mathewhe/aqua_rat huggingface dataset:
Question: If 20 men can build a wall 66 metres long in 4 days, what length of a similar can be built by 86 men in 8 days?
(A) 278.4 mtrs
(B) 378.4 mtrs
(C) 478.4 mtrs
(D) 488.4 mtrs
(E) 567.6 mtrs
Rationale: If 20 men can build a wall 66 metres long in 4 days,
length of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(4*20) = 567.6 mtrs
ANSWER:E
Answer: (E) 567.6 mtrs
Question: As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 9,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule?
(A) 1250
(B) 2,079
(C) 2,200
(D) 2,250
(E) 2,460
Rationale: 24600/12=2050
2050*5=10250
10250-9000=1250
Answer A
Answer: (A) 1250
Question: The average (arithmetic mean)W of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) None of the above
Rationale: Given :
p + q = EVEN (odd + odd =even)
p + q + s + t = EVEN (even + even = even) nothing more....
(p + q + s + t) / 4 = x
I.
x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.
II.
Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.
III.
As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.
Answer E, None.
Answer: (E) None of the above
Question: Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 60 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 6 minutes?
(A) 20
(B) 30
(C) 40
(D) 10
(E) 16
Rationale: Machine B produces 100 part in 60 minutes. Machine A produces 100 parts twice as fast as B, so Machine A produces 100 parts in 60/2=30 minutes.
Now, Machine A produces 100 parts in 30 minutes which is 100/30 = 10/3 parts/minute.
10/3 parts X a total of 6 minutes = 20
A
Answer: (A) 20
Question: Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 24000, how much amount per month would he have spent on clothes and transport?
(A) 2000
(B) 8076
(C) 9691.2
(D) 4845.6
(E) None of these
Rationale: ∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
∵ Amount, spent on clothes and transport
= 24000⁄12 = 2000
Answer A
Answer: (A) 2000
Question: Which of the following cannot be the sum of 3 different prime numbers?
(A) 10
(B) 13
(C) 14
(D) 15
(E) 19
Rationale: Since the options given here are small, we can try the brute fore method.
Option A: 10 = 2+3+5. Sum of 3 different prime numbers.
Option B: 13. This cannot be expressed as a sum of 3 different prime numbers
Option C: 14 = 2 + 5 + 7. Sum of 3 different prime numbers
Option D: 15 = 3 + 5 + 7. Sum of 3 different prime numbers
Option E: 19 = 3 + 5 + 11. Sum of 3 different prime numbers
Correct Option: B
Answer: (B) 13
Question: 7.007/2.002 =
(A) 3.05
(B) 3.50035
(C) 3.501
(D) 3.5035
(E) 3.5
Rationale: 7.007/2.002 = 7007/2002 = 7(1001)/2(1001) = 7/2 = 3.5
The answer is E.
Answer: (E) 3.5
Question: A merchant purchased a jacket for $90 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A) $0
(B) $3
(C) $6
(D) $12
(E) $15
Rationale: Let selling price = x
So, x = 90 + 25x/100
Calculating above, x = 120
Selling price = 120
20% Discount on Selling price = 96
So, profit = 96-90 = 6 Answer = C
Answer: (C) $6
Question: In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 54° of the chart, how much of the Roberts’s $50,000 annual budget is dedicated to clothes and shoes?
(A) $7,500
(B) $3,000
(C) $4,500
(D) $5,000
(E) $5,400
Rationale: Given for clothes and shoes” takes up 54° of the circular chart.
Then clothes and shoes = 54/360 * 50000.
=> 7500.
IMO option A is correct answer...
Answer: (A) $7,500
Question: A cube has a volume of 343 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
(A) 24
(B) 48
(C) 64
(D) 2744
(E) 100
Rationale: Volume = 343 = side^3
i.e. Side of Cube = 7
New Cube has dimensions 14, 14, and 14 as all sides are twice of teh side of first cube
Volume = 14*14*14 = 2744 square feet
Answer: option D
Answer: (D) 2744
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 10
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Answer: (B) 12
Question: Given that A and B are events such that
X(A)= 0.25
X(B)=0.5
X(AnB)=0.5
find X (A|B) and X(A|B)
(A) 1/2
(B) 1/3
(C) 3/2
(D) 1/5
(E) 1/7
Rationale: Here, A and B are events
X(A|B) = X(AnB)/X(B) = 0.5/0.5 = 1
X(A|B) = X(AnB)/X(A) = 0.5/0.25 = 1/2.
