mathewhe/aqua_rat huggingface dataset:
Question: A pipe takes a hours to fill the tank. But because of a leakage it took 7 times of its original time. Find the time taken by the leakage to empty the tank
(A) 50 min
(B) 60 min
(C) 90 min
(D) 80 min
(E) 70 min
Rationale: pipe a can do a work 60 min.
lets leakage time is x;
then
1/60 -1/x=1/420
x=70 min
ANSWER:E
Answer: (E) 70 min
Question: Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
(A) 23
(B) 25
(C) 27
(D) 29
(E) 31
Rationale: Solution:
We know that the average value is 24 therefore (a+b+c)/3 = 24
so a+b+c = 72
and b = a + 11
therefore a + (a + 11) + c = 72
The least value of c is when c = b
so take c = a + 11
hence, a + (a + 11) + (a + 11) = 72
i.e., a = 50/3 a non integer therefore c is not equal to b
so take c = b+1 therefore c = a+12
a + (a + 11) + (a + 12) = 72
i.e., a= 49/3 again a non integer therefore c is not equal to b+1
next take c= b+2 therefore c = a+13
a + (a + 11) + (a + 13) = 72
i.e., a=48/3 = 16
hence, a = 16, b = 27, and c = 29
Answer: D
Answer: (D) 29
Question: X and Y run a 100m race,where X beats Y by 20 m. To do a favor to Y, X starts 10m behind the starting line in a second 100m race. Both run at the same previous speed. Which of the following is true?
(A) X Beats Y by 2m
(B) X Beats Y by 0.5 m
(C) X Beats Y by 4 m
(D) Y Beats X by 10m
(E) Beats X by 11m
Rationale: Let's suppose that the speed of X is 10m/s and that the speed of Y is 8m/s.
So, in the first race, the results are the following:
X crosses the finish line in 10s. In other words, X has run 100m in 10 s.
In 10s, Y has run 80 meters.
Therefore, there is the difference of 20 meters mentioned in the question.
Now, let's review the second race.
In 12 seconds, X can complete the 120 meters race. We have to remember that X is 20 meters behind the starting line.
But in 12 seconds, Y has covered (80+16) =96 meters. Also, it is important to notice that in 12 seconds Y cannot arrive to the finish line.
So, 100 - 96 = 4 meter
Answer: C
Answer: (C) X Beats Y by 4 m
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 25%. What was its profit on the items sold in February?
(A) 12.5%
(B) 30%
(C) 35%
(D) 37.5%
(E) 40%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.75*150x = 112.5x
Hence total profit = 12.5%
Option A
Answer: (A) 12.5%
Question: Which of the following fractions terminates?
(A) 3/160
(B) 5/900
(C) 7/220
(D) 9/120
(E) 11/550
Rationale: For a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values
Hence,
1. 160 = 2 * 2 * 2 * 2 * 2 * 5, hence is terminating
2. There is a 3 in the denominator, hence it is a non terminating decimal
3. There is an 11 in the denominator, hence it is a non terminating decimal
4. There is a 3 in the denominator, hence it is a non terminating decimal
5. There is an 11 in the denominator, hence non terminating
Option A
Answer: (A) 3/160
Question: A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in
(A) 6.75 sec
(B) 12 sec
(C) 15 sec
(D) 20 sec
(E) None of these
Rationale: Length of train = 12 Ã— 15 = 180 m.
Then, speed of train = 180â„9 = 20 m/s
Now, length of train = 9Ã— 15 = 135m
âˆ´ Required time = 135â„20 = 6.75 sec.
Answer A
Answer: (A) 6.75 sec
Question: Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is
(A) 80 m
(B) 100 m
(C) 120 m
(D) 180 m
(E) None
Rationale: Solution
Relative Speed	= (36 + 45) km/hr
= (81 x 5/18) m/sec
= (45/2) m/sec
Length of the train	= (45 / 2 x 8) m
= 180 m.
Answer D
Answer: (D) 180 m
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 40% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?
(A) 26%
(B) 20%
(C) 17%
(D) 18%
(E) None of these
Rationale: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.140.
SP = Rs.140- 10% of 140 = Rs.140-14 = Rs.126.
Gain = Rs.126 â€“ Rs.100 = Rs.26
Therefore, gain/profit percent = 26%.
Answer: Option A
Answer: (A) 26%
Question: the ratio of two no. addition and subtraction be 4:3.the what is the ratio of numbers?
