mathewhe/aqua_rat huggingface dataset:
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 8 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 1 days
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/10 + 10/140) = (1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer: C
Answer: (C) 7 days
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1300, what is the reduced price for kg?
(A) s.40
(B) s.65
(C) s.49
(D) s.41
(E) s.42
Rationale: 1300*(25/100) = 325 ---- 5
? ---- 1
=> Rs.65
Answer: B
Answer: (B) s.65
Question: If 20 typists can type 46 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
(A) 63
(B) 72
(C) 144
(D) 216
(E) 207
Rationale: 20 typists can type 46 letters, so 30 typists can type = 46*30/20
46*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 46*30*60/20*20= 207
E is the answer
Answer: (E) 207
Question: If (A-B-C+D = 18) and (A+B-C-D = 6), what is the value of (B-D)^2?
(A) 4.
(B) 8.
(C) 12.
(D) 16.
(E) 36.
Rationale: EQ1: A - B - C + D = 18
EQ2: A + B - C - D = 6
(1) Subtract EQ1 from EQ2
A - B - C + D = 18
- A +B - C - D = 6
------------------------
-2B + 2D = 12
(2) Simplify
-B + D = 6
B - D = -6
(B-D)^2 = (-6)^2 = 36
My answer: E
Answer: (E) 36.
Question: If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 2
II. 1
III. -3
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.
n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.
It can be 1 for n=2 and 2 for n=5.
Answer: C.
Answer: (C) I and II only
Question: How many repeat sequence of three consecutive numbers are there in the given sequence?
6 9 6 2 4 2 9 6 2 9 2 6 9 4 9 6 2 6 9 2 4
(A) 3
(B) 2
(C) 1
(D) 4
(E) 5
Rationale: 962 repeated 3times
ANSWER:A
Answer: (A) 3
Question: List I: 3, 6, 12, 19
List II: x, 3, 6, 8, 19
(A)  6
(B)  7
(C)  8
(D)  9
(E)  10
Rationale: We start by calculating the median of the numbers of list I: 3, 6, 12, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.
median = (6 + 12)/2
median = 18/2
median =9
The median of list I is 9.
Looking at list II: x, 3, 6,12, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 9 and therefore x is 9.
The answer is D.
Answer: (D)  9
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 31 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 4 books, how many shelves does the bookcase have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
11x - 31 = 7(x-1) + 4
4x = 28
x = 7
The answer is C.
Answer: (C) 7
Question: 1804 x 1804 = ?
(A) A)3254416
(B) B)3624216
(C) C)3624316
(D) D)3625116
(E) E)3625216
Rationale: 1804 x 1804 = (1804)2
= (1800 + 4)2
= (1800)2 + (4)2 + (2 x 1800 x 4)
= 3240000 + 16 + 14400.
= 3254416.
A)
Answer: (A) A)3254416
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
(A) 27
(B) 29
(C) 30
(D) 31
(E) 33
Rationale: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
D
Answer: (D) 31
Question: The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 8 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?
(A) 20 km
(B) 30 km
(C) 40 km
(D) 50 km
(E) 60 km
Rationale: Number of stops in an hour: 60/5 = 12
Distance between stops: 60/12 = 5 km
Distance between Yahya's house and Pinedale Mall: 5 x 8 = 40 km
IMO, correct answer is "C."
Answer: (C) 40 km
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 271
(B) 476
(C) 277
(D) 9898
(E) 212
Rationale: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476
Answer: B
Answer: (B) 476
Question: Three coins are tossed. What is the probability of getting at most two tails?
(A) 7/8
(B) 1/8
(C) 1/2
(D) 1/7
(E) 2/5
Rationale: Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 × 2 × 2 = 8
(∵ i.e., S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH})
E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}
Hence, n(E) = 7
P(E) = n(E)/n(S)=7/8
Answer is A
Answer: (A) 7/8
Question: A salesman`s commission is 5% on all sales upto Rs.10,000 and 4% on all sales exceeding this.He remits Rs.31,100 to his parent company after deducing his commission . Find the total sales.
(A) 32500
(B) 2500
(C) 22500
(D) 30000
(E) 40000
Rationale: Let his total sales be Rs.x.Now(Total sales) – (Commission )=Rs.31,100
x-[(5% of 10000 + 4% of (x-10000)]=31,100
x-[((5/100)*10000 + (4/100)*(x-10000)]=31,100
x-500-((x-10000)/25)=31,100
x-(x/25)=31200  24x/25=31200x=[(31200*25)/24)=32,500.
