mathewhe/aqua_rat huggingface dataset:
Question: Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?
(A) 9 am
(B) 10 am
(C) 6 am
(D) 8 am
(E) 7 am
Rationale: After t hours the distances D1 and D2, in miles per hour, traveled by the two cars are given by
D1 = 40 t and D2 = 50 t
After t hours the distance D separating the two cars is given by
D = D1 + D2 = 40 t + 50 t = 90 t
Distance D will be equal to 450 miles when
D = 90 t = 450 miles
To find the time t for D to be 450 miles, solve the above equation for t to obtain
t = 5 hours.
5 am + 5 hours = 10 am
Answer B
Answer: (B) 10 am
Question: What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x
(A) 124
(B) 165
(C) 36
(D) 178
(E) 215
Rationale: Go on dividing by 6 to the next number
C)
Answer: (C) 36
Question: In how many Y ways can 5 people from a group of 6 people be seated around a circular table
(A) 56
(B) 80
(C) 100
(D) 120
(E) 144
Rationale: Y=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner)
= 6 * 4!
= 6 * 24
= 144
Answer - E
Answer: (E) 144
Question: An athlete starts from point A and complete one circular round exactly in 33 minutes. How much time is required, if an athlete wants to complete half of the circle and reach to point A ?
(A) 26.0042 minutes
(B) 27.0042 minutes
(C) 28.0042 minutes
(D) 29.0042 minutes
(E) 25.0042 minutes
Rationale: Total distance travelled for circular round = 2*pi*r
Distance travelled if athlete wants to complete half of the circle and reach to point A = pi*r +2r
time taken if an athlete wants to complete half of the circle and reach to point A = (33/2 )+(33/Pi) mins
ie answer is 27.0042 minutes
ANSWER:B
Answer: (B) 27.0042 minutes
Question: A, B and C rents a pasture for Rs.1130. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 199
(C) 351
(D) 156
(E) 122
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 1130= 351
Answer: C
Answer: (C) 351
Question: Ms. Rani purchased three bags @ Rs. 600/- from shop and give Rs.2000/- and also she returned the damaged chappel @ Rs. 250/-to the shop keeper to replace or cash back. Shop keeper told you can buy another chappel and cannot give cash back. Rani took another chappel @ 450/- How much amount to be given to shop keeper?
(A) 50
(B) 150
(C) 0
(D) 25
(E) 100
Rationale: Cost of 3 Bags : 600* 3= 1800/-
New Chappel = 450/-
Total : 2250/-
cost of damaged Chappel : 250/-
Paid amount to Shop keeper: 2000/-
Answer is C
Answer: (C) 0
Question: Find the largest number of four digit exactly divisible by 12,15,18 and 27?
(A) 1500
(B) 2579
(C) 9720
(D) 3697
(E) 4589
Rationale: Explanation:
The largest number of four digit is 9999.
LCM of 12,15,18 and 27 is 540
On dividing 9999 by 540 ,we get 279 is reminder
Required Number=(9999-279)=9720
Answer:C
Answer: (C) 9720
Question: What is the value of x^2yz − xyz^2, if x =1, y = 1, and z = 3?
(A)  20
(B)  -6
(C)  30
(D)  32
(E)  48
Rationale: 1*1*3 -(1*1*9)
=3-9 = -6
Ans: B
Answer: (B)  -6
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and 2y percent of x equals 100. What is the value of x?
(A)  50
(B)  100
(C)  140
(D)  1,000
(E)  2,000
Rationale: y = 50% of 50% 0f x
= x/4
and
2y/100 of x = 100
2y /100 *4y =5000
y = 35
and x= 140
Answer - C
Answer: (C)  140
Question: John started driving on a highway at a constant speed of R miles per hour at 13:00. Then, 2 hours later, Tom started driving on the same highway at a constant speed of 6R/5 miles per hour at 15:00. If both drivers maintained their speed, how many miles had John driven on the highway when Tom caught up with John?
(A) 6R
(B) 8R
(C) 9R
(D) 10R
(E) 12R
Rationale: In 2 hours, John drove 2R miles.