(A) 3:2
(B) 4:3
(C) 5:1
(D) 6:5
(E) 7:1
Rationale: (x+y)/(x-y)=4/3
dividing numerator and denominator by y
(x/y)+1/(x/y)-1=4/3
let x/y be z
z+1/z-1=4/3
3z+3=4z-4
z=7
x/y=7
answer E
Answer: (E) 7:1
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
(A) 99.222
(B) 223.22
(C) 157.5
(D) 222.88
(E) 229.11
Rationale: (3500*1.5*3)/100
=> 157.50
Answer: C
Answer: (C) 157.5
Question: Three workers have a productivity ratio of 2 to 5 to 9. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
(A) 12 to 1
(B) 6 to 1
(C) 15 to 2
(D) 1 to 6
(E) 1 to 5
Rationale: The fastest worker who does 9 units of job worked for all 10 hours, so he did 9*10=90 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 90 to 12, or 15 to 2.
Answer: C.
Answer: (C) 15 to 2
Question: A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 127
(B) 120
(C) 882
(D) 272
(E) 323
Rationale: The number of ways to select two men and three women
= 4C₂ * ⁶C₃
= (4*3 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 120
Answer: B
Answer: (B) 120
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) 23
(B) 28
(C) 31
(D) 36
(E) 39
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.
C
Answer: (C) 31
Question: As a bicycle salesperson, David earns a fixed salary of $40 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<2x II. y>x III. y>3
(A) I,II only
(B) I only
(C) II only
(D) II,III only
(E) III only
Rationale: II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>3 --> if David sold 3 bicycles this week then this week he earned 40+3*6=$58, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $40. So y must be more than 3;
I. y<2x --> is not always true.
Answer: D
Answer: (D) II,III only
Question: A certain university will select 3 of 7 candidates eligible to fill a position in the mathematics department and 5 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42232
(B) 42170
(C) 14008
(D) 16510
(E) 41160
Rationale: 7C3*8C5 = 35*56 = 41160
the answer is (E)
Answer: (E) 41160
Question: a light flashes every 20 seconds, how many times will it flash in ? of an hour?
(A) 550
(B) 600
(C) 650
(D) 180
(E) 750
Rationale: 1flash=20sec
for 1 min=3flashes
so for 1 hour=3*60=180 flashes.
ANSWER:D
Answer: (D) 180
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.2 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 3/8
(B) 14/31
(C) 7/15
(D) 17/35
(E) 1/2
Rationale: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.2 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 24 hours.
Total hours = 64.
Then the fraction would be 24/64 = 3/8. Therefore answer A.
Answer: (A) 3/8
Question: log(a(a(a)^1/4)^1/4)^1/4 here base is a.
(A) 0
(B) 21/64
(C) 1
(D) 22/63
(E) 23/65
Rationale: log(a(a(a^1/4)^1/4)^1/4
=> log(a(a^1+1/4)^1/4)^1/4
=> log(a(a^5/4)^1/4)^1/4
=>log(a(a^5/16)^1/4
=>log(a^1+5/16)^1/4
=>log(a^21/16)^1/4
=>log(a^21/64)
=>21/64 log(a)
=>21/64
ANSWER:B
Answer: (B) 21/64
Question: What is the CP of Rs 100 stock at 2 discount, with 1/5% brokerage?
(A) 99.6
(B) 96.2
(C) 97.5
(D) 98.2
(E) None of these
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-2+1/5
98.2
Thus the CP is Rs 98.2.
ANSWER D
Answer: (D) 98.2
Question: The average of the marks of 10 students in a class is 40. If the marks of each student are doubled, find the new average?
(A) 78
(B) 56
(C) 80
(D) 27
(E) 40
Rationale: Sum of the marks for the 10 students
= 10 * 40 = 400. The marks of each student are doubled, the sum also will be doubled.
The new sum = 400 * 2 = 800. So, the new average
= 800/10 = 80.
Answer: C
Answer: (C) 80
Question: A man can row upstream at 20 kmph and downstream at 60 kmph, and then find the speed of the man in still water?
(A) 27
(B) 29
(C) 40
(D) 20
(E) 24
Rationale: US = 20
DS = 60
M = (20 + 60)/2
= 40
Answer: C
Answer: (C) 40
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam.
(A) 15
(B) 25
(C) 30
(D) 45
(E) 55
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 92(x - 5)
80x - (5 * 20) = 92(x - 5)
360 = 12x => x = 30
ANSWER:C
Answer: (C) 30
Question: The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife?
(A) 6.3
(B) 4:3
(C) 5:2
(D) Cannot be determined
(E) 7:8
Rationale: Answer: Option D
Let the present ages of anil and his son be 7x and 3x years respectively.
Let the present age of the son's mother be m years.
(m + 6)/(3x + 6) = 2/1
m = 6x + 6
Ratio of the present ages of anil and his son's mother = 7x/(6x + 6).
This cannot be found uniquely.
