mathewhe/aqua_rat huggingface dataset:
Question: In each term of a sequence, 9 is added to get the next term. If the first term is 2, what is the eighty-first term?
(A) 632
(B) 695
(C) 713
(D) 722
(E) 731
Rationale: Let’s think about the first few terms of this sequence.
a_1=2
a_2=11 = 2 + 9
a_3=20 = 2 + 9 + 9
a_4=29 = 2 + 9 + 9 + 9
To find each new term, we add 9. The result is, each term equals 2 plus a sum of 9’s. How many nines? Well, the second term has one 9, the third term has two 9’s, the fourth term has three 9’s, so it’s clear the nth term would have a sum of (n – 1) 9’s. Thus, the eighty-first term would be 2 plus eighty 9’s. Well, eighty 9’s = 80*9 = 720, so the eighty-first term = 722, answer D.
Answer: (D) 722
Question: How many of the positive factors of 20 are not factors of 24
(A) 2
(B) 3
(C) 4
(D) 1
(E) 5
Rationale: factors of 20 - 1, 2, 4,5, 10, 20
factors of 24 -1, 2, 3, 4, 6, 8, 12 and 24
Comparing both, we have 3 factors of 20 which are not factors of 24- 5,10,20
Answer : B
Answer: (B) 3
Question: If 5 persons can do 5 times of a particular work in 5 days, then, 3 persons can do 3 times of that work in?
(A) 2 days
(B) 3 days
(C) 5 days
(D) 7 days
(E) 9 days
Rationale: That is, 1 person can do one time of the work in 5 days.
Therefore, 3 persons can do 3 times work in the same 5 days itself.
C)
Answer: (C) 5 days
Question: The profits of a firm are to be distributed in a suitable ratio. Suitable ratio is the ratio whose terms differ by 40 and the measure of which is 2/7. Find the suitable ratio.
(A) 280 : 2
(B) 16 : 56
(C) 80 : 7
(D) 40 : 14
(E) none of these
Rationale: Let the ratio be x : y
Given x/y = 2/7,
Also y - x = 40,
Solving we get, x = 16, y = 56
ANSWER:B
Answer: (B) 16 : 56
Question: The probability that a girl student gets scholarship is 0.6 and that of a boy is 0.8,then probability that at least one gets the scholarship is:
(A) 0.72
(B) 0.82
(C) 0.92
(D) 1.12
(E) 1.22
Rationale: Probability that girl gets scholarship = 0.6
Probability that boy gets scholarship = 0.8
Hence, Probability that girl don't get scholarship = 1-0.6 = 0.4
Probability that boy don't get scholarship = 1-0.8 = 0.2
So, Probability that at least one gets scholarship is: (Girl gets and Boy don't get) OR (Boy gets and Girl don't get) OR (Both Gets)
=(0.6*0.2)+(0.8*0.4)+(0.6*0.8)
=0.12+0.32+0.48
=0.92
ANSWER:C
Answer: (C) 0.92
Question: 1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member
(A) A.10%
(B) B.20%
(C) C.45%
(D) D.55%
(E) E.50%
Rationale: A,B, C is too low so I eliminated those answers, E was too high of a number, so I chose D as my final answer.C
Answer: (C) C.45%
Question: An organisation has 3 committees, only 2 persons are members of all 3 committee but every pair of committee has 3 members in common. what is the least possible number of members on any one committee?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 4
Rationale: Total 4 members minimum required to serve only on one committee.
\Answer:E
Answer: (E) 4
Question: What percent of a day is 6 hours?
(A) 6.25%
(B) 20%
(C) 25%
(D) 12.5%
(E) 10 %
Rationale: Total hours in a day = 24
Required percent =6×100=25%
---
24
Answer: Option C
Answer: (C) 25%
Question: In how many ways a committee of 5 members can be selected from 6men and 5ladies, consisting of 3 men and 2 ladies?
(A) 120
(B) 115
(C) 250
(D) 160
(E) 200
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen
Required number of ways = 6C3 * 5C2 = (6*5*4*5*4)/(3*2*1*2*1) = 200
Answer is E
Answer: (E) 200
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is?
