0
So, (x - 1) = 0 or (x - 6) = 0
Since we cannot conclude that (x - 3) = 0 or (x + 1) = 0, the correct answer must be D
Answer: (D) x^2 − 7x + 6
Question: Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 12 hours. How many hours does it take machines X and Y , working simultaneously , to produce 24k bottles?
(A)  48
(B)  42
(C)  45
(D)  98
(E)  96
Rationale: x rate = k/6
y rate = k/12
k/6 + k/12 = 24k / T
solving T = 96
Answer E
Answer: (E)  96
Question: Find the wrong number below mentioned series
17, 600,6000,550,750
(A) 600
(B) 6000
(C) 17
(D) 550
(E) 750
Rationale: 17 is the only prime number or odd number in the series.
ANSWER:C
Answer: (C) 17
Question: Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
(A) 1 13/17 hours
(B) 2 8/11 hours
(C) 3 9/17 hours
(D) 5 1/7 hours
(E) None
Rationale: Solution
Net part filled in 1 hour	= (1/9 + 1/6 -1/12)
= 7/36.
Therefore, the tank will be full in 36/7 hrs.	â€¹=â€º 5 1/7 hrs.
Answer D
Answer: (D) 5 1/7 hours
Question: What is the area of a square with perimeter 16P ?
(A)  16p^2
(B)  4P
(C)  P^2/4
(D)  P/16
(E)  P^2/16
Rationale: Each side is 4p
A = (4p)^2 = 16(p^2)
Answer A
Answer: (A)  16p^2
Question: A company received $2 million in royalties on the first $10 million in sales and then $8 million in royalties on the next $100 million in sales. By what percent did the ratio of royalties to sales decrease from the first $10 million in sales to the next $100 million in sales?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 70%
Rationale: First find out (ratio of royalties to sales):
2:10 First
0.2
8:100 Second
0.08
Decrease = 0.2-0.08 = 0.12
Percent = (0.12/0.20) = 60%.
ANSWER:D
Answer: (D) 60%
Question: If the productivity of a brigade grows by 40% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?
(A) 1.51
(B) 0.82
(C) 1.2
(D) 1.21
(E) 1.44
Rationale: B = 10-men brigade
p = increase in the productivity = 40%
Solution: B x p = B x 1.4 = 1.4B -------> the productivity of 11 men brigade
1.4B x p = 1.4B x 1.1 = 1.51B -----> the productivity of 12 men brigade
The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.51B/B = 1.51
A
Answer: (A) 1.51
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 9 km/hr completes one round in 5 min, then the area of the park (in sq. m) is?
(A) 337500 m
(B) 300000 m
(C) 153600 m
(D) 33750 m
(E) 9000 m
Rationale: Perimeter = Distance covered in 5 min. = (9000 x 5)/60 m = 750 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 750 or x = 75.
Length = 225 m and Breadth = 150 m.
Area = (225 x 150) m2 = 33750 m
D
Answer: (D) 33750 m
Question: If five chimpanzee can eat five mangoes in five minutes.
How many minutes would it take for four chimpanzee to eat four mangoes ?
(A) 5 minutes
(B) 10 minutes
(C) 8 minutes
(D) 14 minutes
(E) 20 minutes
Rationale: A
5 minutes
Answer: (A) 5 minutes
Question: In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Non - Negative ( zero to positive infinity )
Solution to the question :
-4,-3,-2,-1,0 , 1,2,3
Hence ans is 3 ..option D
Answer: (D) Three
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 22 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 2
(E) 8
Rationale: # of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D.
Bag A:
R:W:B = 2:6:9
Bag B
R:W = 1:4
6X + 4Y = 22 i.e 3X + 2Y = 11
X has to be odd to make an odd sum from the eq.
X = 1 , Y = 4 OR X = 3, Y = 1
So R can be 2X i.e 2 or 6.
Answer D
Answer: (D) 2
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 7 minutes?
(A) 36
(B) 54
(C) 108
(D) 216
(E) 378
Rationale: ONE Veggiematik machine can chop 36 carrots in 4 minutes
So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes
In other words, ONE Veggiematik machine can chop 54 carrots in7minutes
So,SIXVeggiematik machines can chop (7)(54) carrots in6minutes
In other words, SIX Veggiematik machines can chop 378 carrots in7minutes
Answer E
Answer: (E) 378
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 33
(B) 77
(C) 48
(D) 99
(E) 22
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer:C
Answer: (C) 48
Question: The ratio of the incomes of Chetan and Dinesh is 3:4. The ratio of their expenditures is 5:7. If each of them saves Rs.200, find the incomes of both?
(A) 1977
(B) 1892
(C) 2928
(D) 2791
(E) 1600
Rationale: The savings of Chetan and Dinesh are 3x - 5y and 4x - 7y respectively.
3x - 5y = 200 --- (1)
4x - 7y = 200 --- (2)
Multiplying (1) by 7 and (2) by 5 and subtracting the resultant equation (2) from resultant equation (1), we get x = 400.
The incomes of Chetan and Dinesh are 3x = Rs.1200 and 4x = Rs.1600 respectively.