Total sales=Rs.32,500
ANSWER A
Answer: (A) 32500
Question: The length of the bridge, which a train 110 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 10 m
(B) 16 m
(C) 245 m
(D) 265 m
(E) 27 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(110 + x) = 750 => x
= 265 m.
Answer: D
Answer: (D) 265 m
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 16 km
(B) 20 km
(C) 18 km
(D) 15 km
(E) 12 km
Rationale: Distance = Relative Speed * Time
= (2 + 3) * 4 = 20 km
[ They are travelling in the opposite direction, relative speed = sum of the speeds].
Answer: B
Answer: (B) 20 km
Question: In western Europe, P bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?
(A) 9% of (x/100)
(B) 14% of (x/100)
(C) 75% of (x/100)
(D) 9% of P
(E) 14% of x
Rationale: Moreover is't question actually asking the the difference between the {(Quantity Produced + Quantity Sold )P in 1990 - (Quantity Produced + Quantity Sold ) in 1993}
Though the Quantity sold in both the years is same it actually boils down to (Quantity Produced in 1990 ) in (Quantity Produced in 1993)=D
Answer: (D) 9% of P
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 5512
(B) 2800
(C) 5550
(D) 2787
(E) 2309
Rationale: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100
= 66600.
Average monthly production of salt for that year = 66600/12
= 5550.
Answer:C
Answer: (C) 5550
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 245
(B) 225
(C) 200
(D) 250
(E) 300
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
ANSWER A
Answer: (A) 245
Question: Simple interest on a certain sum of money for 5 years at 8% per annum is half the compound interest on Rs. 8000 for 2 years at 15% per annum. The sum placed on simple interest is
(A) Rs.3225
(B) Rs.2580
(C) Rs.8000
(D) Rs.1290
(E) None
Rationale: Solution
C.I.	=Rs[8000x(1+15/100)Â²-8000]
Rs.(8000x115/100x115/100-8000)	= Rs.2580.
Sum	=Rs. [1290x100 /5x8]
= Rs.3225.
Answer A
Answer: (A) Rs.3225
Question: Complete the series
13, 9, 5, 1, ...
(A) -4
(B) 0
(C) 3
(D) -2
(E) 3
Rationale: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option E) -3
Answer: (E) 3
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 35% water?
(A) 1.3 kg
(B) 1.5 kg
(C) 1.7 kg
(D) 1.9 kg
(E) None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 65% (100-35).
Therefore 0.5 X Amount of flower-nectar = 0.65 X Amount of honey = 0.65 X 1 kg
Therefore amount of flower-nectar needed =
(0.65/0.51)kg=1.3 kgs
Answer : A
Answer: (A) 1.3 kg
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced.How many parts the company made?
(A) 675
(B) 778
(C) 654
(D) 412
(E) 589
Rationale: Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
correct answer is A)675
Answer: (A) 675
Question: A train 110 meters long completely crosses a 280 meters long bridge in 38 seconds. What is the speed of the train is?
(A) 32
(B) 45
(C) 40
(D) 66
(E) 09
Rationale: S = (110 + 280 /38 = 390/38 * 18/5 = 40
Answer: C
Answer: (C) 40
Question: In a barrel of juice there is 15 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 2:1.
(C) 3:1.
(D) 4:1.
(E) 3:4.
Rationale: Juice barrel : beer Barrel = 15:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 15/80 costs 3/4, ie 15J / 80B = 3/4.
Solving for J/B, we get 4:1
Answer D.
Answer: (D) 4:1.
Question: The compound ratio of 5:6, 3:2 and 4:5?
(A) 1:1
(B) 1:87
(C) 1:6
(D) 1:9
(E) 1:2
Rationale: 5/6 * 3/2 * 4/5 = 1/1
1:1
Answer: A
Answer: (A) 1:1
Question: A type of mixture is prepared by mixing brand at Rs.9 a kg with brand B at Rs.4 a kg.If a mixtue is worth rupees 7 a kg,how many kgs of brand A are needed to make 40 kgs of the mixture?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: 9 4
7
(7-4) 3 2 (9-7)
thus ratio would be 3:2
and thus 3x+2x=40
so x=8 and 3x=24.
thus A type of mixture would be of 24 kg.
ANSWER:D
Answer: (D) 24
Question: the cyclist going at a constant rate of 20 miles per hour is passed by a motor-cyclist traveling in the same direction along the same path at 60 miles per hour. the motor-cyclist stops to wait for the cyclist 10 minutes after passing her, while the cyclist continues to travel at constant rate, how many minutes must the motor-cyclist wait until the cyclist catches up?