(A) 4320
(B) 4325
(C) 4330
(D) 4884
(E) 4336
Rationale: Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 44 = 4884
D
Answer: (D) 4884
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 18 hours and 8 hours respectively. The ratio of their speeds is
(A) 4 : 9
(B) 4 : 3
(C) 4 : 12
(D) 4 : 8
(E) 4 : 5
Rationale: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 18 = 4 : 9.Answer: A
Answer: (A) 4 : 9
Question: Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 25% the new mean is $850.What was original rent of friend whose rent is increased?
(A) 800
(B) 900
(C) 1000
(D) 1100
(E) 1200
Rationale: 0.25X = 4(850-800)
0.25X = 200
X = 800
answer A
Answer: (A) 800
Question: There are 14 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 288
(B) 267
(C) 261
(D) 211
(E) 240
Rationale: The total number of stations = 16
From 16 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 16P₂ ways.
16P₂ = 16* 15= 240.
Answer: E
Answer: (E) 240
Question: If 2x + y = 26 and x + 2y = 10, then (x + y)/3 =
(A)  1
(B)  4/3
(C)  17/5
(D)  18/5
(E)  4
Rationale: We have two equations:
2x + y = 26
x + 2y = 10
Notice that something nice happens when we ADD them. We get:
3x + 3y = 36
Divide both sides by 3 to get:x + y = 12
So, (x + y)/3 =12/3=4
Answer: E
Answer: (E)  4
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
(A) 9:37
(B) 9:31
(C) 9:38
(D) 9:32
(E) 9:35
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: (B) 9:31
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 12 years at the same rate?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: P ---- 2P ---- 8 years3P ---- 12 years Answer: C
Answer: (C) 3
Question: 18 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 32
(B) 87
(C) 36
(D) 99
(E) 77
Rationale: 3W = 2M
18M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
18 * 21 * 8 = 14 * x * 6
x = 36
Answer: C
Answer: (C) 36
Question: A utensil contain the amount of milk which is as much lesser than 80 is more than 42. The amount of milk is?
(A) 45
(B) 49
(C) 71
(D) 61
(E) 56
Rationale: Answer
Let the amount be x.
Then, x - 42= 80- x
’ 2x = 80+ 42= 122
2x = 122
´ x = 61
Correct Option: D
Answer: (D) 61
Question: If 16 men working 7 hours day can plough a fieid in 4l days, inhow many days will 14 men working 12 hours a clay plough the samefield ?
(A) 22
(B) 32
(C) 36
(D) 39
(E) 40
Rationale: Explanation :
(Men 14 : 16) : (Hrs/Day 12 : 7) :: 48 : x14 * 12 * x = 16 * 7 * 48 or x = 32
Answer : B
Answer: (B) 32
Question: The product of two positive integers is 783 and their difference is 2. What is the bigger number?
(A) 23
(B) 25
(C) 27
(D) 29
(E) 31
Rationale: Let's use trial and error to find the two numbers.
30*28 = 840 (too high)
29*27 = 783
The answer is D.
Answer: (D) 29
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 30 days more. What is the reinforcement?
(A) 1800 men
(B) 3900 men
(C) 600 men
(D) 3800 men
(E) 900 men
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*30 = 2000*39
x = 2600
2000
-------
600
ANSWER:C
Answer: (C) 600 men
Question: A girl has nine jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?
(A) 100
(B) 102
(C) 108
(D) 110
(E) 112
Rationale: The girl can select one jeans in nine ways.
The girl can select one shirt in 12 ways.
The number of ways in which he can select one jeans and one shirt is 9 * 12 = 108 ways.
C
Answer: (C) 108
Question: The L.C.M. of two numbers is 36. The numbers are in the ratio 2 : 3. Then sum of the number is:
(A) 28
(B) 30
(C) 40
(D) 53
(E) 54
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 36 or x = 6.
The numbers are 12 and 18.
Hence, required sum = (12 + 18) = 30.