Answer is A
Answer: (A) 1/2
Question: 3/4 of a number is 19 less than the original number. The number is ?
(A) 84
(B) 64
(C) 76
(D) 72
(E) None
Rationale: Answer
Let the original number be N.
So from question N - 3N/4 = 19
⇒ 4N - 3N = 76
∴ N = 76
Option: C
Answer: (C) 76
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 8, 20, 28
(B) 16 years, 28 years, 36 years
(C) 20, 35, 45
(D) 20, 35, 48
(E) None of these
Rationale: Let the present ages are 4x, 7x, 9x.
=> (4x-8) + (7x-8) + (9x-8) = 56
=> 20x = 80
=> x = 4
So their present ages are : 16,28,36
ANSWER:B
Answer: (B) 16 years, 28 years, 36 years
Question: Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 12 years?
(A) 30
(B) 32
(C) 40
(D) 50
(E) 60
Rationale: Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 12 years = (20 + 12) years =32 years.
Answer : B
Answer: (B) 32
Question: A can do a piece of work in 20 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) 24 days
(B) 60 days
(C) 86 days
(D) 45 days
(E) 17 days
Rationale: 10/20 + 10/30 + 10/x = 1
x = 60 days
Answer:B
Answer: (B) 60 days
Question: Which of the following lines has x-intercept and y-intercept that are integers T?
(A) y=3x+1
(B) y=√x+1
(C) y=-2/x
(D) y=x^2-1
(E) xy=1
Rationale: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers T and the correct answer is D.
Answer: (D) y=x^2-1
Question: A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 10 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The mean and the median
(D) The standard deviation only
(E) The mean and the standard deviation
Rationale: The correct answer is C.
Answer: (C) The mean and the median
Question: sahar travels the first 7 hours of his journey at 50 mph speed and the remaining 8 hours at 40 mph speed. What is the average speed of sahar's travel in mph?
(A) 44.3 mph
(B) 44.6 mph
(C) 44.9 mph
(D) 44.1 mph
(E) 44.2 mph
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by sahar = Distance covered in the first 7 hours + Distance covered in the next 8 hours.
Distance covered in the first 7 hours = 7Ã—50=350 miles
Distance covered in the next 8 hours= 8Ã—40=320 miles
Therefore, total distance travelled = 350+320=670 miles.
The total time taken = 7+8=15hours.
Hence, the average speed =670/15= 44.6 mph.
Answer : B
Answer: (B) 44.6 mph
Question: At a certain amateur bands rock show the ratio of freaks to nerds to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yellin grock on!, what are the chances that the next person who yells rock on!will be a freak?
(A) 1
(B) 1/2
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.
P(next person who yells rock on!is a freak) = (# of freaks in the crowd)/(TOTAL # of people in the crowd)
=1/6
= 1/6
Answer:
E
Answer: (E) 1/6
Question: When she chooses a password, Eloise
always uses exactly ten different
characters: five letters (A, B, C, D, and E)
and five numbers (2, 3, 4, 5, and 6).
Additionally, she always ensures that no
pair of letters is consecutive and that no
pair of numbers is consecutive. How many
different passwords conform to these rules?
(A) fewer than 1,000
(B) between 1,000 and 10,000
(C) between 10,000 and 100,000
(D) between 100,000 and 1,000,000
(E) more than 1,000,000
Rationale: The first character of the password can be any letter or number, so Eloise has ten
options. Her second choice must be from the set (letter or number) not yet used, so she
has five options. Choice 3 is from the same set as Choice 1, and she has four options left.
Choice 4 is the second item from the same set as Choice 2, so she has four options.