Answer: (D) Cannot be determined
Question: What should come in place of the question mark(?) in the following equation? 28⁄? = ?⁄112
(A) 70
(B) 56
(C) 48
(D) 64
(E) None of these
Rationale: 28⁄? = ?⁄112
\ ? =√28×112=56
Answer B
Answer: (B) 56
Question: Find the value of 72517 x 9999 = m?
(A) 456578972
(B) 436567874
(C) 653658791
(D) 725097483
(E) 357889964
Rationale: 72517 x 9999 = 72517 x (10000 - 1)
= 72517 x 10000 - 72517 x 1
= 725170000 - 72517
= 725097483
D
Answer: (D) 725097483
Question: On the coordinate plane , points P and B are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?
(A)  (1.5,1)
(B)  (2,-5)
(C)  (0,0)
(D)  (1,1.5)
(E)  (2,2)
Rationale: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.
One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).
Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PB is the diameter of the circle.
There can be a case when PB is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.
If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D
Answer: (D)  (1,1.5)
Question: A does a work in 10 days and B does the same work in 5 days. In how many days they together will do the same work ?
(A) 1/5
(B) 2/7
(C) 3/10
(D) 3/11
(E) 3/17
Rationale: Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/10
B's 1 day work = 1/15
(A+B)'s 1 day work =
(1/10+1/5)=(1+2/10)= 3/10
C
Answer: (C) 3/10
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure e in inches of the width of the foil covered prism?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 = 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2=e =10
Ans E.
Answer: (E) 10
Question: The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the length of the rectangle?
(A) 12 cm
(B) 15 cm
(C) 18 cm
(D) 21 cm
(E) 24 cm
Rationale: 2L+2W = 5W
L = 3W/2
W*L = 150
3W^2/2 = 150
W^2 = 100
W = 10
L = 3(10)/2 = 15
The answer is B.
Answer: (B) 15 cm
Question: A $500 investment and a $1,500 investment have a combined yearly return of 10 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?
(A) 9%
(B) 10%
(C) 105/8%
(D) 11%
(E) 12%
Rationale: The equation we can form the question :
Return on Total Investment = Sum of individual Investments
(500+1500)(10)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.
Solving the equation, we get x = 11% ( Option D )	ANSWER:D
Answer: (D) 11%
Question: What is the diffference between the place value and face value of 4 in the numeral 2694?
(A) 10
(B) 0
(C) 5
(D) 3
(E) 1
Rationale: place value of 4 = 4 * 1 = 4
face value of 4 = 4
4 - 4 = 0
B
Answer: (B) 0
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/5
(B) 5/8
(C) 5/3
(D) 5/1
(E) 5/6
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done 5C1 . 4C1 ways.
The required probability
= (5 * 4)/⁹C₂ = 20/36
= 5/9
Answer:B
Answer: (B) 5/8
Question: Find the average of all prime numbers between 1 and 5.
(A) 30
(B) 3.6
(C) 5.6
(D) 6.6
(E) None
Rationale: Sol.
There are five prime numbers between 1 and 5.
They are 2, 3, 5, 7, 11
âˆ´ Required average = [2 + 3+ 5+ 7+ 11 / 5] = 28/ 5 = 5.6
Answer C
Answer: (C) 5.6
Question: Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart?
(A)  3:30 pm
(B)  3:45 pm
(C)  4:00 pm
(D)  4:15 pm
(E)  4:30 pm
Rationale: Total distance, which should be covered by both cars is 190+35=225 miles.
Let t be the time so the equation will be 46t+54t=225 thus,
t=2.25 hours
Answer: D
Answer: (D)  4:15 pm
Question: Peeta asks Katniss, 'It is 6 am as per my watch right now.Do you know what will be the time 23, 999, 998 hours later?'
Katniss knows the answer. Do you ?
(A) 5pm
(B) 6pm
(C) 4am
(D) 3am
(E) 8pm
Rationale: D
3am
The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: (D) 3am
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 26
(B) 34
(C) 64
(D) 60
(E) 72
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ?
(A) 6
(B) 8
(C) 7
(D) 25
(E) data insufficient
Rationale: given:
x/2y = 3/2
=> (x-2y)/2y = 1/2
=> x = 3y
Putting x = 3y in (7x+4y)/(x-3y) gives value 25.
ANSWER:D
Answer: (D) 25
Question: What is the next number in this series?
4,12,84,3612....
