mathewhe/aqua_rat huggingface dataset:
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer factors does 2xy have?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: The solution should be the same for all numbers that fulfill the condition above. As x and y are odd prime numbers, they must be > 2. Also, they must be distinct as x<y.
I choose x=3 and y=5:
How many factors does 2x3x5=30 have:
1, 2, 3, 5, 6, 10, 15, 30 = 8 distinct positive integer factors.
Hence, the correct answer is D.
Answer: (D) 8
Question: At a meeting, 6 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 12
(B) 72
(C) 120
(D) 144
(E) 720
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
From Gmat Club Math Book (combinatorics chapter):
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
R=n!n=(n−1)!R=n!n=(n−1)!"
(n−1)!=(6−1)!=120(n−1)!=(6−1)!=120
Answer: C
Answer: (C) 120
Question: The average weight of a group of boys is 20 kg. After a boy of weight 34 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 12
(B) 14
(C) 18
(D) 13
(E) 10
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 34 kg joins the group, total weight of boys = 20x + 34
So 20x + 34 = 21(x + 1) = > x = 13.
ANSWER:D
Answer: (D) 13
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) 1261
(B) 1262
(C) 2686
(D) 2687
(E) 2676
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer:A
Answer: (A) 1261
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 9
(B) 8
(C) 6
(D) 4
(E) 10
Rationale: Part filled by pipe A in 1 minute =1/12
=1/12
Part filled by pipe B in 1 minute =1/24
=1/24
Part filled by pipe A and pipe B in 1 minute=
1/12 + 1/24 =1/8
=1/12+1/24=1/8
i.e., both the pipe together can fill the tank in 8 minutes.
Answer: (B) 8
Question: A thief steals a car at 4.05 P.M. and drives it at 55 km/hr. The theft is discovered at 4.20 P.M. and the owner sets off in another car at 70 km/hr. when will he overtake the thief ?
(A) 4.50 P.M.
(B) 5 P.M.
(C) 5.10 P.M.
(D) 5.15 P.M.
(E) None of these
Rationale: Explanation :
Solution: Suppose the thief is overtaken x hrs after 4.05 P.M.
Then, distance covered by the thief in x hrs. = distance covered by owner in (x - 1/4) hrs.
.'. 55x = 70(x - 1/4)
=> 15x = 70/4
=> x = 70/(15*4) hr = 14/12 hr
=> x = (14/12 * 60) min = 70 min.
So, the thief is overtaken at 5.15 pm.
Answer : D
Answer: (D) 5.15 P.M.
Question: A trained covered x km at 70 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 22.25
(B) 99
(C) 26.25
(D) 66
(E) 887
Rationale: Total time taken = x/70 + 2x/20 hours
= 4x/35 hours
Average speed = 3x/(4x/35) = 26.25 kmph
Answer: C
Answer: (C) 26.25
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value R?
(A) 2r
(B) 2s
(C) r +s
(D) 2r-s
(E) 2s-r
Rationale: The simplest way to do this is to assume values.
We are told that r and s are positive integers R.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.
Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4
Hence option A is the greatest.
Answer: (A) 2r
Question: Each shelf of a bookcase contains 24 books. If the librarian took out 40 books and rearranged the remaining books so that all shelves but the last one contained 20 books and the last shelf contained 20 books, how many shelves does the bookcase have?
(A) A)4
(B) B)5
(C) C)6
(D) D)8
(E) E)10
Rationale: Denoting x the number of the shelves,
we can build an equation: 24x=20(x−1)+20+40
Solving the equation, we get x=10
Answer: E
Answer: (E) E)10
Question: The sum of money will be triple itself in 20years and simple interest find rate of interest?