Tom can catch John at a rate of 6R/5 - R = R/5 miles per hour.
The time it takes Tom to catch John is 2R / (R/5) = 10 hours.
In 10 hours, John can drive another 10R miles for a total of 12R miles.
The answer is E.
Answer: (E) 12R
Question: Alex deposited x dollars into a new account that earned 5 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
(A) w/(1+1.08)
(B) w/(1.05+1.05^2)
(C) w/(1.16+1.24)
(D) w/(1.08+1.16)
(E) w/(1.08^2+1.08^2)
Rationale: Account at the end of the first year would be 1.05x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.05x+x) dollars. Account at the end of the second year would be (1.05x+x)*1.05=w --> x(1.05^2+1.05)=w --> x=w/(1.05+1.05^2).
Answer: B
Answer: (B) w/(1.05+1.05^2)
Question: A certain industrial machine requires 20 quarts (640 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 9% special additives. If the machine needs exactly 50 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?
(A) a.	A – 60
(B) b.	B – 180
(C) c. C – 190
(D) d.	D – 300
(E) e.	E – 320
Rationale: 5%*x + 9% *(640-x)=50
7.6 = 4 %*x
x=190
C
Answer: (C) c. C – 190
Question: There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 3 to 7, how many nurses are at the hospital?
(A) 168
(B) 172
(C) 176
(D) 180
(E) 184
Rationale: The number of nurses at the hospital is (7/10)*240=168.
The answer is A.
Answer: (A) 168
Question: Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 20 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
(A) 4
(B) 5
(C) 8
(D) 12
(E) None of these
Rationale: The part of job that Suresh completes in 9 hours
= 9â„15 = 3â„5
Remaining job = 1 - 3â„5 = 2â„5
Remaining job can be done by Ashutosh in 2â„5 Ã— 20 = 8 hours
Answer C
Answer: (C) 8
Question: Find a sum for first 6 prime number'ss?
(A) 25
(B) 28
(C) 30
(D) 35
(E) 41
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13) = 41
Note: 1 is not a prime number
Option E
Answer: (E) 41
Question: A rainstorm increased the amount of water stored in State J reservoirs from 50 billion gallons to 75 billion gallons. If the storm increased the amount of water in the reservoirs to 37.5 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A)  90
(B)  114
(C)  124
(D) 120
(E) 127
Rationale: After the reservoir is filled to 75 gallons the amount of water is at 37.5% - which means that 62.5% of the reservoir is empty. To figure out what that 62.5% is approximate: 75 gallons /37.5 percent = x gallons /62.5 percent , therefore, x = 125 gallons , answer choices A,B,C,D are below 125 . We know that the reservoir must be short more than 125 gallons, therefore, the only possible choice is E.
Answer: (E) 127
Question: A and B start a business with Rs.15000 and Rs.18000 respectively. Hoe should they share their profits at the end of one year?
(A) 1:2
(B) 3:4
(C) 5:6
(D) 3:7
(E) 2:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
15000 : 18000 => 5:6
ANSWER:C
Answer: (C) 5:6
Question: A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $500 and $300 per unit, respectively. What is the fewest number of computer printers that the company can purchase?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: The smallest amount that the company can spend is the LCM of 500 and 300, which is 1500 for each, which is total 3000.
The number of 1st type of computers which costing $500 = 1500/500 = 3.
The number of 2nd type of computers which costing $300 = 1500/300 = 3.
Total = 3+3 = 6
Answer is D.
Answer: (D) 6
Question: The income tax in the area where the Jones family lives is scheduled to increase by 12% next year. Since the Jones family cannot afford an increase in their tax bill, how much will they have to reduce income by to keep their cost the same?
(A) 10.7%
(B) 10%
(C) 10.3%
(D) 10.9%
(E) 10.2%
Rationale: Solution: Let the current tax be represented by Rs. 100.
The tax rate rises 12%. So, to continue to have the same income, they need to increase their tax,
= (100 + 12% of 100) = Rs. 112.