Answer: E
Answer: (E) 1600
Question: Three candidates contested an election and received 1136, 7636 and 15000 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 46%
(B) 63%
(C) 74%
(D) 63%
(E) 68%
Rationale: B
15000/(1136 + 7636 + 15000) = 63%.
Answer: (B) 63%
Question: If 20 percent of the members of a certain organization are women and 2/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of unmarried men in the organization is greater than the number of married men in the organization.
(A) III
(B) II
(C) I
(D) I,II
(E) II,III
Rationale: 2/10 (20%) of the members are women and 2/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:
2/10*80 = 16 women;
80 - 16= 64 men;
2/8*64 = 16 married men;
64 - 16 = 48 unmarried men.
So, only option III is true.
Answer: A
Answer: (A) III
Question: A and B are two stations 125km apart. A train starts from A at 6a.m. and travels towards B at 50kmph. Another train starts from B at 7a.m. and travels towards A at 25kmph. At what time do they meet?
(A) 7a.m.
(B) 8a.m.
(C) 9a.m.
(D) 9.30a.m.
(E) 10a.m.
Rationale: Suppose they meet x hours after 6 a.m.
Distance moved by first train in x hours + distance moved by 2nd train in x-1 hrs = 125
50x+25(x-1) = 125
x = 2hr
So they meet 2hr after 6a.m. is at 8a.m.
Answer is B
Answer: (B) 8a.m.
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A rectangle has a center at (1, 2) and width (x), length (y), 6", 4", respectively. Some points, such as the center (1, 2), are inside the rectangle, but a point such as (4, 2) is on the rectangle, but not in the rectangle. How many lattice points are in the rectangle?
(A) 7
(B) 71
(C) 72
(D) 17
(E) 27
Rationale: The lattice points that are in the rectangle can be calculated as follows: divide the rectangle into 4 quadrants. Now we solve for one quadrant, multiply by 4, and subtract the repeating points along the vertical and horizontal lines that lie along the center point.
For one quadrant we have:
vertical = (1, 2), (1, 3),
horizontal = (2, 2), (3, 2), (don't count center again),
others = (2, 2), (3, 3).
There are 6 points. So, 6 * 4 = 24. Subtract repeating points, 7, we get 17.
There are a total of 17 lattice points in the square.
Answer: D
Answer: (D) 17
Question: A password of a computer used three digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
(A) 1/32
(B) 1/16
(C) 1/8
(D) 2/5
(E) 1/2
Rationale: We have three digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 =1/8 (C)
Answer: (C) 1/8
Question: A boy can reach a certain place in 30 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed.
(A) 3 km/hr.
(B) 6 km/hr
(C) 8 km/hr
(D) 14 km/hr
(E) None of these
Rationale: Explanation :
Solution: Let the speed be x km/hr. then,
30x - (30 * 29x/30) = 3
=> x = 3 km/hr.
Answer : A
Answer: (A) 3 km/hr.
Question: A money lender lent a total of $1400 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1400, how much did he lend to each of the two customers?
(A) 700; 1100
(B) 938; 462
(C) 1000; 800
(D) 1200; 800
(E) None of the above
Rationale: The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1400-x)*6/100 = 1400*5.67/100
Simplifying we get x=462
B
Answer: (B) 938; 462
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?
(A) 28
(B) 26
(C) 31
(D) 87
(E) 24
Rationale: M = 20
S =11
DS = 20 + 11
=31
Answer: C
Answer: (C) 31
Question: A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 954
-459
---------
495
Rearrenge=954
ANSWER:B
Answer: (B) 4
Question: Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.
(A) 40%
(B) 30%
(C) 20%
(D) 10%
(E) 15%
Rationale: Explanation:
Let the sum be x
Simple interest on x for 2 years = Rs.2000
Simple interest = PRT/100
2000 = x Ãƒâ€” R Ãƒâ€” 2100
Ã¢â€¡â€™ x R = 100000 --- (1)
Compound Interest on x for 2 years = 2400
P(1+R/100)T Ã¢Ë†â€™ P = 2400
x (1+R/100)2 Ã¢Ë†â€™ x = 2400
x (1 +2R/100+R210000)Ã¢Ë†â€™x=2400x(2R100+R210000)=2400
2xR/100 + xR2/10000 = 2400--- (2)
Substituting the value of xR from (1) in (2) ,we get
(2Ãƒâ€”100000)/100 + 100000 Ãƒâ€” R10000 = 2400
2000+10R = 2400
10R=400
R=40%
ANSWER IS A
Answer: (A) 40%
Question: The 100-milliliter solution of sugar and water is 21% sugar. How much water (in milliliters) must be added to make a solution that is 12% sugar?
(A) 55
(B) 60
(C) 65
(D) 70
(E) 75
Rationale: In the original solution the amount of sugar is 0.21*100=21 ml.
Let the volume of the new solution be V.
0.12V=21 ml.
V=175 ml.
The amount of water we need to add is 175 - 100 = 75 ml.
The answer is E.
Answer: (E) 75
Question: In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: (x+2)×60+x×120+(x−2)×180 /(x+2)+x+(x−2)=100
⇒ 360x−240 /3x = 100
⇒ 60x = 240 ⇒ x = 4
Answer E
Answer: (E) 7