(A) A)5%
(B) B)10%
(C) C)15%
(D) D)20%
(E) E)25%
Rationale: T = 20 years
P= principle amount = x
A = total amount = 3x
SI = simple interest = A-P = 3x-x = 2x
R = 100SI/PT = 100.2x/20x =10%
Answer is B
Answer: (B) B)10%
Question: 66 out of 100 the how much out of 75
(A) 49.5
(B) 48.5
(C) 47.5
(D) 46.5
(E) 45.5
Rationale: out of 100 -- its 66
out of 75 -- x
x= 75/100 * 66
x = 49.5
ANSWER:A
Answer: (A) 49.5
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
(A) 226
(B) Rs.992
(C) 665
(D) 771
(E) 211
Rationale: (800*3*3)/ 100 = 72
920 + 72 = 992
Answer: B
Answer: (B) Rs.992
Question: A trader bought a car at 20% discount on its original price. He sold it at a 100% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 18%
(B) 13%
(C) 60%
(D) 40%
(E) 15%
Rationale: Original price = 100
CP = 80
S = 80*(200/100) = 160
100 - 160= 60%
Answer: C
Answer: (C) 60%
Question: A shopkeeper sells an item at Rs 36 and incurs a loss of 10 %. At what price should the shopkeeper sell it to gain 30 % ? (in Rs)
(A) 37
(B) 26
(C) 28
(D) 269
(E) 52
Rationale: Explanation:
No explanation is available for this question!
ANSWER: E
Answer: (E) 52
Question: In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
(A) 20
(B) 30
(C) 34
(D) 24
(E) 12
Rationale: Number of matches won by the team in June: 30% of 60 = 18
After a phenomenal winning streak the average is 50%
Let the team played x matches continuously and won all of them to achieve an average winning percentage of 50%.
So total matches played by the team = (60+x)
Total matches won by the team = (18+x)
Total matches won = 50% of Total matches played
(18+x) = 50% of (60+x)
18+x = (50/100)*(60+x)
18+x = (1/2)*(60+x)
36+2x = 60+x
x = 24 ANSWER D
Answer: (D) 24
Question: How many 4-digit Q numbers (ABCD) can be formed such that |A – D| = 2?
(A) 2,000
(B) 1,900
(C) 1,800
(D) 1,600
(E) 1,500
Rationale: 1) A=0 and D-8
2) A and D as 1 and 9..so 3*100= 300 extra ways ans 1800-300 = 1500.
we are looking for |A-D|=2 so any of the two can be bigger..
these two can have values (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14..
another arrangement could be A as 2 and D as 0... D as 2 and A as 0 is not possible as number will become 3 digits..
so the ways A and D can be placed = 14+1=15 ways..
B and C can be placed in 10*10 ways..
Total Q= 15*10*10=1500.E
Answer: (E) 1,500
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 36 kmph, find the speed of the stream?
(A) 12 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) 16 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 36/3 = 12 kmph.
Answer: A
Answer: (A) 12 kmph
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 18 minutes is:
(A) 9.5
(B) 5.5
(C) 7.5
(D) 6.5
(E) 5.1
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(18/60)) km = 7.5 km.
ANSWER:C
Answer: (C) 7.5
Question: A mixture has milk and water in the ratio 5:1. 20 liters of water is added and the ratio now becomes 5:6. How much milk was present in original mixture?
(A) 20 liters
(B) 22 liters
(C) 24 liters
(D) 26 liters
(E) 28 liters
Rationale: If milk and water in original mixture is 5x and x respectively, then
5x/(x+20) = 5/6, x=4
So milk in original mixture=5*4=20 liters
ANSWER:A
Answer: (A) 20 liters
Question: Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 4x boxes?
(A) 3 minutes
(B) 4 minutes
(C) 8 minutes
(D) 6 minutes
(E) 12 minutes
Rationale: Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 4x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10
Now combine Time = combine work needs to be done / Combine Rate = 4x/5x * 10 = 8 Min
Ans: C
Answer: (C) 8 minutes
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord Q, in feet?
(A) 30
(B) 25
(C) 15
(D) 10
(E) 5
Rationale: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
Q=pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long.D
Answer: (D) 10
Question: A rectangular garden is to be twice as long as it is wide. If 240 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
(A) 40
(B) 50
(C) 60
(D) 80
(E) 100
Rationale: ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 240
So, 2 ( L + B ) = 240
Or, L + B = 120
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 40
L = 40 ; B = 20
L + b = 60
(B) 50
L = 50 ; B = 25
L + b = 75
(C) 60
L = 60; B = 30
L + b = 90
(D) 80
L = 80; B = 40
L + b = 120
(E) 100
L = 100; B = 50
L + b = 150
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (D)
Answer: (D) 80
Question: A car is traveling 55 kilometers per hour. How many meters does the car travel in one minute?