But, they want to keep tax expense the same, so they have to cut Rs. by 12 to keep it to Rs. =100.
The % decrease in income is,
(12/112)*100 = 10.7%.
Mental Calculation Method;
100-----12%↑---→112------X%↓---→100.
Here, X = (12/112)*100 = 10.7%.
Answer: Option A
Answer: (A) 10.7%
Question: At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ?
(A) 20
(B) 45
(C) 55
(D) 90
(E) 80
Rationale: number of handshakes = 10C2= 10*9/2 = 45
ANSWER:B
Answer: (B) 45
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 18 hours
(B) 28 hours
(C) 98 hours
(D) 16 hours
(E) 12 hours
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer:B
Answer: (B) 28 hours
Question: Walking at 4/7 of its usual speed, a train is 9 minutes late. Find its usual time to cover the journey.
(A) 8min.
(B) 10min.
(C) 12min.
(D) 15min.
(E) 17min.
Rationale: Explanation :
Solution: New speed = 4/7 of the usual speed. Let usual time be x.
.'. New time taken = 7/4 of usual time = 7x/4
so, (7x/4 ) - x = 9 min.
=> 3x = 36
=> x = 12 min.
Answer : C
Answer: (C) 12min.
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
(A) 17/28
(B) 17/27
(C) 17/19
(D) 17/20
(E) 17/22
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 17/20
Question: 7,11,19,35,67, (...)
(A) 131
(B) 245
(C) 142
(D) 76
(E) 426
Rationale: 7
7Ã— 2 - 3 =11
11 Ã— 2 - 3= 19
19 Ã— 2 - 3 = 35
35 Ã— 2 - 3 = 67
67 Ã— 2 - 3 = 131
Answer is A
Answer: (A) 131
Question: What is the greatest of 3 consecutive integers whose sum is 30 ?
(A) 11
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 30;
=> 3n = 27;
=> n = 9
The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A
Answer: (A) 11
Question: A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
(A) 2 days
(B) 3 days
(C) 6 days
(D) 5 days
(E) 8 days
Rationale: Sol. (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Ans: C
Answer: (C) 6 days
Question: Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 30 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 20 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
(A) 0.1
(B) 0.6
(C) 1
(D) 1.2
(E) 2
Rationale: Option C
20+30t=50t
t=1
Answer: (C) 1
Question: The sale price sarees listed for Rs.540 after successive discount is 5% and 2% is?
(A) 288
(B) 500
(C) 502
(D) 540
(E) 262
Rationale: 540*(95/100)*(98/100)
= 502
Answer: C
Answer: (C) 502
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
(A) 3 1/3%
(B) 3 1/8%
(C) 3 7/3%
(D) 3 1/7%
(E) 3 1/1%
Rationale: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Answer: (A) 3 1/3%
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 900. What is their H.C.F.?
(A) 5
(B) 15
(C) 25
(D) 35
(E) 45
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x
60x = 900
x = 15
The numbers are (3 x 15), (4 x 15) and (5 x 15).
The H.C.F. is 15.
The answer is B.
Answer: (B) 15
Question: A jar of 264 marbles is divided equally among a group of marble-players. If 2 people join the group, each one would receive 1 marble less. How many people are there in the group today?
(A) 20
(B) 21.
(C) 22
(D) 23
(E) 24
Rationale: only 22 and 24 divide 264 perfectly,
assume initially, there are 22 people,, each will get 12 marbles
two people join, then 24 will get 11 marble each.
hence answer E = 24
Answer: (E) 24
Question: If Jake loses 32 pounds, he will weigh twice as much as his sister. Together they now weigh 212 pounds. What is Jake’s present weight, in pounds?
(A) 131
(B) 135
(C) 139
(D) 152
(E) 188
Rationale: Lets say J is the weight of Jack and S is the wt of his sister.
If he loses 32 pounds, he s twice as heavy as his sister.
J-32=2*S
Also, together they weight 212 pounds
J+S=212
solvong the 2 equation ,we get J=152 pounds !
