mathewhe/aqua_rat huggingface dataset:
Question: Machine A and machine B are each used to manufacture 550 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?
(A) 5.5
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: time taken by B = t
time taken by A = t+10
qty produced by A = q
qty produced by B = 1.1 q
for B: t(1.1q) =550
qt=500
for A: (t+10)(q) =550
qt+10q=550
500+10q=550
q=5
so A can produce 5/hour.
then B can produce = 5(1.1)=5.5/hour.
A
Answer: (A) 5.5
Question: Which of the following numbers is two more than the square of an odd integer?
(A) 14,173
(B) 14,361
(C) 15,131
(D) 15,737
(E) 15,981
Rationale: If a square has an odd unit's digit, then its ten's digit must be even.
Only 15,131-2 = 15,129 satisfies this condition.
The answer is C.
Answer: (C) 15,131
Question: How many positive integers S less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
(A) 19
(B) 18
(C) 17
(D) 16
(E) 15
Rationale: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?
The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?
1, 3, 5, 7
None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E
Answer: (E) 15
Question: Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 16 km apart, if they walk in the same direction?
(A) 5hours
(B) 6hours
(C) 8hours
(D) 16hours
(E) 12hours
Rationale: To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 16 =8 hours
Answer is C
Answer: (C) 8hours
Question: John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 19.9
(D) 20.9
(E) 21
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B
Answer: (B) 19.7
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother six years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 7 years
(E) 8 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 6) years = 44 years.
Required difference = (44 - 36) years = 8 years.
Answer: Option E
Answer: (E) 8 years
Question: A group of tourists wants to visit only two or three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
(A) 24
(B) 28
(C) 32
(D) 36
(E) 40
Rationale: The number of ways to choose two cities is 4C2=6.
The number of itineraries for each pair of 2 cities is 2!.
So the number of itineraries to two cities is 6*2!=12.
The number of ways to choose three cities is 4C3=4.
The number of itineraries for each group of 3 cities is 3!.
So the number of itineraries to three cities is 4*3!=24.
The total number of itineraries is 12+24=36.
The answer is D.
Answer: (D) 36
Question: The difference between a number and its two-fifth is 510. What is 12% of that number?
(A) 58
(B) 110
(C) 76
(D) 102
(E) 86
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
12% of 850 = 102.
Answer:D
Answer: (D) 102
Question: A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then?
(A) 144
(B) 121
(C) 256
(D) 320
(E) 169
Rationale: If each of 6 tractors ploughed 120 hectares a day and they finished the work in 4 days, then the whole field is: 120⋅6⋅4=720⋅4=2880 hectares. Let's suppose that each of the four tractors ploughed x hectares a day. Therefore in 5 days they ploughed
5⋅4⋅x=20⋅x hectares, which equals the area of the whole field, 2880 hectares.
So, we get 20x=2880
x=288020=144. Hence, each of the four tractors would plough 144 hectares a day.
So answer is A
Answer: (A) 144
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 10 pages.
(A) 8
(B) 10
(C) 12
(D) 4
(E) 16
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(10/2.5)=4 hrs
ANSWER:D
Answer: (D) 4
Question: What is the absolute value of twice the difference of the roots of the equation W=5y^2 − 20y + 15 = 0 ?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: W=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.
Answer: E.
Answer: (E)  4
Question: The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z?
(A) 35
(B) 33
(C) 28
(D) 21
(E) 15
Rationale: The smallest possible product is 33 which is 3*11.
All other products are too big.
The answer is B.
Answer: (B) 33
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction Z of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
(A) 1/(3x)
(B) 3x/(x-3)
(C) (x – 3)/(3x)
(D) x/(x-3)
(E) (x-3)/x
Rationale: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete Z=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Answer: (C) (x – 3)/(3x)
Question: The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool?
(A) 1400
(B) 1600
(C) 1800
(D) 1500
(E) 2000
Rationale: volume of pool = 80*150*10 cu.ft ,100% full = 60*100*10*1 cu.ft water is available to drain.
draining capacity =60 cu.ft /min therefore time taken = 80*150*10*1/ 60 min= 2000 min
E
Answer: (E) 2000
Question: If one-third of one-fourth of a number is 25, then three-tenth of that number is:
A. 35
(A) 23
(B) 90
(C) 26
(D) 54
(E) 01
Rationale: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 25
Number is 300 then 300 Ã— 3/10 = 90
Answer: B
Answer: (B) 90
Question: 13 sheeps and 9 pigs were bought for Rs. 1291.85.If the average price of a sheep be Rs. 74. What
is the average price of a pig.