(A) 1250m/min
(B) 1360m/min
(C) 2560m/min
(D) 916.67m/min
(E) 1890m/min
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
55 kilometers per hour = 55 km/hr
= (55 × 1000 meters) / (60 minutes) = 916.67 meters / minute
correct answer is D)916.67m/min
Answer: (D) 916.67m/min
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
(A) 16:00.
(B) 18:00
(C) 20:00
(D) 22:00.
(E) 24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 6 hours
Time taken by both buses to meet again in St. Louis will be LCM of 2 and 6 = 12
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Answer: (B) 18:00
Question: The value of a machine depreciates at 20% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
(A) $250000
(B) $430000
(C) $120000
(D) $170000
(E) $150000
Rationale: C
$1,20,000
The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = $96,000
SP such that a profit of $24,000 is made = 96,000 + 24,000 = $1,20,000
Answer: (C) $120000
Question: consider the sequence 1,-2,3,-4,5,-6........what is the average of first 200 terms of sequence?
(A) -1
(B) -0.5
(C) 0
(D) 0.5
(E) 1
Rationale: 1-2+3-4+5-6....................+199-200
= (1-2)+(3-4)+(5-6)....................+(199-200)
= -1-1-1......................(100 terms)
= -100
so, average= (-100)/200= -0.5
ANSWER:B
Answer: (B) -0.5
Question: How many factors of 270 are odd numbers greater than 1?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
Rationale: prime factors of 810 are 2^1,3^4,5^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,) = (4+1)(1+1) =10
since we need odd divisors other than 1 =>10-1 =9 odd divisors
E is the answer
Answer: (E) 9
Question: If 28% of a number exceeds 18% of it by 7.2, then find the number?
(A) 50
(B) 34
(C) 55
(D) 60
(E) 90
Rationale: Use the elimination method to find the correct option.
Of all the options only 90 fits
28% of 90 = 25.2
18% of 90 = 16.2
25.2 - 16.2 = 7.2
Required number is 90.
ANSWER:E
Answer: (E) 90
Question: If z = 4p, where p is a prime number greater than 2, how many different positive even divisors does z have, including z ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: z=4p
since z = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C)
Answer: (C)  Four
Question: A and B undertake to do a piece of work for Rs 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they can finish it in 3 days, Find the share of each?
(A) 300, 225, 75
(B) 200, 225, 80
(C) 400, 300, 100
(D) 500, 300, 100
(E) None of these
Rationale: C’s one day’s work = (1/3) - (1/6 + 1/8) = 1/24
Therefore, A : B : C = Ratio of their one day’s work = 1/6 : 1/8 : 1/24 = 4 : 3 : 1.
A’s share = Rs (600 x 4/8) = 300
B’s share = Rs (600 x 3/8) = 225
C’s share = Rs[600 - (300 + 225)] = Rs 75
ANSWER:A
Answer: (A) 300, 225, 75
Question: The cash realised on selling a 14% stock is Rs.109.25, brokerage being 1/4% is?
(A) 366
(B) 106
(C) 102
(D) 109
(E) 122
Rationale: Cash realised= Rs. (109.25 - 0.25)
= Rs. 109.
Answer: D
Answer: (D) 109
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
(A) 13
(B) 31
(C) 49
(D) 55
(E) 67
Rationale: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
55
Answer: D
Answer: (D) 55
Question: Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had?
(A) A)5
(B) B)11
(C) C)19
(D) D)3
(E) E)4
Rationale: 13-10=3. Answer is D
Answer: (D) D)3
Question: Indu gave Bindu Rs.4375 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) s.10
(B) s.7
(C) s.5
(D) s.3
(E) s.4
Rationale: 4375 = D(100/4)2
D = 7
ANSWER:B
Answer: (B) s.7
Question: The number of defects in the first five cars to come through a new production line are 8, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
Rationale: C
for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8
Answer: (C) III only
Question: Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team Q. If team A's average speed was 5 mph greater than team Q's, what was team Q's average mph?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.
Say Team Q's speed was s. Then Team Q's time is 300/s.
Team A's speed was then s+5, and Team A's time was then 300/(s+5).
We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team Q. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer D, you find the time for Team Q is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, D is correct.