D
Answer: (D) 152
Question: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
(A) 173 m
(B) 200 m
(C) 273 m
(D) 300 m
(E) 373 m
Rationale: Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, ACB = 30° and ADB = 45°.
AB	= tan 30° =	1 AC = AB x 3 = 1003 m.
AC	3
AB	= tan 45° = 1 AD = AB = 100 m.
AD
CD = (AC + AD)	= (1003 + 100) m
= 100(3 + 1)
= (100 x 2.73) m
= 273 m.
Answer = C
Answer: (C) 273 m
Question: A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?
(A) 100 Marks
(B) 200 Marks
(C) 280 Marks
(D) 371 Marks
(E) 827 Marks
Rationale: 30% ------------ 50
45% ------------ 25
----------------------
15% ------------- 75
30% -------------- ?
150 + 50 = 200 Marks
Answer:B
Answer: (B) 200 Marks
Question: Lake A has a duck population of 30 females and 36 males. Lake B’s duck population consists of the same ratio of females to males. If 5 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?
(A) 144
(B) 105
(C) 77
(D) 51
(E) 36
Rationale: Lake A has a duck population of 30 females and 36 males --> the ratio is F:M = 30:36 = 5:6.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 5:6.
C
Answer: (C) 77
Question: P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
(A) 15
(B) 24
(C) 78
(D) 96
(E) 32
Rationale: Explanation :
Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days
ANSWER:A
Answer: (A) 15
Question: A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $3200 and the total price paid for type B products was $5800. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,755
(B) $15,325
(C) $11,129
(D) $16,225
(E) $17,155
Rationale: cost of type A products next year = 1.3 * 3200 = 4160
cost of type B products next year = 1.2 * 5800 = 6960
total 4169 + 6960 = 11129
ANSWER:C
Answer: (C) $11,129
Question: The number of boxes in a warehouse can be divided evenly into 5 equal shipments by boat or 24 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
(A)  27
(B)  33
(C)  54
(D)  81
(E)  120
Rationale: Answer is the LCM of 5 and 24
= 120
Answer E
Answer: (E)  120
Question: What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142
(A) 35
(B) 38
(C) 46
(D) 49
(E) 52
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 .
Answer: (C) 46
Question: A popular website requires users to create a password consisting of the digits {1,2,3,4,5}. If no digit may be repeated and each password must be at least 4 digits long, how many passwords are possible?
(A) 4! + 5!
(B) 2 x 5!
(C) 4! x 5!
(D) 9!
(E) 10!
Rationale: If we choose the 5 different digits then they can be arranged in 5! ways.
The number of possible 4-digit passwords is 5*4*3*2 = 5!
The total number of passwords is 5! + 5! = 2*5!
The answer is B.
Answer: (B) 2 x 5!
Question: If x, y, and z are all factors of 15, which of the following must be true?
(A) The product xyz > 15
(B) Either x = y, y = z, or x = z
(C) x – y – z = even
(D) The product xyz is odd
(E) yz/x is an integer
Rationale: All the factors of 15 are odd numbers.
The product of odd numbers is odd.
The answer is D.
Answer: (D) The product xyz is odd
Question: If n is an integer greater than 6, which of the following must be divisible by 10 ?
(A) n(n + 1)(n – 4)
(B) n(n + 2)(n – 1)
(C) n(n + 3)(n – 5)
(D) n(n + 4)(n – 2)
(E) n(n + 5)(n – 6)
Rationale: If n= 7 , then n+3 is divisible by 10 .
C
Answer: (C) n(n + 3)(n – 5)
Question: The workers of a factory is 10000. It decreases annually at the rate of 20% p.a. What will be its population after 4 years?
(A) 8500
(B) 7000
(C) 5282
(D) 4096
(E) 5250
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 Ã— 80/100 Ã— 80/100 x 80/100 x 80/100 = 4096
D
Answer: (D) 4096
Question: Several people are sitting around a round table playing a card game with a deck of 51 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?