(A) Rs. 26.65
(B) Rs. 36.55
(C) Rs. 35.65
(D) Rs. 36.65
(E) Rs. 33.65
Rationale: Average price of a sheep = Rs. 74
: . Total price of 13 sheeps
= (74*13) = Rs. 962
But, total price of 13 sheeps and 9 pigs
= Rs. 1291.85
Total price of 9 pigs
= Rs. (1291.85-962) = Rs. 329.85
Hence, average price of a pig
= (329.85/9) = Rs. 36.65
Answer is D.
Answer: (D) Rs. 36.65
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is ?
(A) 17/27
(B) 17/25
(C) 17/17
(D) 17/88
(E) 17/22
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 =17/25.
Answer:B
Answer: (B) 17/25
Question: What percent is 36 paisa's of 12 rupees?
(A) 3 %
(B) 4 %
(C) 5 %
(D) 6 %
(E) 7 %
Rationale: 12 Rupees = 1200paisa's
36/1200 × 100 = 3/12
12/3 = 3 %
A
Answer: (A) 3 %
Question: add 11% of 36 and 12% of 64.
(A) 9.5
(B) 10.5
(C) 11.5
(D) 12
(E) 15
Rationale: 11% of 36 + 12% of 64
36*11/100+64*12/100
3.9+7.6=11.5
answer C
Answer: (C) 11.5
Question: Without stoppages, a train travels certain distance with an average speed of 400 km/h, and with stoppages, it covers the same distance with an average speed of 360 km/h. How many minutes per hour the train stops ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Due to stoppages, it covers 40 km less .
Time taken to cover 40 km = 40â„400h = 1â„10h
= 1â„10 Ã— 60 min = 6 min
Answer D
Answer: (D) 6
Question: 30 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
(A) 625
(B) 870
(C) 576
(D) 676
(E) 700
Rationale: we can go in any bus out of the 30 buses.
Hence He can go in 30 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 29 ways.
Total number of ways = 30 x 29 = 870
ANSWER:B
Answer: (B) 870
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 240 envelopes
(A) 6 minutes
(B) 5 minutes
(C) 7 minutes
(D) 3 minutes
(E) 4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 240 envelopes they will take 240/60 mins. i.e., 4 mins.
ANSWER:E
Answer: (E) 4 minutes
Question: A man buys 25 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 25 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
(A) 55
(B) 82
(C) 73
(D) 75
(E) 85
Rationale: 20% in 25 lts is5. So water = 25-5 = 20 lts. 30% of 25 lts =7.5. So water in 2nd mixture = 25-7.5 =17.5 lts. Now total quantity = 25 + 25 =50 lts. Total water in it will be 20 + 17.5= 37.5 lts. % of water = (100*37.5)/50 = 75.
ANSWER:D
Answer: (D) 75
Question: 1300 boys and 700 girls are examined in a test; 52% of the boys and 43% of the girls pass. The percentage of the total who failed is ?
(A) A)63.3%
(B) B)52.4%
(C) C)81.2%
(D) D)51.15%
(E) E)69.1%
Rationale: Total number of students = 1300+700 = 2000
Number of students passed = (52% of 1300+43% of 700) = 676+301 = 977
number of failures = 1023*100/2000= 51.15%
Answer is D
Answer: (D) D)51.15%
Question: he population of a city is 160,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
(A) 1797787
(B) 1797723
(C) 179776
(D) 179728
(E) 179718
Rationale: Population after n years = P [1 + (R/100)]2
Population after 2 years = 160000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 179776
ANSWER: C
Answer: (C) 179776
Question: How many positive integers less than 50 are multiples of 2 but NOT multiples of 5?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 20
Rationale: IMO the answer is C (8 numbers)
The LCM of 2 and 5 is 10.
If x <50 and x is divisible by 2 not by 5 --> x is NOT divisible by 10.
From 1--> 50, we have 5 numbers which is divisible by 10: 10, 20, 30, 40, 50.
From 1-->50, we have (50-2)/2 +1 = 25 numbers divisible by 2.
Therefore, our answer is 25-5 = 20 numbers.
E
Answer: (E) 20
Question: Rewrite (10^38) – 85 as a base 10 integer, what is the sum of the digits in that integer?
