mathewhe/aqua_rat huggingface dataset:
Question: One side of a rectangular field is 14 m and one of its diagonal is 17 m. Find the area of the field.
(A) 134.4
(B) 120
(C) 150
(D) 180
(E) None
Rationale: Solution
Other side = √(17)2 - (14)2
= √289 - 196
= √93
= 9.6 m.
∴ Area = (14 x 9.6)m2 = 134.4 m2.
Answer A
Answer: (A) 134.4
Question: 337.62+8.591+34.4=?
(A) 370.611
(B) 380.511
(C) 380.611
(D) 426.97
(E) None of them
Rationale: 337.62
8.591
34.4
----------
380.611
Answer is C
Answer: (C) 380.611
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 40 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
(A) a. 43
(B) b. 45
(C) c. 55
(D) d. 68
(E) e. 60
Rationale: 40 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (40 * 12.5 * 100) / (2.5 * 200)
thus, X = 100
Thus, more men needed to finish the task = 100-40=60
hence Answer is E
Answer: (E) e. 60
Question: In the next Cricket World Cup T-20, Team W has decided to score 200 runs only through 4s and 6s. In how many ways can the Team W score these 200 runs?
(A) 13
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Team W can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.
So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.
Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17
Answer: D
Alternate solution: 4x + 6y = 200 --> 2x + 3y = 100
x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.
There are 17 even multiples of 3 between 0 and 100.
Answer: D
Answer: (D) 17
Question: Suresh borrowed some money at the rate of 4% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
(A) s.8500
(B) s.6000
(C) s.8500
(D) s.9000
(E) s.7000
Rationale: using the formula S.I=P*T*R/100
(x*4*3/100)+(x*9*5/100)+(x*13*3/100)=8160
x=8500
i.e money borrowed is Rs.8500
ANSWER:C
Answer: (C) s.8500
Question: Convert the 11/36 m/s into kilometers per hour?
(A) 1.7
(B) 1.5
(C) 1.3
(D) 1.1
(E) 1.2
Rationale: 11/36 m/s = 11/36 * 18/5 = 11/10
= 1.1 kmph.
Answer: D
Answer: (D) 1.1
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
(A) area=3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: S = (1 + 2 + 3) /2 = 3
=> No triangle exists
Answer: A
Answer: (A) area=3
Question: The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 30 more than the number who did not, and if receipts for registration and lunch totaled $75,360, how many people paid just for registration at the meeting?
(A) 700
(B) 800
(C) 600
(D) 1,500
(E) 1,800
Rationale: Hope this might be useful to you.
Let the number of people who have opted only to register = x
Now since the registration cost is 50$ per person, the total amount sums to = 50x $
As per the information given in the question, the number of registrants who paid for lunch was 30 more than the number who did not. That means, total number of people who registered and paid for lunch = 30 + x.
For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.
Total amount in this case sums to = 72(30 + x) = 2160 + 72x
Now, total amount received was 75360.
Thus, from the above data,
50x + 2160 + 72x = 75360
122x = 75360 - 2160
122x = 73200
x = 600.
Hence the correct Ans is C
Answer: (C) 600
Question: You have been given a physical balance and 5 weights of 45, 42, 37, 36 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 157 kgs.
(A) 160
(B) 151
(C) 154
(D) 153
(E) 152
Rationale: 45+42+67 = 154
Answer: C
Answer: (C) 154
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 42 . The largest number is:
(A) 28
(B) 32
(C) 36
(D) 50.4
(E) 45
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 42
15x = 126
x = 8.4
Largest number = 6x = 50.4.
ANSWER D
Answer: (D) 50.4
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 20 m
(B) 60 m
(C) 40 m
(D) 80 m
(E) 90 m
Rationale: 1/2 * d (10 + 6) = 640
d = 80
ANSWER:D
Answer: (D) 80 m
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?