(A) 4
(B) 5
(C) 7
(D) 11
(E) 13
Rationale: Let n be the number of people at the table.
If Martin gets the first and the last card, it means Martin got one more card than the others.
Thus 51/n has a remainder of 1 and so 51-1 = 50 is a multiple of n.
The answer is B.
Answer: (B) 5
Question: If twenty four men and sixteen women work on a day, the total wages to be paid is 11,600. If twelve men and thirty seven women work on a day, the total wages to be paid remains the same. What is the wages paid to a man for a day’s work?
(A) 33
(B) 38
(C) 37
(D) 299
(E) 22
Rationale: Answer:B
Answer: (B) 38
Question: Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 15
Rationale: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.
So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes.
If the average of 10 and 20-pound boxes is to be 16, the ratio of 10-pound boxes:20-pound boxes should be 2:3.
The number of 10 pound boxes remains the same so we still have 4 of them.
To get a ratio of 2:3, the number of 20-pound boxes must be 6.
We need to remove 10 of the 20-pound boxes.
The answer is B.
Answer: (B) 10
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability J that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
(A) (a) 4/10
(B) (b) 4/9
(C) (c) 1/2
(D) (d) 6/10
(E) (e) 5/9
Rationale: Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability J= 50/90 = 5/9
Correct answer E
Answer: (E) (e) 5/9
Question: Anne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?
(A) 3%
(B) 4%
(C) 7%
(D) 10%
(E) 12%
Rationale: Cost of Computer = $2000
Sales tax = (5/100)*2000 = $100
Total Cost of Computer = 2000 + 100 = 2100
For Henry
Cost of Computer = $1800
Sales tax = (12/100)*1800 = $216
Total Cost of Computer = 1800 + 216 = 2016
% that Henry paid less than Anne = (2100 - 2016)*100/2100 = 4%
Answer: Option B
Answer: (B) 4%
Question: (2^2+4^2+6^2+.....+18^2)=?
(A) 1322
(B) 2356
(C) 6544
(D) 1140
(E) 7954
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x9)^2
=2^2 x (1^2+2^2+3^2+.......+9^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x9x10x19)
=(4x285)=1140
Answer is D
Answer: (D) 1140
Question: 1=5,2=10,3=253,4=254,5=255,6=256,7=257,8=258 then 10=?
(A) 2
(B) 255
(C) 345
(D) 445
(E) 235
Rationale: 1=5,2=10,3=253,4=254,5=255,6=256,7=257,8=258 then 10=?
10=2
check the first eqn.
ANSWER:A
Answer: (A) 2
Question: We can rent a bike for x cents per minute for the first 15 minutes and then y cents for each additional minute. How much will it cost to rent a bike for z minutes, where z>15?
(A) 15x+(z-15)y
(B) 15x + zy
(C) 15y +(z-15)x
(D) x + zy
(E) x + (z-15)y
Rationale: The first 15 minutes cost 15x.
The next (z-15) minutes cost (z-15)y.
The total cost is 15x+(z-15)y.
The answer is A.
Answer: (A) 15x+(z-15)y
Question: In a kilometer race, If Abhishek gives Bharti a 40 m start, Abhishek wins by 19 sec. But if Abhishek gives Bharti a 30 sec start, Bharti wins by 40 m. Find the time taken by Bharti to run 5,000 m?
(A) 150 sec
(B) 750 sec
(C) 450 sec
(D) 825 sec
(E) None of these
Rationale: Explanation :
If Abhishek takes x seconds and Bharti takes y seconds to run 1 km, then:
=>y=150 sec and x=125 sec
=>x+19=960y/1000 and
=(960x/1000)+30=y
=>y=150 sec and x=125 sec
Answer =(150/1000)×500
= 750 sec
Answer : B
Answer: (B) 750 sec
Question: Find the arithmetic mean B of all roots of the following equation- see an attachment.
(A) 2
(B) 1
(C) 0.5
(D) -1/3
(E) 0.3
Rationale: arithmetic mean B your answer C and E are same, can you correct one of them please. thanks.C
Answer: (C) 0.5