(A) 354
(B) 357
(C) 330
(D) 370
(E) 360
Rationale: We know that (10^38) is ending 00, so (10^38) – 85=9....9915
total number of digits in (10^38) – 85 is 38, or 36 digits of 9 and two digits 1 and 5.
answer choice is 36*9+6=330
Answer is C 330
Answer: (C) 330
Question: JC has to visit at least 2 European cities on his vacation trip. If he can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can JC create?
(A) 12
(B) 36
(C) 48
(D) 60
(E) 72
Rationale: The question asks the different itineraries, and we need to count the order. For example, visiting city A first and visiting city B later is different from visiting city B first and visiting city A later.
To visit 2 cities from 4 cities, there are 4Ã—3=124Ã—3=12 different itineraries
To visit 3 cities from 4 cities, there are 4Ã—3Ã—2=244Ã—3Ã—2=24 different itineraries
To visit 4 cities from 4 cities, there are 4Ã—3Ã—2Ã—1=244Ã—3Ã—2Ã—1=24 different itineraries
The total different itineraries are 12+24+24=6012+24+24=60 different itineraries.
Answer: D
Answer: (D) 60
Question: If two of the four expressions a + b , b + 7b, a - b, and 7a - b are chosen at random, what is the probability that their product will be of the form of a^2-(xb)^2, where x is an integer?
(A) 1/2
(B) 1/7
(C) 1/6
(D) 1/8
(E) 1/5
Rationale: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (a+b)(a-b) = a^2 - (1b)^2
If you see any other combination we are always going to have one term of ab since 7a and 7b are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : C
Answer: (C) 1/6
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 65% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
(A)  7/12
(B)  1/4
(C)  1/2
(D)  7/24
(E)  17/24
Rationale: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
E
Answer: (E)  17/24
Question: Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE?
(A) 1/15
(B) 1/14
(C) 1/12
(D) 1/13
(E) 1/17
Rationale: Explanation :
Let two digit number that Shiwani thought be 'xy', where x and y are single digit number.
Therefore, 10x+y=p(x+y)+3, where p is a natural number
p=10x+y−3x+y.
Also, y+x>3.
Possible values of x and y for which p is a natural number are :-
(x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9),
(x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null),
(x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4)
There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits.
Probability that Devesh thought of the same number as Shiwani = 1/14
Answer : B
Answer: (B) 1/14
Question: In a certain pond, 90 fish were caught, tagged, and returned to the pond. A few days later, 90 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
(A) 400
(B) 625
(C) 1250
(D) 2500
(E) 4091
Rationale: The percent of tagged fish in the second catch is 2/90*100 = 2.22%.
We are told that 2.22% approximates the percent of tagged fish in the pond. Since there are 90 tagged fish, then we have 0.022x = 90 --> x = 4,091.
Answer: E.
Answer: (E) 4091
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 338
(B) 277
(C) 500
(D) 127
(E) 181
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Answer: (C) 500
Question: In how many of ways can 4 balls be placed in 3 tins if any number of balls can be placed in any tin?
(A)  5C4
(B)  5P4
(C)  3^4
(D)  4^5
(E)  5^5
Rationale: Now, each of the 4 different balls has 3 choices (3 tins to go to), so total # of distribution is 3*3*3*3=3^4.
Answer: C.
Answer: (C)  3^4
Question: If the number 653ab is divisible by 90, then (a + b) = ?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: 90 = 10 x 9
Clearly, 653ab is divisible by 10, so b = 0
Now, 653a0 is divisible by 9.
So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4.
Hence, (a + b) = (4 + 0) = 4.
ANSWER:C
Answer: (C) 4
Question: For all positive integers x, f(x)=f(x+1). If f(3)=15, then what is f(7)?
(A) 8
(B) 12
(C) 15
(D) 21
(E) 35
Rationale: Here we go---
f(x) = f(x+1) ---(1)
f(3) = 15 ----(2)
Now
f(7) = f(6+1)-----> f(6) = f(5+1)-------> f(5) = f(4+1) ------> f(4) = F(3+1)---> f(3) = 15
Now backtrack
f(4) = 15-----> f(5) = 15 ------> f(6) = 15 ----> f(7) = 15
Though I picked option C
I am still not 100% sure of the answer(don't know why)
My bets on C.
Answer: (C) 15
Question: A shopkeeper sold an article for 720 after giving 10% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’?