(A) 80
(B) 86
(C) 92
(D) 94
(E) 96
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86
B)
Answer: (B) 86
Question: If n = 2×3×5×7×11×13, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
IV . n is Divisible by 35
(A) none and IV only
(B) b- II only
(C) III only
(D) I and III only
(E) e None
Rationale: 2×3×5×7×11×13= 2310
I. not divisible by 600
II 2310+19=2329 not divisible by 19
III. 2310+4/2= odd
iv. divisible by 35
A
Answer: (A) none and IV only
Question: 700 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
(A) 162
(B) 138
(C) 60
(D) 38
(E) 14
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 700 = 14
Answer: E
Answer: (E) 14
Question: A group of 16 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
(A)  E/(12 - n)
(B)  nE / [16(16-n)]
(C)  E/[12(12-n)]
(D)  (12 - n)/E
(E)  (12-n)E/(12n)
Rationale: total cost =E
no of people willing to participate initially =16
initial cost for each =E/16
when n people decided not to participate
Cost for each =E/16-n
B
Answer: (B)  nE / [16(16-n)]
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
(A) 8 days
(B) 10 days
(C) 11 days
(D) 12 days
(E) 14 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days
A)
Answer: (A) 8 days
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 27
(B) 29
(C) 17
(D) 10
(E) 86
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer:D
Answer: (D) 10
Question: The side of a square has the length of 5. What is the area of the region shaded?
(A) 48-8π
(B) 48-6 π
(C) 24+6π
(D) 16-5π
(E) 64-8π
Rationale: The area of a square whose side is 5 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is D.
Answer: (D) 16-5π
Question: x - y = 4
2x = 2y + 8
The system of equations above has how many solutions?
(A)  None
(B)  Exactly one
(C)  Exactly two
(D)  Exactly three
(E)  Infinitely many
Rationale: x-y=4 ---------------1
2x=2y+8 ---------------2
Divide equation 2 by 2:
2x/2=(2y+8)/2
x=y+4
x-y=3----------------3
Equation 1 and 3 are equal and thus have infinitely many solutions:
x-y=4
x=8, y=4
x=6, y=2
x=7, y=3
Ans:E
Answer: (E)  Infinitely many
Question: A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both spade. Find the probability of the lost card being a spade.
(A) 10/50
(B) 10/53
(C) 11/50
(D) 11/53
(E) 12/53
Rationale: total cards:52
drawn cards(spade):2
now, actual present total cards=total cards-drawn cards=52-2=50
total spade=spade-drawn cards(spade)=13-2=11
so,probability=11/50
ANSWER:C
Answer: (C) 11/50
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 15 percent during the third year. What is the value of the account today?
(A) $10,350
(B) $9817.50
(C) $10,500
(D) $11,500
(E) $12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.85 = 10,395
Answer B is correct.
Answer: (B) $9817.50
Question: Integer d is the product of the integers a,b, and c and 1<a<b<c. If the remainder when 233 is divided by d is 79, what is the value of a+c?
(A) 7
(B) 9
(C) 13
(D) 14
(E) 18
Rationale: 79 is the remainder, therefore the number(a*b*c) or multiple of the number we need is 79 less than 233
Hence 233- 79 = 154
Therefore, 154 is either a number we want or it is a multiple of the number we want
But the largest factor of 154 is 77 because 77 * 2 =154
But 77 is less than 79 hence it can not be a number
Thus 154 is the number we want
a*b*c= 154
now factorize 154 =1*2*7*11 all are prime
Also we know 1<a<b<c
thus a = 2 and c = 11
therefore a+c= 2+11= 13
ANSWER:C
Answer: (C) 13
Question: If 2/X - 2 = 3/X - 3, then X =
(A) -3/2
(B) 2/3
(C) -1
(D) 1
(E) 3/2
Rationale: We're given the equation 2/X - 2 = 3/X - 3. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...
2X/X - 2X = 3X/X - 3X
We can then eliminate that denominator, which gives us....
2 - 2X = 3 - 3X
1 = X
D
Answer: (D) 1
Question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
(A) 535 m
(B) 100 m
(C) 186 m
(D) 168 m
(E) 150 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 6
= 100 m
Answer:B
Answer: (B) 100 m
Question: The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
(A) 120
(B) 388
(C) 278
(D) 298
(E) 271
Rationale: 4*5*6 = 120
Answer: A
Answer: (A) 120
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 30
(B) 36
(C) 40
(D) 45
(E) 50
Rationale: Speed => x
two trains = 2x
2x = 120+120/12==>2x=20
x=10
speed = 10 m/sec = 10*18/5=36
ANSWER B
Answer: (B) 36
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 6 min
(B) 7 min
(C) 9 min
(D) 4 min
(E) 2 min
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute
= (1/6 - 1/10)
= 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) '
= 6 min.
So, the tank will be emptied in 6 min.
Answer:A
Answer: (A) 6 min
Question: The speed of a boat in still water is 30 kmph. What is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time?
