mathewhe/aqua_rat huggingface dataset:
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?
(A) 120
(B) 122
(C) 124
(D) 128
(E) 126
Rationale: length =9 feet
breadth =37−92=14 feet
Area =9×14=126 square feet
Answer is E.
Answer: (E) 126
Question: If four coins are tossed, the probability of getting two heads and two tails is
(A) 3/8
(B) 3/4
(C) 3/5
(D) 3/3
(E) 3/1
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24
= 3/8
Answer:A
Answer: (A) 3/8
Question: If −y ≥ x, and −x < −8, then which of the following must be true?
(A) y = −8
(B) y > −8
(C) −y > 8
(D) y ≤ −8
(E) y ≥ −8
Rationale: −y ≥ x, and −x < −8
y <= -x < -8
As '-x' is less than '-8' and Y is less than or equal to '-x'
we have y < -8 which is similar to -y > 8.
C) -y > 8
Answer: (C) −y > 8
Question: A rectangular swimming pool is 20 feet by 18 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 624 square feet. What is the width of the deck?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Let the width =W
Total Area of the pool and deck= (2W+20)(2W+18)
We can Test the answer choices along with unit digit method
A) 2 feet ...........24*22 has unit digit 8..........Eliminate
B) 2.5 feet.........25*23 has unit digit 5..........Eliminate
C) 3 feet............26*24 has unit digit 4...........Hold
D) 4 feet............28*26 has unit digit 8...........Eliminate
E) 5 feet............30*38 has unit digit 0...........Eliminate
Answer: B w=3
Answer: (B) 3
Question: If 3 girls can do 3 times of a particular work in 3 days, then, 7 girls can do 7 times of that work in
(A) 1 1/5 days
(B) 2 days
(C) 2 1/5 days
(D) 3 days
(E) 4 days
Rationale: Answer: Option 'D'
That is, 1 girl can do one time of the work in 3 days.
Therefore, 7 girls can do 7 times work in the same 3 days itself.
Answer: (D) 3 days
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
(A) 2/113
(B) 3/114
(C) 1/108
(D) 2/213
(E) 3/111
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: (C) 1/108
Question: 2056 x 987 = ?
(A) 1936372
(B) 2029272
(C) 1896172
(D) 1923472
(E) None of them
Rationale: =2056 x 987
=2056 x (1000 - 13)
=2056 x 1000 - 2056 x 13
=2056000 - 26728
=2029272
Answer is B
Answer: (B) 2029272
Question: Which of the following is not a composite number ?
(A) 234
(B) 211
(C) 525
(D) 603
(E) 217
Rationale: Clearly 211 is not a composite number. All others are divisible by 3. Ans : A
Answer: (A) 234
Question: By how much does the larger root of the equation 2b^2+5b = 12 exceed the smaller root?
(A)  5/2
(B)  10/3
(C)  7/2
(D)  14/3
(E)  11/2
Rationale: For 2b^2+5b = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).
Answer: (E)  11/2
Question: The sum of the ages of 4 children born at the intervals of 3 years each is 38 years. What is the age of the youngest child?
(A) 2 years
(B) 3 years
(C) 4 years
(D) 5 years
(E) 6 years
Rationale: Let the ages of the children be x, (x + 3), (x + 6), (x + 9) years.
Then, x + (x + 3) + (x + 6) + (x + 9) = 38
4x = 20 => x = 5.
Age of youngest child = x = 5 years.
ANSWER:D
Answer: (D) 5 years
Question: At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score S of team B?
(A) 1)8
(B) 2)10
(C) 3)20
(D) 4)40
(E) 5)80
Rationale: A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
Answer: (A) 1)8
Question: The difference between two positive integers is 3.if the sum of their squares is 369, the the sum of the numbers is:
(A) 12
(B) 29
(C) 71
(D) 48
(E) 23
Rationale: x^2 +(x+3)^2=369
x^2+x^2+9+6x=369
2x^2+6x-360=0
x^2+3x-180=0
(x+15)(x-12)=0
x=12
correct answer A
Answer: (A) 12
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 972 sq m, then what is the breadth of the rectangular plot?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 972
3b2 = 972
b2 = 324
b = 18 m.
Answer: Option C
Answer: (C) 18
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
(A) 22
(B) 23
(C) 25
(D) 35
(E) 30
Rationale: Explanation:
Clearly, we have :
B-3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 => 5B = 125=> B = 25.
ANSWER IS C
Answer: (C) 25
Question: A discount electronics store normally sells all merchandise at a discount of 5 percent to 25 percent off the suggested retail price. If, during a special sale, an additional 25 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $300 before any discount?