Choices 5 and 6 are from different sets, each with three options; Choices 7 and 8 are from
different sets, each with two options; Choices 9 and 10 are from different sets, each with
only one option remaining. You can see this information in the following chart:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
10 5 4 4 3 3 2 2 1 1
To find the total number of possible passwords, multiply these numbers together:
10 × 5 × 4 × 4 × 3 × 3 × 2 × 2 × 1 × 1 = 28,800
correct anser C)between 10,000 and 100,000
Answer: (C) between 10,000 and 100,000
Question: In what time a sum of money double itself at 8% per annum simple interest?
(A) 33 1/8%
(B) 33 1/3%
(C) 83 1/3%
(D) 33 4/3%
(E) 12 1/2%
Rationale: P = (P*8*R)/100
R = 12 1/2%
Answer:E
Answer: (E) 12 1/2%
Question: At 10 am 2 trains started travelling towards each other from station 287 miles apart they passed each other at 1:30 pmthe same dayy .if average speed of the faster train exceeded by 6 miles /hr what is speed of faster train in miles/hr
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: let the speed of slower train is x
then speed of faster train is=x+6
now, 287/x+x+6=7/2(3 and half hour)
after solving the equation we will get x=38
so faster train=x+6
38+6=44
ANSWER:C
Answer: (C) 44
Question: Solve the set of linear equations using subtraction:
4x-3y = 3
2x+6y = 4
(A) x=1/3, y=2/3
(B) x=1, y=2/3
(C) x=3, y=1/3
(D) x=2, y=2
(E) x=1, y=1/3
Rationale: Multiply the first equation by 2 so y will have a coefficient of 6 in both equations.
4x-3y = 3
Multiplying by 2: 8x-6y = 6
Add the new equation with the original second equation and solve for x.
8x-6y = 6
+2x+6y = 4
10x = 10
x=1
Substitute the solution for x into the first equation and solve for y.
4x-3y = 3
4(1)-3y = 3
-3y = -1
y=1/3
Substitute the solutions into the second equation to check the answer.
2*1+6*(1/3) ?= 4
2+(6/3) ?= 4
2+2 ?= 4
4=4
x = 1 and y=1/3
Answer E
Answer: (E) x=1, y=1/3
Question: The banker's discount on Rs.1150 due a certain time hence is Rs.115. Find the true discount and the banker's gain.
(A) 10
(B) 15
(C) 18
(D) 21
(E) None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1650 / 165
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.165,
T.D	= Rs.(10 / 11 x 165)
= Rs.150.
And, B.G	= Rs(165 - 150)
= Rs.15.
Answer B
Answer: (B) 15
Question: In the Lakeside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
(A) 50.
(B) 45.
(C) 40.
(D) 30.
(E) 25.
Rationale: Given there are 50 students In the Lakeside summer camp , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.
Now boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).
IMO option A is correct.
Answer: (A) 50.
Question: In what time will a railway train 110 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 6 sec
(B) 7 sec
(C) 8 sec
(D) 11 sec
(E) 2 sec
Rationale: T = 110/36 * 18/5
= 11 sec
Answer:D
Answer: (D) 11 sec
Question: A grocer has a sale of Rs. 6435, 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. 6700?
(A) s. 4991
(B) s. 5991
(C) s. 6001
(D) s. 6191
(E) s. 7991
Rationale: total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009.
Reqd.sale=Rs.[(6700*6)-34009]
= Rs.(40200-34009)
= Rs.6191.
ANSWER:D
Answer: (D) s. 6191
Question: 60% of male in a town and 70% of female in a town are eligible to vote. out of which 70% of male and 60% of female who are eligible to vote voted for candidate A. what is the value of votes in % did A get?
(A) 22
(B) 221
(C) 288
(D) 2212
(E) 2211
Rationale: Let the ratio of men and women are 100 : k
Male eligible votes = 60 and female eligible votes = 70% (k)
Number of males who voted for A = 70% (60) = 42
Number of females who voted for A = 60%(70% (K) = 42% (k)
Percentage of votes got by A = 42+42100(K)60+70100(K)×100=4200+42K6000+70K×10042+42100(K)60+70100(K)×100=4200+42K6000+70K×100
So this value cannot be determined as the value of K is not known
Answer:	B
Answer: (B) 221
Question: What is the maximum number T of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
(A) 36
(B) 32
(C) 24
(D) 21
(E) 15
Rationale: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get T=24 cubes.