(A) 10
(B) 20
(C) 25
(D) 30
(E) 40
Rationale: For the 10 minutes the motor-cyclist continues to overtake the cyclist, she is going at 40 miles per hour faster than the cyclist.
Once the motor-cyclist stops, the cyclist is going at 20 miles per hour while the motor-cyclist is at rest
So the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds. 40/20 * 10 or 20 minutes
Answer is (B)
Answer: (B) 20
Question: Divide Rs.32000 in the ratio 3:5?
(A) 12000, 20000
(B) 12000, 200098
(C) 12000, 20007
(D) 12000, 20006
(E) 12000, 20001
Rationale: 3/8 * 32000 = 12000
5/8 * 32000 = 20000
Answer: A
Answer: (A) 12000, 20000
Question: A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?
(A) 1/35
(B) 2/35
(C) 3/45
(D) 4/25
(E) 4/27
Rationale: Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35
A)
Answer: (A) 1/35
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32
(B) 82
(C) 83
(D) 89
(E) 73
Rationale: Explanation:
S = (100 + 300)/45 = 400/45 * 18/5 = 32
Answer: Option A
Answer: (A) 32
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 287
(B) 891
(C) 277
(D) 666
(E) 161
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer:B
Answer: (B) 891
Question: In an examination, 25% of total students failed in Hindi, 50% failed in English and 25% in both. The percentage of these who passed in both the subjects is :
(A) 23
(B) 37
(C) 28
(D) 40
(E) 50
Rationale: Explanation:
Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)
Fail in Hindi or English = 25 + 50 â€“ 25 = 50
Therefore students who passed = 100 â€“ 50 = 50.
Answer: E
Answer: (E) 50
Question: Which of the below number is the odd one out?
(A) 36142
(B) 36119
(C) 84129
(D) 50246
(E) 72927
Rationale: D
50246
All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.
Answer is D
Answer: (D) 50246
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 240
(B) 235
(C) 245
(D) 250
(E) 260
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: Option C
Answer: (C) 245
Question: P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
(A) 9(3/5) days
(B) 9(1/5) days
(C) 9(2/5) days
(D) 10 days
(E) 10(1/5) days
Rationale: Explanation :
Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days
Answer : Option A
Answer: (A) 9(3/5) days
Question: If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?
(A) 0 and 3/20
(B) 3/20 and 1/5
(C) 1/5 and 1/4
(D) 1/4 and 3/10
(E) 3/10 and 1/2
Rationale: A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts
B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts
C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts
D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts
E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest.
Answer (E)
Answer: (E) 3/10 and 1/2
Question: Sohan purchased a horse for Rs.2000 and sold it to Mohan at a loss of 10 percent. Mohan sold it to Sham at a loss of 10 percent while sham sold it to Gopi at a gain of 10 percent. The amount Gopi paid for it would be
(A) 2399
(B) 788
(C) 1782
(D) 67591
(E) 1122
Rationale: Explanation:
Cost price = 2000
Selling price = 90% (2000) = 1800.
Mohan sold this to Sham at a loss of 10%. So selling price = 90% (1800) = 1620
Sham sold this at 10% profit. So selling price = 110% (1620) = 1782
Answer:C
Answer: (C) 1782
Question: A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: The distance between the nest and the ditch is 200 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 200 = 6000.
D = ST
6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km)
D)
Answer: (D) 4
Question: If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b + c ?
(A) 12
(B) 2
(C) -1
(D) -3
(E) -4
Rationale: consectutive even , X , X + 2 , X + 4 where X = Even
now subtract X + (X+2) + (X+4)
doing this leaves us with 3X + 6
what even number can we substitute in X to yield an answer choice
A works 12 (plug in 2 for X)
Answer: (A) 12
Question: A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
(A) 1400
(B) 1500
(C) 1600
(D) 1200
(E) None of these
Rationale: Explanation :
Assume that the total profit is x.
Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3: 2
=> A's profit = (95x/100) * (3/5) = 855
=> 95x/100 = 855*5/3 = 285*5 = 1425
=> x = 1425 * 100/95 = 285 * 100/19 = 1500
Hence the total profit = 1500. Answer : Option B
Answer: (B) 1500
Question: A box contains eight bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
(A) 10/35
(B) 11/35
(C) 9/35
(D) 8/35
(E) 6/35
Rationale: Required probability = (4C3 . 4C1)/8C4 = (4 * 4)/70
= 8/35
Answer:D
Answer: (D) 8/35
Question: Two thirds of the roads from A to B are at least 5 miles long, and 1/2 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
(A) 5/6
(B) 1/4
(C) 2/3
(D) 3/4
(E) 11/12
Rationale: So please:
Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-1/3*1/2=5/6.