(A) $130.00
(B) $160.75
(C) $168.75
(D) $182.00
(E) $168.00
Rationale: Original price : 300 $
Max first discount = -25%
Thus : 300âˆ—(1âˆ’25/100)=225
Second discount on the discounted price = -25%
Thus : 225âˆ—(1âˆ’25/100)=168.75
Answer C
Answer: (C) $168.75
Question: Alice and Bob race around a running track. Alice runs at a constant rate of one lap every 5 minutes and Bob runs at a constant rate of one lap every 6 minutes. If they both start at the same time, how many minutes will it take for Alice to get exactly one lap ahead of Bob?
(A) 30
(B) 32
(C) 35
(D) 36
(E) 40
Rationale: Let x be the number of minutes it takes for Alice to get one lap ahead.
Then Alice ran x/5 laps and Bob ran x/6 laps.
x/5 = 1+x/6
6x=30+5x
x=30
The answer is A.
Answer: (A) 30
Question: What is the next number of the following sequence
125, 25, 175, 35, 245, 49 (...)
(A) 282
(B) 343
(C) 393
(D) 434
(E) 515
Rationale: The series is
125/5=25
25*7=175
175/5=35
35*7=245
245/5=49
49*7=343
ANSWER: B
Answer: (B) 343
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 3.5 km long?
(A) 4
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: D = 25 * 60 + 3500 = 5000 m
T = 5000/60 * 18/5 = 300 sec = 5 mins
Answer: C
Answer: (C) 5
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2500 m^2
(B) 2540 m^2
(C) 2520 m^2
(D) 2600 m^2
(E) 3000 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 m^2
Question: If z is a positive integer, which of the following could NOT be the square of z?
(A)  5,008,644
(B)  5,004,169
(C)  4,999,696
(D)  4,995,225
(E)  4,990,752
Rationale: A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E)
9*9=1
1,4,9,6,5
Ans:E
Answer: (E)  4,990,752
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
(A) 2388
(B) 2380
(C) 2888
(D) 2663
(E) 2922
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer: B
Answer: (B) 2380
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 10 days before the completion of the work. In how many days was the work completed?
(A) 12.5 days
(B) 16 days
(C) 18 days
(D) 11 days
(E) 38 days
Rationale: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 10 days = 10*(1/24 + 1/30) = 3/4
Remaining work = 1/4
The number of days required for this initial work = 2.5 days.
The total number of days required = 10 + 2.5 = 12.5 days.
Answer: A
Answer: (A) 12.5 days
Question: Following the approval of crude oil production cuts by OPEC, the price of crude which has slumped by 28% in the last 3 months is expected to rally and increase by about 5% in the next one month. This will bring the price of crude oil to $60.
(A) 79.4
(B) 75.1
(C) 80.7
(D) 68.3
(E) 89.6
Rationale: -28+5-(28*5)/100=-24.4% net decrease
let initial price be Y
Y(1-24.4/100)=60
Y=60/0.756 = ~79.4
Ans is A)
Answer: (A) 79.4
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
(A) 5/7
(B) 4/7
(C) 5/12
(D) 4/7
(E) 1/6
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12
Option C
Answer: (C) 5/12
Question: A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?
(A) 3:2:4
(B) 2:2:4
(C) 1:2:4
(D) 4:2:4
(E) 5:2:4
Rationale: c
1:2:4
WC of A: B = 1:2
B: C = 1:2
---------------------
A: B: C = 1:2:4
Answer: (C) 1:2:4
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 17
(B) 19
(C) 17
(D) 12
(E) 91
Rationale: 2 * 22/7 * 14 * x = 1056 => x
= 12
Answer: D
Answer: (D) 12
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 16
(B) 17
(C) 12
(D) 16
(E) 16
Rationale: T = 9/45 * 60
12
Answer:C
Answer: (C) 12
Question: Machine X and machine B are each used to manufacture 660 sprockets. It takes machine X 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine X. How many sprockets per hour does machine X produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: I think the correct answer is A.
Machine X produces at a speed of X sp/hour and B at a speed of B sp/hour.
so, 660/X=(660/B)+10 and X=1,1 X--->1,1*660=660+11X--->A=6, so answer A is correct
Answer: (A) 6
Question: Sujit incurred a loss of 45% on selling an article for Rs.3960/-. What was the cost price of the article?
(A) Rs.5725/-
(B) Rs.5080/-
(C) Rs.7200/-
(D) Rs.6750/-
(E) None of these
Rationale: Explanation:
45% loss means SP of Rs.3960/- is 55% of CP
:. CP = 3960x100/55 = Rs.7200/-
Answer: Option C
Answer: (C) Rs.7200/-
Question: 10 men working 12 hours daily finish a work in 24 days. In how many days will they finish 1/4th of the work working 8 hours daily?