Ans. C
Answer: (C) 24
Question: The area of a parallelogram is 288sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 15
(B) 9
(C) 16
(D) 14
(E) 12
Rationale: 2x * x = 288 => x
= 12
Answer: E
Answer: (E) 12
Question: Find the simple interest on Rs.750 for 9 months at 6 paisa per month?
(A) Rs.415
(B) Rs.405
(C) Rs.450
(D) Rs.345
(E) Rs.564
Rationale: Explanation:
I = (750*9*6)/100 = 405
Answer: Option B
Answer: (B) Rs.405
Question: One-fourth of a number is greater than one-fifth of the number succeeding it by 1. Find the number.
(A) 24
(B) 42
(C) 36
(D) 48
(E) 50
Rationale: number is 24
as 1/4 th of 24= 6
1/5 th of 25(24+1) =5
6=5+1
ANSWER:A
Answer: (A) 24
Question: If .002^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 0.002^5= (2*10^-3)^5 = 32*10^-15 = 0.32*10^-13 which would have 13 zeros to the right of the decimal point. The answer is D.
Answer: (D) 13
Question: The volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate S, in cubic meters per minutes, at which the water is flowing into the swimming pool?
(A) 0.125
(B) 0.25
(C) 0.5
(D) 0.75
(E) Not enough information to determine the rate
Rationale: The correct answer is E.
There are not enough info to answer the question.
A 840 cubic meters rectangle is built from: height*length*width.
From the question we know the volume of the pool and the filling rate.
A pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = E
Answer: (E) Not enough information to determine the rate
Question: The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,302 for a cell phone, then what was the cost price of the cell phone?
(A) Rs.5,845
(B) Rs.6,750
(C) Rs.5,700
(D) Rs.6,925
(E) None of these
Rationale: Explanation:
123% of CP =SP
Therefore, CP = Rs.8,302x100/123 = Rs.6750
Answer: Option B
Answer: (B) Rs.6,750
Question: If (x/y)=(10/5), find the value (x^2+y^2)/(x^2-y^2)
(A) 5/3
(B) 59/11
(C) 51/77
(D) 41/11
(E) None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(10/5)^2+1] / [(10/5)^2-1]
= [(100/25)+1] / [(100/25)-1] = 5/3
Answer is A.
Answer: (A) 5/3
Question: What is the sum of all the numbers between 300 and 1000 which are divisible by 179?
(A) 2517
(B) 2527
(C) 2607
(D) 2506
(E) 2606
Rationale: 358/179 ….. 895/179
179(2 + 3 + 4 + 5) => 2506
ANSWER:D
Answer: (D) 2506
Question: Define w* by the equation w* = π-w. Then ((−π)*)* =
(A)  −2π
(B)  -1
(C)  −π
(D)  2π
(E)  4π
Rationale: for w* f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π=C
Answer: (C)  −π
Question: A palindrome is a number that reads the same forward and backward, such as 145. How many odd, 4-digit numbers are palindromes?
(A) 40
(B) 45
(C) 80
(D) 90
(E) 2500
Rationale: A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc
You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.
Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.
In how many ways can you pick two digits such that the first one is an odd digit?
The first digit can be selected in 5 ways.(1/3/5/7/9)
The second digit can be selected in 10 ways.(0/1/2/3...8/9)
Total = 5*16 = 80 ways
C
Answer: (C) 80
Question: The cost of the paint is rs.30 per kg. if 1kg of paint covers 18sq.ft, how much will it cost to paint outside of a cube having 6 feet each side
(A) Rs.962
(B) Rs.672
(C) Rs.540
(D) Rs.876
(E) None of these
Rationale: Explanation:
surface area of a cube= 6 x 6^2 = 216 sq.ft
quantity of paint required=(216/18)=12kg
cost of painting= 30 x 18 = Rs.540
Answer: C
Answer: (C) Rs.540
Question: A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: Average speed = (2 * 3 * 2) / (3 + 2) = 12/5 km/hr.
