mathewhe/aqua_rat huggingface dataset:
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following?
(A) 1/7
(B) 1/14
(C) 1/28
(D) 2/49
(E) 2/81
Rationale: There are 7*7 = 49 possibilities.
Bob has 2 chances so the probability is 2/49.
The answer is D.
Answer: (D) 2/49
Question: 5n + 7 > 12 and 7n - 5 < 44; n must be between which numbers?
(A) 1 and 8
(B) 2 and 6
(C) 0 and 9
(D) 1 and 7
(E) 2 and 9
Rationale: 5n > 5 --> n > 1
7n < 49 --> n < 7
1 < n < 7
Answer: D
Answer: (D) 1 and 7
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 35 hrs
(B) 20 hrs
(C) 10 hrs
(D) 15 hrs
(E) 50 hrs
Rationale: Pipe A alone take x hrs
then pipe B and C will take x/2 and x/4 hrs
=>1/x+2/x+4/x=1/x=>7/x=1/5
x = 35 hrs
ANSWER A
Answer: (A) 35 hrs
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 35 pounds and 33 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
(A) 31
(B) 33
(C) 35
(D) 37
(E) 39
Rationale: Total weight of the 4 dogs = (25+31+35+33) = 124
Avg = 124/4 = 31
Total weight of 5 dogs = 124+y or 4(31)+y
Average of 5 dogs as per Question = 31
Equation:
4(31) + y = 5 (31), or y = 31.
Choose A
Answer: (A) 31
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
(A) 5
(B) 8
(C) 96
(D) 32
(E) 14
Rationale: Explanation:
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
Answer E
Answer: (E) 14
Question: 200 liters of a mixture contains milk and water in the ratio 4:1. If 20 liters of this mixture be replaced by 20 liters of milk, the ratio of milk to water in the new mixture would be?
(A) 6:1
(B) 1:6
(C) 2:3
(D) 3:2
(E) 4:1
Rationale: Quantity of milk in 200 liters if mix = 200*4/5 =160 liters
Quantity of milk in 210 liters of new mix = 160+20 = 180 liters
Quantity of water in it = 210-180 = 30 liters
Ratio of milk and water in new mix = 180:30 = 6:1
Answer is A
Answer: (A) 6:1
Question: A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percentage of total number of cars are silver?
(A) 35%
(B) 37.5%
(C) 45%
(D) 47.5%
(E) 50%
Rationale: Number of silver cars before shipment = 30% of 40 = 12
Number of silver cars after shipment = 60% of 80 = 48
Total number of silver cars out of 120 = 48+12 = 60, which is 50%
E is my answer.
Answer: (E) 50%
Question: a, b, c, and d are positive integers where a is a factor of b and c is a factor of d. Which of the following is NOT necessarily an integer?
(A) (ac)/(bd)
(B) (bd)/(ac)
(C) (bcd)/a
(D) d/c + b/a
(E) (a + b)d/c
Rationale: As per the question, let a = 2, b = 6, c = 5, and d = 10. Plugging these into the answer choices, only A does not yield an integer.
Answer: (A) (ac)/(bd)
Question: Operation#is defined as adding a randomly selected two digit multiple of 14 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?
(A) 0%
(B) 10%
(C) 20%
(D) 30%
(E) 40%
Rationale: Any multiple of 14 is even.
Any two-digit prime number is odd.
(even+odd)/2 is not an integer. Thus # does not yield an integer at all.
Therefore P=0.
Answer: A.
Answer: (A) 0%
Question: An bus covers a certain distance at aspeed of 180 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 560 km/h
(B) 567 km/h
(C) 779 km/h
(D) 723 km/h
(E) 540 km/h
Rationale: Distance = (180 x 5) = 900 km.
Speed = Distance/Time
Speed = 900 /(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 900 x 3/5 km/hr = 540 km/hr.
E
Answer: (E) 540 km/h
Question: Kim finds a 4-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
(A) 2/5
(B) 7/5
(C) 3/5
(D) 8/15
(E) 1/2
Rationale: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be
2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15
Which gives us 2/5 + 1/15 + 2/15 -----> 3/5
Answer is C
Answer: (C) 3/5
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
(A) 22C10 - 6
(B) 22C10 - 4
(C) 22C12 - 1
(D) 22C10 - 1
(E) 12C10 - 1
Rationale: The total number of ways of forming the group of ten representatives is 22C10.