(A) 6526884
(B) 6526888
(C) 6626884
(D) 6527884
(E) 6526984
Rationale: ((4^2)/2)+4=12
((12^2)/2)+12=84
((84^2)/2)+84=3612
((3612^2)/2)+3612=6526884
ANSWER:A
Answer: (A) 6526884
Question: In how many ways, a committee of 5 members can be selected from 4 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 40
(B) 152
(C) 175
(D) 200
(E) 212
Rationale: (3 men out 4) and (2 ladies out of 5) are to be chosen
Required number of ways = (4C3 * 5C2) = 40
Answer is A
Answer: (A) 40
Question: Rs.360 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 388
(B) 266
(C) 120
(D) 299
(E) 270
Rationale: 4x 5x 6x
100 50 25
400x + 250x + 150x = 36000
x = 45
6x = 270
Answer: E
Answer: (E) 270
Question: In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/5 . If the probability that a number 12 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 20 is drawn?
(A)  8/15
(B)  1/6
(C)  1/3
(D)  1/2
(E)  5/6
Rationale: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 12 or larger
Set 2: Number 20 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)
2/3 + P(Set 2) - 1/5 = 1
P(Set 2) = 8/15
Answer (A)
Answer: (A)  8/15
Question: Find the average of first 6 multiples of 5?
(A) 10
(B) 15
(C) 12.5
(D) 13
(E) 17.5
Rationale: average = (5+10+15+20+25+30)/6 = 17.5
Answer is E
Answer: (E) 17.5
Question: A car is purchased on hire-purchase. The cash price is $24 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?
(A) $503
(B) $504
(C) $555
(D) $576
(E) $587
Rationale: Explanation:
Cash price = $24 000
Deposit = 10% Ã— $24 000 = $2400
Loan amount = $24000 âˆ’ $2400
Number of payments = 60
= $21600
I=p*r*t/100
I=12960
Total amount = 21600 + 12960 = $34560
Regular payment = total amount /number of payments=576
Answer: D
Answer: (D) $576
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 600
(B) 400
(C) 500
(D) 670
(E) 800
Rationale: E
25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: (E) 800
Question: cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
(A) 1002
(B) 2899
(C) 1000
(D) 2807
(E) 2800
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 10 * 10 * 10
= 1000
Answer: C
Answer: (C) 1000
Question: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 80 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
(A) 20%
(B) 40%
(C) 60%
(D) 80%
(E) 100%
Rationale: Let T be the total number of passengers.
Let x be the number of people with round trip tickets.
0.2T had round trip tickets and took their cars.
0.2x had round trip tickets and took their cars.
0.2x = 0.2T
x = T
The answer is E.
Answer: (E) 100%
Question: There are 15 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl and 2 boys are selected ?
(A) 950
(B) 1050
(C) 2150
(D) 2050
(E) 1000
Rationale: n(s) = sample space = 25C3 = 2300
E = event that 1 girl and 2 boys are selected
n(E) = we have to select 2 boys from 15 and 1 girl from 10
= 15C2 * 10C1
= 1050
Ans - B
Answer: (B) 1050
Question: consider the sequence 1,-2,3,-4,5,6.....what is the average of the first 200 terms of the sequence?
(A) -1/2
(B) -3/2
(C) 0
(D) 1/2
(E) 3/2
Rationale: suppose n=2 => avg is (1+-2)/2= -1/2, when n=4 => avg is -1/2 , similarly for n=200 avg will be -1/2.
ANSWER:A
Answer: (A) -1/2
Question: 3 balls are drawn randomly from a bag contains 3 black, 5 red and 4 blue balls. What is the probability that the balls drawn contain balls of different colors?
(A) 1/3
(B) 1/2
(C) 2/11
(D) 3/11
(E) 11/13
Rationale: Total number of balls = 3 + 5 + 4 = 12
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 12 = 12C3
Let E = Event of drawing 3 different coloured balls
To get 3 different coloured balls,we need to select one black ball from 3 black balls,
one red ball from 5 red balls, one blue ball from 4 blue balls
Number of ways in which this can be done = 3C1 × 5C1 × 4C1
i.e., n(E) = 3C1 × 5C1 × 4C1
P(E) = n(E)/n(S)=3C1×5C1×4C1/12C3
=3×5×4/(12×11×10/3×2×1)=3×5×4/2×11×10=3×4/2×11×2=3/11
ANSWER:D
Answer: (D) 3/11
Question: Of the four numbers, whose average is 40, the first is one-fourth of the sum of the last three. The first number is ?
(A) 28
(B) 29
(C) 11
(D) 32
(E) 10
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 40 or x = (40 * 4) / 5 = 32
Answer: D
Answer: (D) 32
Question: In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?
(A) 6
(B) 10
(C) 8
(D) 12
(E) 14
Rationale: Explanation:
Let the number of buffaoes be x and number of ducks be y.
Then 4x + 2y = 2(x + y) + 24
=> 2x = 24
=> x = 12.
Answer: D
Answer: (D) 12