Answer: A.
Answer: (A) 5/6
Question: I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 1 senior and 1 junior staff officers, how many possible committees are there?
(A) 12
(B) 44
(C) 56
(D) 24
(E) 200
Rationale: 6C1*4C1
=24=D
Answer: (D) 24
Question: A train 360 m long is running at a speed of 42 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 29 sec
(C) 26 sec
(D) 27 sec
(E) 43 sec
Rationale: Speed = 42 * 5/18 = 35/3 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 3/35
= 43 sec
Answer:E
Answer: (E) 43 sec
Question: Some people are standing square. From them 32 are removed and then form a small square and
then 8 more removed. now we cannot form the square. so how many people are there at the
beginning?
(A) 31
(B) 32
(C) 33
(D) 34
(E) can't be determined
Rationale: We should find the two square numbers whose difference is 32. Starting from 9,16,25,36,49,64,81,100,....
We observe 81-49=32 & 49-8=41 which is not a square.
ANSWER:E
Answer: (E) can't be determined
Question: 28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
(A) 25
(B) 30
(C) 50
(D) 55
(E) 70
Rationale: I came up with (E) 70
Think of 100 people total:
From the first fact, 28 of these are women with fair hair.
From the second fact, these 20 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair.
Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women.
70%E
Answer: (E) 70
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
(A) 12
(B) 16
(C) 24
(D) 48
(E) 60
Rationale: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
Answer: Option D
Answer: (D) 48
Question: Working simultaneously at their respective constant rates, machine A and B produces 20 widgets in c hours. Working alone at its constant rate, Machine A produces 20 widgets in 'a' hours.In terms of a and c, how many hours does it take Machine B, working alone at its constant rate, to produce 10 widgets
(A) ac/a+c
(B) 2ac/a+c
(C) ac/2a+2c
(D) ac/2a-2c
(E) ac/2c-2a
Rationale: Let the individual rates be R(a) and R(b) for machines a and b respectively. Given than combined rate is 20 widgets in c hours => 20/c
R(a) + R(b) = 20/c
Also given is the individual rate for machine a = R(a) = 20/a
Therefore, R(a) + R(b) = 20/c => 20/a + R(b) = 20/c => R(b) = 20/c - 20/a = 20(a-c)/ac = 20/(ac/(a-c)), which basically means that b produces 20 widgets in ac/a-c Hrs. We have to calculate how much does it take to produce 10 widgets. So divide the rate by 2 which gives us ac/2(a-c).
Hence the answer is D
Answer: (D) ac/2a-2c
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.6, 0.7, and 0.8 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
(A) 0.006
(B) 0.012
(C) 0.024
(D) 0.029
(E) 0.904
Rationale: The probability that eachdoesn'thit is: 0.4, 0.3, and 0.2. When we have multiple independent events, we multiply the probabilities:
.4*.3*.2 = 0.024.
Option: C
Answer: (C) 0.024
Question: Find the smallest number that must be added to 1780 to make it a perfect square.
(A) 17
(B) 42
(C) 69
(D) 47
(E) 52
Rationale: 4 1780 (42
16
82	180
164
16
Number to be added = (43)2 - 1780 = 1849 - 1780 = 69.
ANSWER C
Answer: (C) 69
Question: square of 99=?
(A) 9001
(B) 9621
(C) 9431
(D) 9801
(E) 9601
Rationale: Square of (100-1)=10000+1-200
9801
answer D
Answer: (D) 9801
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1:96
(B) 1:76
(C) 1:92
(D) 1:28
(E) 1:39
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: A
Answer: (A) 1:96
Question: The positive number a is q percent greater than the positive number b, which is z percent less than a itself. If a is increased by z percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: Let q = 10% then z = 100/11 %
let b = 100 then a = 110
after increasing a by z and decreasing by q we get c= 108
therefore c<a
C it is answer
Answer: (C) III only
Question: Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?
(A) 234
(B) 345
(C) 267
(D) 355
(E) 512
Rationale: Let suppose total number of students in class are X.
Then from the question we can conclude it that,
X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512
E
Answer: (E) 512