(A) 11 kmph
(B) 10 kmph
(C) 12 kmph
(D) 16 kmph
(E) 15 kmph
Rationale: X = the speed of the stream
(30 + X) / (30 - X) = 2/1
30+ X = 60 - 2X
3X = 30
X = 10 km/hour
If the speed of the stream is 10km/hour, then the 'downstream' speed of the boat is 30+10= 40km/hour and the 'upstream' speed of the boat is 30-10 = 20km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x40 = 80km downstream and 2x20 = 40 km/hour upstream.
Answer : B
Answer: (B) 10 kmph
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:5
(B) 3:4
(C) 3:8
(D) 3:9
(E) 3:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer:B
Answer: (B) 3:4
Question: Jill has 21 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
(A) 3
(B) 6
(C) 9
(D) 36
(E) 14
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 21 1 3/4w = 21w=12The total number of jars = 3w =36Answer: D
Answer: (D) 36
Question: There are 10 magazines lying on a table; 6 are sports magazines and the other 4 are current affairs magazines. If 4 magazines are to be selected at random from the 10 magazines, what is the probability that at least one of the current affairs magazines will be selected?
(A) 2/5
(B) 3/5
(C) 4/5
(D) 6/5
(E) 7/5
Rationale: Total probability=10C4=210
4C4 +4C3*6C1+4C2*6C2+4C1*6C3=1+24+21+80=126
therefore the probability that at least one of the current affairs magazines will be selected= 126/210=3/5
answer is B
Answer: (B) 3/5
Question: 5a=15625. Find 5a-3
(A) 125
(B) 228
(C) 270
(D) 778
(E) 101
Rationale: ANSWER : A
Answer: (A) 125
Question: A factory has a fixed cost of $41,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 14,000
(C) 16,400
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =41000
no of items required = 41000/2.5 = 16400
Answer: C
Answer: (C) 16,400
Question: You are renting an apartment and you need √729 for each side, how many feet are you looking to measure?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 27
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 729
Answer E
Answer: (E) 27
Question: Find the area of trapezium whose parallel sides are 20 cm and 10 cm long, and the distance between them is 10 cm.
(A) 187 cm2
(B) 185 cm2
(C) 150 cm2
(D) 185 cm2
(E) 195 cm2
Rationale: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 10) * (10) = 150 cm2
Answer: Option C
Answer: (C) 150 cm2
Question: A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
(A) 5 km/hr
(B) 6 km/hr
(C) 12 km/hr
(D) 17 km/hr
(E) 18km/hr
Rationale: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr
Ans: E
Answer: (E) 18km/hr
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
(A) 260 cm2
(B) 240 cm2
(C) 280 cm2
(D) 220 cm2
(E) 250 cm2
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
ANSWER:B
Answer: (B) 240 cm2
Question: The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments.
(A) 2:3:4
(B) 3:5:6
(C) 3:2:4
(D) 2:4:3
(E) 2:5:3
Rationale: The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:14.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (14/7) = 1:3/2:2 = 2:3:4.
ANSWER:A
Answer: (A) 2:3:4
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected?
(A) 159
(B) 194
(C) 210
(D) 209
(E) 166
Rationale: Out of 10 students 4 children should to be selected.
So the combination will be 10C4.
10C4=10!/6!*4!=10*9*8*7*6!/6!*(4*3*2*1)
10C4=210
There are 210 differect possible ways to select 4 children out of 10 students.
Answer: (C) 210
Question: A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: if average of 3 is 9 so sum of 3 should be 27
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 10 and 10
so a has to be 7
E
Answer: (E) 7
Question: At Jerri’s Pet Shop, 60 cups of bird seed are used every 5 days to feed 20 parakeets. How many cups of bird seed would be required to feed 10 parakeets for 5 days?
(A) 45.6
(B) 20
(C) 9
(D) 30
(E) 65
Rationale: Let's go step-by-step.
60 cups are used over a 5 day period, which means 12 cups a day. This feeds 20 parakeets, which means each parakeet needs .60 of a cup every day.
For 10 parakeets, we need 10*.60cups = 6 cups a day. Over 5 days, we need 30 cups. Choice D.
Answer: (D) 30
Question: Which of the following must be subtracted from 2^48 so that the resulting integer will be a multiple of 3?