Answer: Option B
Answer: (B) 30
Question: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
(A) 9
(B) 10
(C) 11
(D) 14
(E) 2
Rationale: B
10
This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
Answer: (B) 10
Question: The minimum number of tiles of size 16 by 24 required to form a square by placing them adjacent to one another is
(A) 4 tiles
(B) 5 tiles
(C) 6 tiles
(D) 7 tiles
(E) 8 tiles
Rationale: LCM of 16,24 = 48
48*48 is the minimum size of square made with 16 by 24 tiles
Number of tiles required = area of square/area of one tile
=48*48/(16*24)
= 6 tiles
ANSWER:C
Answer: (C) 6 tiles
Question: If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of an orange fruit ?
(A) Green
(B) BLUE
(C) PINK
(D) ORANCE
(E) BLACK
Rationale: Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of an orange fruit is 'Orange' but in coding language, 'Orange' is called 'Blue'.
ANSWER: B
Answer: (B) BLUE
Question: A bag contains 2 yellow balls, 3 white balls and 5 red balls. In how many ways can two balls be drawn from the bag?
(A) 2C2
(B) 10C2
(C) 8C2
(D) 5C2
(E) 6C2
Rationale: Total number of balls= 2+3+5 = 10
2 balls can be drawn from 10 balls in 10C2
ANSWER:B
Answer: (B) 10C2
Question: If a train, travelling at a speed of 160 kmph, crosses a pole in 18 sec, then the length of train is?
(A) 800
(B) 125
(C) 288
(D) 266
(E) 121
Rationale: D = 160 * 5/18 * 18
= 800 m
Answer: A
Answer: (A) 800
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 6hrs if the speed of the bike is twice speed of the tractor?
(A) 400 km
(B) 500 km
(C) 360 km
(D) 540 km
(E) 600 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 6 h is
90 × 6 = 540 km
Ans.(D)
Answer: (D) 540 km
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 50 milliliters of solution X to create a solution that is 25 percent alcohol by volume?
(A) 150
(B) 500/3
(C) 400
(D) 480
(E) 600
Rationale: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?
W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.
If X = 50 then Y = 150
ANSWER:A
Answer: (A) 150
Question: What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?
(A) 227
(B) 814
(C) 168
(D) 686
(E) 218
Rationale: In this type of questions, first we need to calculate the area of tiles. With we can get by obtaining the length of largest tile.
Length of largest tile can be obtained from HCF of length and breadth.
So lets solve this,
Length of largest tile = HCF of (1517 cm and 902 cm)
= 41 cm
Required number of tiles =
Area of floorArea of tile=(1517×90241×41)=814
Answer:B
Answer: (B) 814
Question: How much does a watch lose per day, if its hands coincide ever 64 minutes?
(A) 32 8/11
(B) 32 8/19
(C) 32 8/12
(D) 32 8/13
(E) 32 8/17
Rationale: 55min spaces are covered in 60min
60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.
loss in 64min=(65+5/11)- 64 =16/11
Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.
Answer: A) 32 8/11
Answer: (A) 32 8/11
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
(A) 22
(B) 77
(C) 26
(D) 20
(E) 99
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
Answer: D
Answer: (D) 20
Question: Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second vessel. In what ratio should the contents be mixed such that the resultant mixture has milk and water in the ratio of 2:5.
(A) 1:5
(B) 2:5
(C) 3:5
(D) 4:5
(E) 5:5
Rationale: Let 1st vessel contains X liters of mixture of milk and water.
Milk in 1st vessel = 4/13x
Water in 1st vessel=9/13x
Let 2nd vessel contains Y liters of mixture of milk and water
Milk in 2nd vessel = 2/9y
Water in 2nd vessel =7/9y
Let the two mixture combine such that the milk to water ratio is 2:5
4x/13 + 2y/9 / 9x/13 +7/9y =2/5
36x+26y/81x+91y=2/5
180x+130y=162x+182y
18x=52y
x/y=26/9
Hence mixture from vessel 1 and vessel 2 should be mixed in the ratio 26/9 for milk and water to be in ratio 2:5
ANSWER:B
Answer: (B) 2:5
Question: In six successive games, a baseball team scored 2 runs once, 5 runs twice, and 6 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: 2 runs once (one game)
5 runs twice (two game)
6 runs three times (three games)
SO we have (2*1 + 5*2 + 6*3)/6 = 30/6 = 5.