(A) 9 days
(B) 10 days
(C) 11 days
(D) 12 days
(E) 18 days
Rationale: The number of days needed to finish 1/4 of the work =1/4*12/8*24 =9 days. Answer : A
Answer: (A) 9 days
Question: What sum of money will produce Rs.75 as simple interest in 4 years at 3 1/2 percent?
(A) 337
(B) 500
(C) 266
(D) 288
(E) 536
Rationale: 75 = (P*4*7/2)/100
P = 536
Answer: E
Answer: (E) 536
Question: The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.
(A) 33
(B) 38
(C) 29
(D) 40
(E) 48
Rationale: if the present age be x years.
father's will be (3x+3)years..
so, (3x+3+3)=2(x+3)+10
or, x=10
so the fathers present age =(3x+3)=(3*10+3)years =33years..
ANSWER : OPTION A
Answer: (A) 33
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 34
(B) 45
(C) 64
(D) 76
(E) 80
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
(A) 1040
(B) 2080
(C) 3120
(D) 4160
(E) None of these
Rationale: Number of male employees = 6400 * 65/100 = 4160
Required number of male employees who are less than 50 years old = 4160 * (100 - 25)%
= 4160 * 75/100 = 3120.
ANSWER:C
Answer: (C) 3120
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 40
(B) 60
(C) 70
(D) 80
(E) 20
Rationale: A
800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: (A) 40
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 140?
(A) 28
(B) 29
(C) 30
(D) 31
(E) 32
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 140
5x -20 = 140
5x = 160
x = 32
The answer is E.
Answer: (E) 32
Question: At a tanning salon, customers are charged $10 for their first visit in a calendar month and $8 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?
(A) $1220
(B) $1240
(C) $1300
(D) $1340
(E) $1880
Rationale: I get B. This question seems too straightforward for 600+. Am I missing something?
100 first-time visits --> 100(10) = $1000
30 + 10 = 40 subsequent visits --> 40(8) = $320
Total revenue: 1000+ 320 = $1320
The answer is B.
Answer: (B) $1240
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability R that the team will have exactly 2 women?
(A) 1/14
(B) 1/7
(C) 2/7
(D) 3/7
(E) 1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2*3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: (D) 3/7
Question: What number is 70 more than one-fourth of itself?
(A) 93
(B) 225
(C) 288
(D) 324
(E) 336
Rationale: 1/4x+70= x
That means 70=3/4x
x= (70*4)/3= 280/3=93
A is the answer.
Answer: (A) 93
Question: 387 x 387 + 114 x 114 + 2 x 387 x 114 = ?
(A) 250001
(B) 251001
(C) 260101
(D) 261001
(E) None of these
Rationale: Answer
Given expression = a2+b2+2ab = (a+b)2
where a = 387 and b = 114
= (387 + 114 )2
= (501)2
=(500 +1 )2
=(500)2 + (1)2+ 2 x 500 x 1
= 250000 + 1 +1000 = 251001.
Option: B
Answer: (B) 251001
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 22
(B) 45
(C) 66
(D) 88
(E) 12
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B
Answer: (B) 45
Question: If m and n are positive integers of T such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
(A) 2m/n + 1
(B) 2n/m + 1
(C) 2n/(m+1)
(D) 2m/n
(E) 2n/m
Rationale: Lets say N=10, M=5
2N=20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).
I would choose E.
Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M
Again - Answer is E.
Answer: (E) 2n/m
Question: If the seventh day of a month is three days earlier than Friday, What day will it be on the nineteenth
day of the month?
(A) Saturday
(B) Monday
(C) Sunday
(D) Wednesday
(E) None of these
Rationale: Explanation :
Given that seventh day of a month is three days earlier than Friday
=> Seventh day is Tuesday
=> 14th is Tuesday
=> 19th is Sunday
Answer : Option C
Answer: (C) Sunday
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 9 m of the same rod?
(A) 22.8 kg
(B) 34.2 kg
(C) 28 kg
(D) 26.5 kg
(E) None of these
Rationale: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 9 :: 42.75 : x
=> 11.25 x x = 9 x 42.75
=> x = (9 x 42.75) / 11.25
=> x = 34.2
Answer : B
Answer: (B) 34.2 kg
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
(A) 33
(B) 20
(C) 88
(D) 66
(E) 21
Rationale: P = (P*5*R)/100
R = 20%
Answer: B
Answer: (B) 20
Question: There are 70 doors marked with numbers 1 to 70. There are 70 individuals marked 1 to 70.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, and 70. If every individual in the group gets one turn, then how many doors are open at the end?
(A) 0
(B) 2
(C) 5
(D) 8
(E) 10
Rationale: If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors.
The doors which are open at the end are: 1, 4, 9, 16, 25, 36, 49, 64 for a total of 8 doors.
The answer is D.