The total number of ways of forming the group that consists of no seniors is 10C10 = 1 way
The required number of ways
= 22C10 - 1
Answer: D
Answer: (D) 22C10 - 1
Question: A 750 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 300
(B) 875
(C) 360
(D) 770
(E) 380
Rationale: Speed = 750/18 = 125/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 750)/39 = 125/3
=> x = 1625 m.
L=1625-750=875
Answer: Option B
Answer: (B) 875
Question: The average age of a group of 12 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 22 years
(B) 30 years
(C) 34 years
(D) 32 years
(E) None of these
Rationale: Answer
The average age of a group of 12 students is 20.
Therefore, the sum of the ages of all 12 of them = 12 * 20 = 240
When two new students join the group, the average age increases by 2.
New average = 22.
Now, there are 14 students.
Therefore, the sum of the ages of all 14 of them = 14 * 22 = 308
Therefore, the sum of the ages of the two new students who joined = 308 - 240 = 68
And the average age of each of the two new students = 68/2 = 34 years.
Answer C
Answer: (C) 34 years
Question: An design manager has 10patterns of chairs & 10patterns of tables. In how many ways can he make a pair of table & chair?
(A) 20
(B) 40
(C) 80
(D) 90
(E) 100
Rationale: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 10 ways
Hence one chair and one table can be arranged in 10 x 10 ways = 100 ways
E
Answer: (E) 100
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
(A) 22
(B) 23
(C) 24
(D) 26
(E) 27
Rationale: EXPLANATION
Let the number of hens be x and the number of cows be y.
Then, x + y = 48 …. (i)
and 2x + 4y = 140 x + 2y = 70 …. (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.
Answer D
Answer: (D) 26
Question: What will be the compound interest on a sum of Rs. 30,000 after 3 years at the rate of 12% p.a.?
(A) s.10123.77
(B) s.10123.21
(C) s.10123.20
(D) s.12147.84
(E) s.10123.21
Rationale: Amount = [30000 * (1 + 12/100)3]
= 30000 * 28/25 * 28/25 * 28/25
= Rs. 42147.84
C.I. = (42147.84 - 30000)
= Rs. 12147.84
Answer:D
Answer: (D) s.12147.84
Question: Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 3 miles per hour, how many miles had Lionel walked when he met Walt?
(A) 12
(B) 16
(C) 20
(D) 27
(E) 28
Rationale: In the first 2 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=3*2=6 miles. So, the distance between him and Walt was 48-6=42 miles when Walt left his house. Now, their combined rate to cover this distance was 3+3=6 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=42/6=7 hours. Total time that Lionel was walking is 2+7=9 hours, which means that he covered in that time interval distance=rate*time=3*9=27 miles.
Answer: D.
Answer: (D) 27
Question: In a box, there are 12 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 12/23
(B) 10/21
(C) 7/12
(D) 11/31
(E) 13/17
Rationale: Total number of balls = 10+6+5 = 23
E = event that the ball drawn is neither red nor green
= event that the ball drawn is red
n(E) = 12
P(E) = 12/23
Answer is A
Answer: (A) 12/23
Question: A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together?
(A) 16 days
(B) 12 days
(C) 3 days
(D) 5 days
(E) 9 days
Rationale: Sol. (A + B)'s 1 day's work = (1/18) (B + C)'s 1 day's work = (1/24)
and (A + C)'s 1 day's work = (1/36)
Adding, we get: 2 (A + B + C)'s 1 day's work =¬(1/18 + 1/24 + 1/36)
=9/72 =1/8
(A +B + C)'s 1 day's work =1/16
Thus, A, Band C together can finish the work in 16 days.