ANS: D.
Answer: (D) 5
Question: If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true?
I. (x + z)^2 > y
II. yz > x
III. x+y>z
(A) III only
(B) II only
(C) II,III only
(D) I only
(E) I,III only
Rationale: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.
III) x+y>z
Not necessarily true as 1+5<7
II) yz>x
Not necessarily true as 5.7<1
I) We don't need to check option as all the options except D can be discarded.
Thus Answer D
Answer: (D) I only
Question: A and B started a business with initial investments in the ratio 6 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?
(A) 6 months
(B) 8 months
(C) 21 months
(D) 5 months
(E) 7 months
Rationale: Let Sumit in the business for ‘a’ months.
Investment Ratio Amit to Sumith = 6 : 3.
Profit sharing ratio = 8 : 7.
Amit is in the business for 12 months.
Then Sumit in the business for
(6× 12) / (3 × a) = 8 / 7 => 24a = 504 or
a = 504 / 24 = 21 or 21 months
Option C
Answer: (C) 21 months
Question: a little girl went to the farm to buy fruits. she bought 10 apples, 10 oranges and 30 strawberries. what is the ratio of the apples to all the fruits bought?
(A) 1/2
(B) 1/5
(C) 1/10
(D) 10/30
(E) 3/5
Rationale: total # of fruits is 10+10+30=50; ratio of her apples to all the fruits bought is 10/50 = 1/5
ANSWER:B
Answer: (B) 1/5
Question: The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: The average of 24, 35, and 58 is 39.
The average of 19, 51 and x is 33.
Then 19 + 51 + x = 99.
x = 29.
The answer is D.
Answer: (D) 29
Question: A train traveling at 40 kms / hr while inside the tunnel meets another train of half its length traveling at 60 kms / hr and passes it completely in 4.5 seconds. Find the length of the tunnel if the first train passes completely through it in 4 minutes 37.5 seconds.
(A) 2000 meters
(B) 3000 meters
(C) 4000 meters
(D) 5000 meters
(E) 6000 meters
Rationale: 3000meters
ANSWER:B
Answer: (B) 3000 meters
Question: A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 240
(B) 250
(C) 260
(D) 230
(E) 220
Rationale: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 36
=> 300+L = 15×36 = 540
=> L = 540-300 = 240 meter
Answer is A.
Answer: (A) 240
Question: How many times the keys of a writterhave to bepressed in order to write first 400 counting no.'s?
(A) 980
(B) 990
(C) 1092
(D) 1100
(E) 1230
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
C
Answer: (C) 1092
Question: If j and k are integers, and 2j + k = 15, which of the following must be true?
(A) j + k is odd.
(B) j + k is even.
(C) j is odd.
(D) k is odd.
(E) k > j
Rationale: 2j+k=15
even+odd=odd
So k is odd. D is the answer.
Answer: (D) k is odd.
Question: Sheik Abdullah decides to buy 4 new cars for his collection. If he has to choose between eight different cars, what is the number of purchasing possibilities he has?
(A) A)7
(B) B)11
(C) C)14
(D) D)18
(E) E)21
Rationale: Sheik Abdullah decides to buy 4 new cars for his collection. He has to choose between eight different cars
8C3= 8*7*6/(4*3*2*1) = 14 ANS:C
Answer: (C) C)14
Question: A man took a loan from a bank at the rate of 11% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :
(A) Rs. 16363.64
(B) Rs. 10,000.64
(C) Rs. 15,000,64
(D) Rs. 21,353.64
(E) None
Rationale: Solution
Principal = Rs.(100x5400/11x3)= Rs. 16363.64.
Answer A
Answer: (A) Rs. 16363.64
Question: A certain league has three divisions. The respective divisions had 10, 12 and 15 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
(A)  70
(B)  72
(C)  73
(D)  78
(E)  80
Rationale: Overall, there can be 73 minuses. Tus, it is C.