Answer: (D) 20
Question: A triangle has two angles with ratio of 4:3, and the third angle is the sum of the first two. Find the smallest angle of the triangle in degrees.
(A) 130/11
(B) 270/7
(C) 270/11
(D) 310/7
(E) 35
Rationale: The angles are 4x, 3x, and (4x+3x) = 7x for some value x
the three angles of a triangle add up to 180, so
4x+3x+7x=180
14x=180
x=180/14
x=90/7
the smallest angle is 3x = 3*(90/7) = 270/7
B
Answer: (B) 270/7
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 2/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 3/140
(B) 1/280
(C) 3/280
(D) 4/56
(E) 77/280
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 2/5*3/8*5/7 + 2/5*5/8*2/7 + 3/5*3/8*2/7 = 77/280.
Answer: E.
Answer: (E) 77/280
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 19
(B) 22
(C) 27
(D) 29
(E) 31
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
C)
Answer: (C) 27
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 36 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4P
W = 36 = 6K+4P
=> K =4, P=3
Total Red's in bag A will be 2K = 8
E
Answer: (E) 8
Question: Sum of the squares of three numbers is 314 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 25
(C) 26
(D) 28
(E) 24
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 314 + 2* 131
a + b + c = √576 = 24
E
Answer: (E) 24
Question: Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
(A)  13%
(B)  22.2%
(C)  20%
(D)  12.5%
(E)  11.1%
Rationale: Welcome, just post the question and the choices
Let's see, the way I did it was
1/6 are clerical out of 3600 so 600 are clerical
600 reduced by 1/4 is 1200*1/4
so it reduced 150 people , so there is 450 clerical people left
but since 150 people left, it also reduced from the total of 3600 so there are 3450 people total
since 450 clerical left / 3450 people total
you get (A) 13%
Answer : A
Answer: (A)  13%
Question: Birla company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
(A)  3,024
(B)  4,536
(C)  5,040
(D)  9,000
(E)  10,000
Rationale: Birla company plans to assign identification numbers to its employees.The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.
Total = 9*9*8*7 = something with the units digit if 6.
Answer: B.
Answer: (B)  4,536
Question: The duplicate ratio of 3:4 is?
(A) 9:19
(B) 9:13
(C) 9:16
(D) 9:12
(E) 9:11
Rationale: 32: 42 = 9:16
Answer: C
Answer: (C) 9:16
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8463 for a computer table, then what was the cost price of the computer table?
(A) 6825
(B) 2977
(C) 2871
(D) 6725
(E) 2981
Rationale: Explanation:
CP = SP * (100/(100 + profit%))
= 8463(100/124) = Rs. 6825.
Answer: A
Answer: (A) 6825
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2777
(C) 2667
(D) 2908
(E) 2712
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: (A) 1000
Question: Allay's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Allay makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0?
(A)  15
(B)  24
(C)  25
(D)  26
(E)  13
Rationale: day 0- payment of $7 is made in the morning (after 12 am midnight)
day 1 onwards(after 12 am midnight) internet service will begin and will run for 7*2=14 days i.e. at the end of day 15 balance will be zero.
now Allay can still use the internet till her debt reaches $5 which means total of 5*2=10 days.
now the question states for how many days, including today, will she be connected to the internet without any additional paymentsi.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25=C
Answer: (C)  25
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:4
(B) 3:6
(C) 3:1
(D) 3:2
(E) 3:0
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4 .
Answer:A
Answer: (A) 3:4
Question: Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)
(A) 1/4
(B) 2/5
(C) 2/7
(D) 3/7
(E) 3/11
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
A)
Answer: (A) 1/4
Question: Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age.
(A) 60 years
(B) 80 years
(C) 70 years
(D) 76 years
(E) 86 years
Rationale: Let Kumar’s present age be x years and Sailesh’s present age be y years.
Then, according to the first condition,
x - 10 = 3(y - 10) or, x - 3y = - 20 ..(1)
Now. Kumar’s age after 10 years = (x + 10) years
Sailesh’s age after 10 years = (y + 10)
(x + 10) = 2 (y + 10) or, x - 2y = 10 ..(2)
Solving (1) and (2), we get x = 70 and y = 30
Kumar’s age = 70 years and Sailesh’s age = 30 years.
ANSWER:C
Answer: (C) 70 years