Ans: A
Answer: (A) 16 days
Question: A, Band C can do a piece of work in 11 days, 20 days and 67 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
(A) 7.1 days
(B) 8.1 days
(C) 9.1 days
(D) 10 days
(E) 11 days
Rationale: (A+B)'s 1 day's work = 1/11+1/20 = 31/220
(A+C)'s 1 day's work = 1/11+1/67 = 78/737
work done in 2 day's = 31/220+78/737 = 19/77
19/77th work done in 2 days
work done= 77/19*2 = 8.1 days
ANSWER:B
Answer: (B) 8.1 days
Question: After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
(A) 1/12
(B) 0
(C) 12/212
(D) 11/12
(E) 11/13
Rationale: 0
If one letter is in wrong envelope, the letter corresponding to that letter will also be in wrong envelope.
ANSWER:B
Answer: (B) 0
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was
(A) 2500
(B) 2700
(C) 3000
(D) 3100
(E) Nobe
Rationale: Solution
Number of valid votes = 80% of 7500
= 6000.
Valid votes polled by other candidates	= 45% of 6000
(45/100×6000)
= 2700.
Answer B
Answer: (B) 2700
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
(A) 287 m
(B) 704 m
(C) 278 m
(D) 298 m
(E) 286 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm
= 704 m
Answer:B
Answer: (B) 704 m
Question: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long T would it take Victor to complete 10 jobs without any supervision?
(A) 34
(B) 52
(C) 60
(D) 70
(E) 92
Rationale: Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).
For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.
Victor to complete 10 jobs without any supervision will need T 10(t + 3) = 60 days.
Answer: C.
Answer: (C) 60
Question: how many three digit number are thre in which if one digit is 3 then it must be follwed by 7 . repetetion is not allowed
(A) 466
(B) 463
(C) 14
(D) 17
(E) 18
Rationale: 1st case: three digits no without considering 3
first place can be filled using 8 numbers (excluding 0 and 3)=8
second place can be filled using 8 numbers (excluding 3 and digit filled in first place)=8
last place can be filled using 7 numbers (excluding 3 and digit filled in first place & second place)=7
therefore, three digits formed are= 8*8*7=448
2nd case: now consider number using 3
if 3 and 7 are first two digit then last digit can be filled using 8 digits
if 3 and 7 are last two digits then first place can be filled using 7 digits
therefore, total 3 digit no including 3 are= 8+7=15
hence, total 3 digits numbers are= 448+15=463
ANSWER:B
Answer: (B) 463
Question: There are two inlets and one outlet to a cistern. One of the inlets takes 5/2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:00AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 5 hours
Rationale: The combined inflow rate of the two inlets is 2/5 + 1/5 =3/5 cistern/hour. Thus, working together, it takes 5/3 hours (time is reciprocal of rate) to fill the cistern.
From 9:00 AM to 10:00 AM, so in 1 hour, the inlet pipes will fill (time)*(rate) = 1*3/5 = 3/5 th of the cistern .
Then the outlet is turned on and the remaining 2/5 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/5 - x = 2/5 --> x = 1/5 cistern/hour, which means that it takes 5 hours the outlet working alone to empty the cistern.
Answer: E.
Answer: (E) 5 hours
Question: If 5% more is gained by selling an article for Rs. 420 than by selling it for Rs. 380, the cost of the article is?
(A) 500
(B) 688
(C) 200
(D) 121
(E) 800
Rationale: Let C.P. be Rs. x.
Then, 5% of x = 420 - 380= 40
x/20 = 40 => x = 800
Answer: E
Answer: (E) 800
Question: In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many D different victory circles are possible?
(A) 24
(B) 52
(C) 96
(D) 144
(E) 648
Rationale: Possible scenarios are:
1. Gold/Silver/Bronze /No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.
Total: 24+12+12+4=52
Answer: B.
Answer: (B) 52
Question: A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
(A) 79.2 km/hr
(B) 69 km/hr
(C) 74 km/hr
(D) 61 km/hr
(E) none of these
Rationale: Let x is the length of the train and v is the speed
Time taken to move the post = 8 s
=> x/v = 8
=> x = 8v --- (1)
Time taken to cross the platform 264 m long = 20 s
(x + 264)/v = 20
=> x + 264 = 20v ---(2)
Substituting equation 1 in equation 2, we get
8v +264 = 20v
=> v = 264/12 = 22 m/s
= 22 × 36/10 km/hr = 79.2 km/hr
ANSWER:B
Answer: (B) 69 km/hr
Question: Diana is painting statues. She has 1/2 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?