Answer: (C)  73
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 277
(B) 299
(C) 245
(D) 888
(E) 291
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer:C
Answer: (C) 245
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
(A) 39
(B) 23
(C) 20
(D) 27
(E) 26
Rationale: 1/x + 1/(x + 10)
= 1/12
x = 20
Answer:C
Answer: (C) 20
Question: A charity collected $3,199 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
(A) 145
(B) 150
(C) 155
(D) 159
(E) 165
Rationale: Min fund = 20
Total = 3199
The closest multiple of 20 to 3199 is : 159
Which implies 158 people gave 20 and 1 person gave 39
Ans. D
Answer: (D) 159
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 17, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:
(A) 6
(B) 7
(C) 9
(D) 10
(E) 11
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 17
5x = 15
x = 3.
Hence, B's age = 2x = 6 years.
Answer: Option A
Answer: (A) 6
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
(A) 21000
(B) 22882
(C) 12112
(D) 27788
(E) 27712
Rationale: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000
Answer: A
Answer: (A) 21000
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 76
(B) 87
(C) 72
(D) 11
(E) 26
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Answer: (C) 72
Question: What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?
(A) 0
(B) 1
(C) 5
(D) 7
(E) 8
Rationale: 1/3 + 1/9 + 1/27 = 13/27. = .481481…
1/37=.027027…
13/27 + 1/27 = .508508..
Hence 101st digit is 0.(3*33 +2=> hence the second digit of the recurring decimal which is 0)
Answer:A
Answer: (A) 0
Question: Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 50% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
(A) 1 to 4
(B) 1 to 3
(C) 3 to 6
(D) 3 to 4
(E) 3 to 2
Rationale: Correct Answer: C
Solution: C. We know that when Pam and Stanley were both working, the ratio was 3 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 3 to 6. Answer C is correct.
Answer: (C) 3 to 6
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 15 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
(A) 40.2
(B) 40.4
(C) 40.5
(D) 40.8
(E) None of the above
Rationale: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 15 = 405
Hence, new average = 405⁄10 = 40.5
Answer C
Answer: (C) 40.5
Question: Solve the equation :
A) 7(3x – 6) + 5(x - 3) - 2(x - 7) = 5 ,
B) (x -3)(x + 4) - 2(3x - 2) = (x - 4)2,
C) (x + 1)3 – (x - 1)3 = 6(x2 + x + 1)
(A) 3, 8, -2/3
(B) 2, 8, -2/3
(C) 4, 8, -2/3
(D) 5, 8, -2/3
(E) None
Rationale: Solution:
A) 21x - 42 + 5x - 15 - 2x + 14 = 5<=>
21x + 5x - 2x = 5 + 42 + 15 - 14<=>
24x = 48 <=> x = 2
B) x2 + 4x - 3x - 12 - 6x + 4 = x2 - 8x + 16 <=>
x2 - 5x – x2 + 8x = 16 + 12 – 4 <=>
3x = 24 <=> x = 8
C) x3 + 3x2 + 3x + 1 – (x3 - 3x2 + 3x - 1) = 6x2 + 6x + 6 <=>
x3 + 3x2 + 3x + 1 – x3 + 3x2 + 1 = 6x2 + 6x + 6 <=>
2 = 6x + 6 <=> 6x = -4 <=> x = -2/3
Answer B
Answer: (B) 2, 8, -2/3
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.9
(B) 31.2
(C) 31.6
(D) 71.2
(E) 31.1
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6'
Answer: C
Answer: (C) 31.6
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 12 times the probability that both events A and B occur. What is the probability that event A occurs?
(A) 21/26
(B) 25/26
(C) 11/26
(D) 6/26
(E) 22/33
Rationale: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 12 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 12*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 12*2b*b
3b-2b^2 = 24b^2
3b = 26b^2
b = 3/26 = 3/26
So, a = 2b = 6/26
THE CORRECT ANSWER IS D.
Answer: (D) 6/26
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
(A) Rs. 50000
(B) Rs. 52000
(C) Rs. 57000
(D) Rs. 60000
(E) Rs. 62000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs. 57000
C
Answer: (C) Rs. 57000