(A) 2
(B) 1
(C) 3
(D) 4
(E) 5
Rationale: {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : B
Answer: (B) 1
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
(A) 2400
(B) 2408
(C) 2487
(D) 2429
(E) 2123
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer:A
Answer: (A) 2400
Question: A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
(A) 26 minutes and 18 seconds
(B) 45 minutes
(C) 42 minutes and 36 seconds
(D) 46 minutes and 12 seconds
(E) 48minutes and 15 seconds
Rationale: L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.
answer :D
Answer: (D) 46 minutes and 12 seconds
Question: What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
(A) 9800
(B) 9600
(C) 9400
(D) 9200
(E) 9000
Rationale: Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
Answer: Option B
Answer: (B) 9600
Question: If the average (arithmetic mean) of (2a+16) and (3a-8) is 69, what is the value of a?
(A) 26
(B) 30
(C) 28
(D) 36
(E) 42
Rationale: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 69
a= 26
The answer is A.
Answer: (A) 26
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 22
(B) 96
(C) 60
(D) 88
(E) 12
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/5 = 3x => x = 40/3.
So, speed of the faster train = 80/3 = 80/3 * 18/5 = 96 km/hr.
Answer:B
Answer: (B) 96
Question: 1, 0.2, 0.08, 0.48, 0.0384, ____
(A) 0.0584
(B) 0.0484
(C) 0.0434
(D) 0.0384
(E) None
Rationale: 1, 0.2, 0.08, 0.48, 0.0384, .....
1*0.2=0.2
0.2*0.4=0.08
0.08*0.6=0.048
0.048*0.8=0.0384
So 0.0384*1=0.0384
ANSWER:D
Answer: (D) 0.0384
Question: The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?
(A) 32 kg
(B) 36 kg
(C) 40 kg
(D) 44 kg
(E) None of these
Rationale: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 45
=> 5k = 45 => k = 9
Therefore the weight of the lightest boy
= 4k = 4(9) = 36 kg.
ANSWER:B
Answer: (B) 36 kg
Question: A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 1
II. -4
III. 5
(A) I only
(B) II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
Answer: (C) I and III only
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 19 : 9
(B) 19 : 1
(C) 19 : 2
(D) 19 : 5
(E) 19 : 3
Rationale: Explanation:
Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Answer:D
Answer: (D) 19 : 5
Question: A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 470 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?
(A) 400
(B) 475
(C) 550
(D) 560
(E) 700
Rationale: Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour.
7A+11B=470 ---(1)
8A+22C=600 ---(2)
Dividing (2) by 2
4A+11C=300.....(3)
Adding (1)(3)
11A+11B+11C = 770
A+B+C=70 per hour
So for eight hrs = 70*8 = 560 = Answer = D
Answer: (D) 560
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 625 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 8 units?
(A) 140 sq.units
(B) 158 sq.units
(C) 187 sq.units
(D) 80 sq.units
(E) 815 sq.units
Rationale: Given that the area of the square = 625 sq.units
=> Side of square = √625 = 25 units
The radius of the circle = side of the square =25 units
Length of the rectangle = 2/5 * 25 = 10 units
Given that breadth = 8 units
Area of the rectangle = lb = 10 * 8 = 80 sq.units
Answer: D
Answer: (D) 80 sq.units
Question: If the a radio is sold for rs 490 and sold for rs 465.50.find loss%.
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Option D
Answer: (D) 5
Question: 120 liters of a mixture contains milk and water in the ratio 4:2. If 10 liters of this mixture be replaced by 10 liters of milk, the ratio of milk to water in the new mixture would be?
(A) 8:6
(B) 9:3
(C) 9:4
(D) 9:6
(E) 8:2
Rationale: Quantity of milk in 120 liters if mix = 120*4/6 =80 liters
Quantity of milk in 130 liters of new mix = 80+10 = 90liters
Quantity of water in it = 130-90 = 40 liters
Ratio of milk and water in new mix = 90:40 = 9:4
Answer is C
Answer: (C) 9:4
Question: What is the sum of 80 consecutive integers from -39 inclusive, in a increasing order?
(A) -29
(B) 39
(C) -30
(D) 40
(E) 60
Rationale: From -39 to -1 --> 39 nos.
zero --> 1 number
from +1 to +39 --> 39 nos.
When we add up nos. from -39 to +39 sum will be zero. Total 79 nos will be added.
80th number will be 40.
Sum of these 80 nos. = 40.
D is the answer.
Answer: (D) 40