(A) 8
(B) 20
(C) 28
(D) 14
(E) 19
Rationale: number of statues=all the paint÷amount used per statue
=1/2 ÷ 1/16
=8/16*16/1
=8/1
=8
Answer is A.
Answer: (A) 8
Question: If 50% of x is 25 less than 25% of 2500, then x is?
(A) 1880
(B) 2160
(C) 1200
(D) 8400
(E) 1210
Rationale: 50% of x = x/2 ; 25% of 2500 = 25/100 * 2500 = 625
Given that, x/2 = 625 - 25 => x/2 = 600 => x = 1200.
Answer: C
Answer: (C) 1200
Question: The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?
(A) 40
(B) 36
(C) 25
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Since, thief escaped with 1 diamond,
Before 3rd watchman, he had ( 1 + 2 ) x 2 = 6 diamonds.
Before 2nd watchman, he had ( 6 + 2 ) x 2 = 16 diamonds.
Before 1st watchman, he had ( 16 + 2 ) x 2 = 36 diamonds.
Answer : B
Answer: (B) 36
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y ?
(A) 360 m
(B) 420 m
(C) 460 m
(D) 320 m
(E) 380 m
Rationale: Explanation:
Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
ANSWER IS B
Answer: (B) 420 m
Question: Find the highest common factor of 36 and 84.
(A) 4
(B) 6
(C) 12
(D) 18
(E) 19
Rationale: 36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.
Answer: Option C
Answer: (C) 12
Question: During a Thanksgiving weekend, a car rental company rented six-tenths of their vehicles, including two-fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: 4/10 of all the vehicles were not rented.
(3/5)(3/5) = 9/25 of all the vehicles are 4WDs that were not rented.
(9/25) / (4/10) = 9/10 is the fraction of non-rented vehicles that were 4WDs
1 - 9/10 = 10% of non-rented vehicles were not 4WDs.
The answer is A.
Answer: (A) 10%
Question: Two dice are rolled. What is the probability the sum will be greater than 4?
(A) 1/9.
(B) 1/12.
(C) 5/36.
(D) 7/18.
(E) 1/5.
Rationale: Combinations possible: (6,6) , (5,6) , (6,5), (4,6), (6,4) , (5,5) , (5,4), (4,5), (4,4), (4,3) , (3,4), (3,3) , (3,2), (2,3) = 14
Total combinations possible: 6*6=36
Answer = 14/36 = 7/18 Option D.
Answer: (D) 7/18.
Question: What is the 8th term in this sequence?
1,2,3,10,18,28,51
(A) 84
(B) 37
(C) 89
(D) 90
(E) 78
Rationale: 1+2 =3 +0 =3
3+2 =5+5 =10
10+3 =13+5 =18
18+10=28+0 =28
28+18=46+5 =51
51+28=79+5 =84
so 8th term is 84
ANSWER:A
Answer: (A) 84
Question: Percentage of profit earned by selling a book for $2200 is equal to the percentage loss incurred by selling the same book for $1800. What price should the book be sold to make 25% profit?
(A) $2250
(B) $2100
(C) $2500
(D) $2700
(E) $3000
Rationale: Let C.P. be Rs. x.
Then,(2200 - x)	x 100 =(x - 1800)x 100
2200 - x = x - 1800
2x = 4000
x = 2000
Required S.P. = 125% of Rs. 2000 = 1.25x 2000 = $2500
Answer : C
Answer: (C) $2500
Question: The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability M that 3 of Sam’s 4 funds grew by at least 10% over last year?
(A)  6C3 / 10C4
(B)  6C3 * 4C1 / 10C4
(C)  6C3 * 4C1 / 10P4
(D)  6P3 * 4P1 / 10C4
(E)  6P3 * 4P1 / 10P4
Rationale: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.
We know this is a combination, not a permutation. This rules out choices C, DE.
A clearly isn't the answer because M 6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.
B it is.
Answer: (B)  6C3 * 4C1 / 10C4
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 18 seconds. What is the length of each train (in meters)?
(A) 20
(B) 25
(C) 35
(D) 50
(E) 65
Rationale: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 18 seconds, the relative difference in distance traveled is 18 * 25/9 = 50 meters
This distance is twice the length of each train.