(A) 25%
(B) 30%
(C) 23%
(D) 28%
(E) None of these
Rationale: Cost price = 720×100/120= 600
S.P. at no discount = 720×100/90 = 800
∴ % profit = 200×100/600 = 33 1⁄3 %
Answer E
Answer: (E) None of these
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 337
(B) 280
(C) 299
(D) 266
(E) 299
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: (B) 280
Question: In the new budget the price of milk rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
(A) 7.5%
(B) 9.1%
(C) 10.9%
(D) 16.67%
(E) 15%
Rationale: Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67%
Answer is D
Answer: (D) 16.67%
Question: A car is running at a speed of 90 kmph. What distance will it cover in 15 second?
(A) 375 m
(B) 395 m
(C) 373 m
(D) 372 m
(E) 371 m
Rationale: Explanation:
Given : Speed = 108 kmph = (90 x (5/18)) m/sec = 25 m/sec
Distance covered in 15 second = (25 x 15) m = 375 m.
ANSWER: A
Answer: (A) 375 m
Question: A motor car starts with the speed of 70km/hr with its speed increasing every two hours by 10kmph. In how many hours will it cover 345 kms
(A) 4 hrs
(B) 5 hrs
(C) 6 hrs
(D) 4 ½ hrs
(E) 5 hrs
Rationale: Explanation:
Distance covered in first 2 hours = 70×2 =140km
Distance covered in next 2 hours = 80×2 =160km
Remaining distance = 345 -140-160 =45km
Speed of the fifth hour =90km/hr
Time taken to cover 45km = 45/90 = ½ hr
Total time taken = 2+2+ ½ = 4 ½ hrs
Answer: Option D
Answer: (D) 4 ½ hrs
Question: A military commander has to choose 2 soldiers out of a company of 4 for guarding the headquarters. How many different group combinations of 2 does he have to choose from?
(A) 4
(B) 10
(C) 12
(D) 15
(E) 35
Rationale: A military commander has to choose 2 soldiers out of a company of 5.
different group combinations of 2
He can do this in 5C2 ways
5*4/2*1= 10 ways
ANSWER:B
Answer: (B) 10
Question: In a group of 140 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
(A) 0.35
(B) 0.55
(C) 0.65
(D) 0.75
(E) 0.85
Rationale: Number of people whose age is less than 20 is given by
140 - 90 = 50
Probability P that a person selected at random from the group is less than 20 is given by
50 / 140 = 0.35
correct answer A
Answer: (A) 0.35
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/3
(B) 2/7
(C) 2/5
(D) 3/7
(E) 3/11
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: (C) 2/5
Question: If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result is 18 26/27. Find the fraction.
(A) 8/27
(B) 1 1/3
(C) 2 2/3
(D) 3 /3
(E) None of these
Rationale: Answer
If the required fraction be P
According to the question
(P x P) / (1/P) = 1826/27
⇒ P3 = 512/27
∴ P = 8/3 = 2 2/3
Correct Option: C
Answer: (C) 2 2/3
Question: If 6 spiders make 3 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)6:1
(webs) 1:7}::x:3
â‡’6Ã—1Ã—7=1Ã—3 Ã— x
â‡’x=14
Answer: Option C
Answer: (C) 14
Question: Company A has 13 employees, 8 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift?
(A) 56
(B) 231
(C) 336
(D) 350
(E) 406
Rationale: There are total of 13 employees, 8 of whom belong to the union and 5 doesn't. Out of 5 people working a shift at least 4 must belong to the union.
Now, at lest 4 out of 5 means that 4 or all 5 employees must belong to the union:
Out of 5 people working a shift 4 employees belong to the union and 1 doesn't: C48∗C15=3500;
Out of 5 people working a shift all 5 employees belong to the union: C58=56
Total # of ways: 350+56=406
Answer: E.
Answer: (E) 406
Question: 3 Years ago, the average age of a family of 5 members was 20 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
(A) 1 year.
(B) 1.5 Years.
(C) 2 Years.
(D) 3 Years.
(E) 5 Years.
Rationale: We're told that 3 YEARS AGO, the average age of a family of 5 members was 20 years.
This means that the SUM of their ages was (5)(20) = 100 years.
A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.
This means that the sum of the ages is (6)(20) = 120 years.
We're asked for the PRESENT age of the baby.
Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...
100 + (5)(3) = 115.
120-115 =5
E
Answer: (E) 5 Years.
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
(A) 910% increase
(B) 10% increase
(C) 9% decrease
(D) 12% decrease
(E) 15% increase
Rationale: (30 * 30)/100 = 9% decrease
ANSWER C
Answer: (C) 9% decrease