Answer: (D) 8
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 12
(B) 56
(C) 54
(D) 67
(E) 19
Rationale: S = 240/16 * 18/5
= 54 kmph
Answer:C
Answer: (C) 54
Question: A man crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 7km/hr
(B) 7.2km/hr
(C) 5.2km/hr
(D) 10km/hr
(E) 5km/hr
Rationale: Speed =600/5 *60 = 2 m/sec
Converting m/sec to km/hr .
=2*18/5=7.2km/hr
Answer is B
Answer: (B) 7.2km/hr
Question: A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 75 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year?
(A) −5%
(B) 5%
(C) 15%
(D) 20%
(E) 22.5%
Rationale: The actual answer is obtained by multiplying 175% by 70% and subtracting 100% from this total. That is: 175% × 70% = 122.5%; 122.5% − 100% = 122.5%.
Answer: E
Answer: (E) 22.5%
Question: In 1978, a kg of paper was sold at Rs25/-.If the paper rate increases at 1.5% more than the inflation rate which is 6.5% a year, then what wil be the cost of a kg of paper after 2 years?
(A) 29.12
(B) 29.16
(C) 30.12
(D) 32.65
(E) None of these
Rationale: 1.5%+6.5% = 8% ( rate increase every year)
25*8% = 2/- 25+2= 27
27*8% = 2.16/- 27+2.16 = 29.16 /-
ANSWER:B
Answer: (B) 29.16
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 21 more than the first integer. Find the three integers?
(A) 7, 9, 29
(B) 7, 2, 10
(C) 15,17,19
(D) 7, 9, 11
(E) 7, 9, 29
Rationale: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 21 => x = 15
Hence three consecutive odd integers are 15, 17 and 19
Answer:C
Answer: (C) 15,17,19
Question: If a train, travelling at a speed of 360 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 381 m
(B) 112 m
(C) 500 m
(D) 125 m
(E) 433 m
Rationale: C
C = 360 * 5/18 * 5 = 500 m
Answer: (C) 500 m
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 20 such machines produce in 4 minutes ?
(A) 648
(B) 1800
(C) 2700
(D) 10800
(E) 3600
Rationale: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
âˆ´ 6 Ã— 1 Ã— x = 20 Ã— 4 Ã— 270 â‡” x = 20x4x270/6= 3600 . Answer E
Answer: (E) 3600
Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
(A) 15
(B) 16
(C) 18
(D) 25
(E) 27
Rationale: Explanation :
Let the cost price of 1 article be z.
So, the cost price of 20 article = 20z ------------------------- (1)
Selling Price of 20 articles = 20z + 25% of 20z = 25z
=> Selling Price of 1 article = 25z/20 = (5/4)*z
=> Selling Price of x articles = (5/4)*z*x ------------------------- (2)
Given that Selling Price (S.P.) of x articles = Cost Price (C.P.) of 20 articles
=> (5/4)*z*x = 20z => x = 16
Answer : B
Answer: (B) 16
Question: A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% sunflower. If a customer purchases a mix of the two types of birdseed that is 50% sunflower, what percent of the mix is Brand A?
(A) 40%
(B) 45%
(C) 50 %
(D) 55 %
(E) 60 %
Rationale: Yes there is a simple method :
Consider the following method
Brand A : 40% millet and 60% sunflower
Brand B : 65% millet and 35% sunflower
Mix : 50% sunflower
Here the weighted average is 50%,
Now Brand A has 60 % sunflower, which is 10% more than the weighted average of mix = + 0.10 A --------------- I
Similarly, Brand B has 35 % sunflower, which is 15 % less than the weighted average of mix = - 0.15 B ------------ II
Now, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II
implies, 0.10 A = 0.15 B
Therefore A/B = 0.15/0.10 = 3/2
A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5
We have to find, percent of the mix is Brand A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 %
Here is a pictorial representation :
Brand A= 60%------------------------10% or 0.10 above average, A times-----------------Total below = + 0.10 A
----------------------------------------------------------------------------------------Average = 50% or 0.50
Brand B = 35 %--------------------------15% or 0.15 below average, B times-----------------Total above = - 0.15 B
Since the amount below the average has to equal the average above the average; therefore,
0.10 A = 0.15 B
A/B = 3/2
A:B: Total = 3:2:5
Therefore
A/Total = 3:5 = 60 %
Answer: E
Answer: (E) 60 %
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 772 m
(B) 167 m
(C) 245 m
(D) 267 m
(E) 127 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: (C) 245 m
Question: A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at p.a for 2 years. Find his gain in the transaction per year
(A) 112.50
(B) 119.5
(C) 112.58
(D) 112.57
(E) 112.52
Rationale: Explanation:
= Rs. (625 - 400)
= Rs. 225
Answer: A) Rs. 112.50
Answer: (A) 112.50