The length of each train is 50/2 = 25 meters
The answer is B.
Answer: (B) 25
Question: If taxi fares were $3.00 for the first 1/5 mile and $0.20 for each 1/5 mile there after, then the taxi fare for a 4-mile ride was
(A) $6.80
(B) $6.50
(C) $16.80
(D) $6.85
(E) $61.80
Rationale: In 4 miles , initial 1/5 mile charge is $3
rest of the distance = 4 - (1/5) = 19/5
rest of the distance charge = 19(0.2) = $3.8 (as the charge is 0.2 for every 1/5 mile)
=> total charge for 4 miles = 3+3.8 = 6.8
Answer is A
Answer: (A) $6.80
Question: 1/3 -2/5+1/2 - 5/6 + 1/5 + 1/4 - 9/20 =
(A) 0
(B) 2/15
(C) 2/5
(D) 9/20
(E) 5/6
Rationale: We need to determine the result of 1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20
Let’s add the given fractions in two groups. In the group of the first three fractions, notice that1/3 and 1/2 share a common denominator of 6 with 5/6.
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Thus, 5/6 – 5/6 = 0
Looking at the 2nd group of the fractions (1/5, 1/4, and 9/20), notice that1/5 and 1/4 share a common denominator of 20 with 9/20.
1/5 + 1/4 = 4/20 + 5/20 = 9/20
Thus, 9/20 – 9/20 = 0.
Thus, the result of 1/3 + 1/2 – 5/6 + 1/5 + 1/4 – 9/20 is 2/5.
Answer: C
Answer: (C) 2/5
Question: How many ways are there to award a gold, silver, bronze and platinum medal to 10 contending teams?
(A) 10 × 9 × 8
(B) 10!/(3!7!)
(C) 10!/3!
(D) 10!7
(E) 10 * 9 * 8 * 7
Rationale: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways
if gold medal is given to 1 of the teams then only possible 9 teams can be considered for silver medal. we can do selection in 9 ways
similarly if gold and silver medals are awarded then only remaining 8 teams can be considered for a bronze medal. we can do the selection in 8 ways
similarly if gold and silver medals are awarded then only remaining 7 teams can be considered for a bronze medal. we can do the selection in 7 ways
Total number of ways to select the 4 possible medal winners = 10 * 9 * 8 * 7
Correct answer - E
Answer: (E) 10 * 9 * 8 * 7
Question: How many numbers amongst the numbers 28 to 42 are there which are exactly divisible by 7 but not by 5?
(A) Nil
(B) 1
(C) 2
(D) 3
(E) More than 3
Rationale: 28,35,42 are divisible by 7.
35 is divisible by 5 also.
So there are 2 numbers exactly divisible by 7 but not by 5
ANSWER:C
Answer: (C) 2
Question: Ram and Shyam distribute some coins amongst them in the ratio 4:5. If Ram steals 3 coins from Shyam, the ratio of coins they have becomes 5:4. How many coins did they distribute initially?
(A) 81
(B) 27
(C) 15
(D) 12
(E) 3
Rationale: Initially, the ratio of coins with Ram and Shyam was 4:5. So, let 4x be the number of coins with Ram and 5x be the number of coins with Shyam, making a total of 9x coins.
If Ram steals 3 coins from Shyam, Ram will have 4x + 3 coins and Shyam will have 5x -3 coins. The new ratio of the coins with them is given to be 5 : 4.
This means,
(4x+3)/(5x-3) = 5/4
Solving this equation we get, x = 3.
So the total number of coins they distributed originally was 9x = 9 times 3 = 27.
Ans B
Answer: (B) 27
Question: The price of an item is discounted 4 percent on day 1 of a sale. On day 2, the item is discounted another 4 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 82.5%
(B) 89.9%
(C) 87.7%
(D) 86.4%
(E) 83.3%
Rationale: Let initial price be 100
Price in day 1 after 4% discount = 96
Price in day 2 after 4% discount = 92.16
Price in day 3 after 10% discount = 82.94
So, Price in day 3 as percentage of the sale price on day 1 will be = 82.94/96*100 => 86.4%
Answer will definitely be (D)
Answer: (D) 86.4%