Distance traveled = 12/5 * 5 = 12 km.
Distance between house and school = 12/2 = 6 km.'
Answer: C
Answer: (C) 6
Question: A certain high school has 500 students. Of these students, 40 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
(A) 430
(B) 440
(C) 450
(D) 460
(E) 470
Rationale: We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 40
Y = 20
Z = 10
So, we have 40 students taking music, 20 taking art and 10 taking BOTH music and art.
30 student taking JUST music
10 student taking JUST art
10 student taking BOTH music and art
Total = 50 students
We're asked for the total number of students who are taking NEITHER Course. That is 500 - 50 = 450.
C
Answer: (C) 450
Question: A man on tour travels first 100 km at 64 km/hr and the next 100 km at 80 km/hr. Find the average speed for first 200 km of tour.
(A) 50.11 km/hr
(B) 51.11 km/hr
(C) 52.11 km/hr
(D) 58.00 km/hr
(E) None of these
Rationale: Explanation:
We know Time = Distance/speed
So total time taken =
(100/60+100/80)=35/12hours
Time taken for 200 Km = 200∗35/12=58.00km/hr
Option D
Answer: (D) 58.00 km/hr
Question: How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together?
(A) 9
(B) 8
(C) 5
(D) 6
(E) 4
Rationale: Explanation:
(700 â€“ 300)/42 = 9 22/42 => 9 Numbers
Answer:A
Answer: (A) 9
Question: An article is bought for Rs.575 and sold for Rs.675, find the gain percent?
(A) 17.39%
(B) 33 1/6%
(C) 33 1/3%
(D) 38 1/3%
(E) 33 2/3%
Rationale: 575 ---- 100
100 ---- ? => 17.39%
Answer:A
Answer: (A) 17.39%
Question: Two ropes are given to you. Both of the ropes will take exactly an hour each to burn fully.
You are asked to measure forty five minutes using the two ropes. How will you achieve to do it?
(A) 30 minutes
(B) 40 min
(C) 50 minutes
(D) 60 minutes
(E) 70 minutes
Rationale: Solution:
Take both the ropes. Now light the first rope from both the ends. Light the second rope from just one end. In thirty minutes, the first rope will burn fully. At this point of time, the second rope will be left exactly half and you have to light it from the second end now. It will take half of the actual time (thirty minutes) to burn now i.e. fifteen minute.
Thirty Minutes + Fifteen minutes = Forty Minutes
Answer B
Answer: (B) 40 min
Question: Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 115 barrels of oil?
(A) 2
(B) 3
(C) 4
(D) 18
(E) 180
Rationale: Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute.
So for 115 barrels they will take a bit less than 115 mins which will be more than 1 hrs but less than 2 hrs.
Answer (A)
Answer: (A) 2
Question: If x and y are positive integers such that y is a multiple of 5 and 3x + 6y = 600, then x must be a multiple of which of the following?
(A) 3.
(B) 6.
(C) 7.
(D) 8.
(E) 10.
Rationale: If y is a multiple of 5, then 6y is also a multiple of 5.
3x = 600 - 6y
600 - 6y is even and it is a multiple of 5.
Thus x must also be even and a multiple of 5.
Therefore x must be a multiple of 10.
The answer is E.
Answer: (E) 10.
Question: Which resistive component is designed to be temperature sensitive?
(A) 27
(B) 66
(C) 25
(D) 18
(E) 11
Rationale: Explanation:
No answer description available for this question. Let us discuss.
Answer: Option A
Answer: (A) 27
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 5.6%
(B) 6 %
(C) 8.2 %
(D) 9.3 %
(E) 2%
Rationale: Explanation:
Cost Price of 1 toy = Rs.(375/12)= Rs. 31.25
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 - 31.25) = Rs. 1.75
Profit % =(1.75/31.25*100)%=28/5%=5.6%
ANSWER:A
Answer: (A) 5.6%