mathewhe/aqua_rat huggingface dataset:
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point E at the same time, how long, in hours, after the trains depart will they again meet at Point E?
(A) 3
(B) 6
(C) 9
(D) 18
(E) 22
Rationale: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train A be X, thus that covered by the train B will be 12*3.14-X
dA = X dB = 12*3.14 - X
Times taken by A and B are
tA= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of A and B: totalSpeed E= 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tA =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5=B
Answer: (B) 6
Question: The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
(A) 42
(B) 44
(C) 46
(D) 48
(E) 50
Rationale: The time it takes Cara to drive to City B is 120 / 30 = 4 hours.
Dan needs to take less than 2.5 hours for the trip.
Dan needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour.
The answer is D.
Answer: (D) 48
Question: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 30 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 30 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
(A) 10
(B) 11
(C) 13
(D) 14
(E) 15
Rationale: Let number of Apples = A
number of oranges = B
A+B=30 --- 1
.56 =(.4A + .6 B)/30
=> 56 = 4A + 6B ----2
Solving 1 and 2, we get
A= 6
B= 24
Let the number of oranges put back = C
52*(30-c) = 40*6 + 60(24-C)
=> C= 15
Answer E
Answer: (E) 15
Question: 19/6 = 4/27 . which method did you use to determine whether this proportion is true or false?
(A) true
(B) neutral
(C) false
(D) not sure
(E) none
Rationale: 19/6= 4/27. cross multiplication: 19 * 27 = 513, 6 * 4 = 24,
we see that 513 are not equal to 24. so there is no proportion. corrcet answer: (C)
Answer: (C) false
Question: The water level in a rectangular swimming pool measuring 40 feet by 25 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)
(A) 100
(B) 250
(C) 750
(D) 3750
(E) 5625
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 40*25*1/2=500 feet^3 of water must be removed, which equals to 500*7.5=3750 gallons.
Answer: D.
Answer: (D) 3750
Question: Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
(A) 20 1/2 hours
(B) 20 1/6 hours
(C) 20 3/2 hours
(D) 23 1/2 hours
(E) 21 1/2 hours
Rationale: n:
1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours
Answer: A
Answer: (A) 20 1/2 hours
Question: The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
(A) 18 years
(B) 88 years
(C) 77 years
(D) 10 years
(E) 17 years
Rationale: Let their ages be x and (x + 20) years.
5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years
Answer:D
Answer: (D) 10 years
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 22.5 miles ahead of Joe?
(A) 15
(B) 60
(C) 75
(D) 90
(E) 120
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Joe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +22.5 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 22.5 miles in 90 mins
So answer 30+90= 120 mins.(ANSWER E)
Answer: (E) 120
Question: A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 662
(B) 672
(C) 652
(D) 642
(E) 721
Rationale: 8 * 84 = 672 – 10 = 662
ANSWER:A
Answer: (A) 662
Question: Alice took out a charge account at the General Store and agreed to pay 3% simple annual interest. If she charges $40 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
(A) $41.20
(B) $41.60
(C) $42.00
(D) $42.40
(E) $42.80
Rationale: 1.03*$40=$41.20
The answer is A.
Answer: (A) $41.20
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 10800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
(A) 9000
(B) 98000
(C) 60000
(D) 11000
(E) 12000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 10800 ( 18 × 600 = 10800)
100% -------> 60000 votes (100 × 600 = 60000)
C
Answer: (C) 60000
Question: Tough and Tricky questions: Work/Rate Problems.
A group of 4 junior lawyers require 2 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?
Source: Chili Hot GMAT
(A) 13
(B) 10
(C) 9
(D) 6
(E) 4
Rationale: # of people times the # of hours:
4*2 = 8 --> 4 lawyers do 8worksin 2 hours.
3*4/3 = 4--> 3 assistants do 4worksin 4/3 hours
So, since the amount of work the assistants do is half the work the lawyers do, the time will be double, soANS E
Answer: (E) 4
Question: A train running at the speed of 30 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 75 m
(B) 180 m
(C) 324 m
(D) Cannot be determined
(E) None of these
Rationale: Speed = 30 * 5/18 = 25/3 m/sec
Length of the train = speed * time = 25/3 * 9 = 75 m
ANSWER:A
Answer: (A) 75 m
Question: In a certain pond, 30 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A) 750
(B) 625
(C) 1,250
(D) 2,500
(E) 10,000
Rationale: This is a rather straight forward ratio problem.
1. 30 fish tagged
2. 2 out of the 50 fish caught were tagged thus 2/50
2/50=30/x
thus, x=750
Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?
You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch.
A
Answer: (A) 750
Question: John throws a coin until a series of four consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fifth throw?
(A) 1/16
(B) 2/16
(C) 3/16
(D) 7/16
(E) 9/16
Rationale: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
H-T-T-T-T ----> P = (1/2)^5 = 1/32
T-H-H-H-H ----> P = (1/2)^5 = 1/32
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/32 + 1/32 = 2/32 = 1/16
Answer(A).
Answer: (A) 1/16
Question: A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 6 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
(A) 258
(B) 426
(C) 324
(D) 542
(E) 410
Rationale: Pretty simple actually
Number of 1 letter symbols = 6
Number of 2 letter symbols = 6*6
Number of 3 letter symbols = 6*6*6
The answer is sum of the 3. = 258
The answer choices have their units digits unique. All 3 of the above end in 6 (6 to the power of anything ends in 6) so 6+6+6 = 18 i.e. ends with 8.
So the answer is A.
Answer: (A) 258
Question: In a Don Bosco college students, 80 percent are third year students and 90 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?
(A)  3/4
(B)  2/3
(C)  4/7
(D)  1/2
(E)  3/7
Rationale: = 10/20. = 1/2
my answer is D too
Answer: (D)  1/2
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,64,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
(A) 0.20833
(B) 0.14544
(C) 0.21978
(D) 0.35466
(E) 0.63435
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 364000x
\therefore Required percentage = \inline \frac{800x}{364000}\times 100 = 0.21978
C
Answer: (C) 0.21978
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) Rs. 135
(B) Rs. 162
(C) Rs. 189
(D) Rs. 198
(E) None of these
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
ANSWER:C
Answer: (C) Rs. 189
Question: What is the color code for a 220 omega.gif 5% resistor?
(A) Red, Red, Brown, Gold
(B) Red, Red, Brown,Pink
(C) Red, Red, Brown, Black
(D) Red, Red, Brown, BROUNE
(E) Red, Red, Brown, ASHE
Rationale: Resistor colour coding series:
Black 0
Brown 1
Red 2
Orange 3
Yellow 4
Green 5
Blue 6
Violet 7
Gray 8
White 9
None 20%
Silver 10%
Gold 5%
Therefore Red, Red, Brown, Gold
2 2 101 5%
Answer:B
Answer: (B) Red, Red, Brown,Pink
Question: 52 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
(A) 30.33
(B) 34.44
(C) 26.1
(D) 28.0
(E) 21.0
Rationale: Explanation:
Let the two parts be (52 - x) and x.
Then, 10 (52 - x) + 22x = 780
=> 12x = 260
=> x = 21.66.
Bigger part = (52 - x) = 30.33.
Answer: A) 30.33
Answer: (A) 30.33
Question: A man whose speed is 8 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 3 kmph, find his average speed for the total journey ?
(A) 1 kmph
(B) 5 kmph
(C) 6 kmph
(D) 4 kmph
(E) 6.8 kmph
Rationale: Explanation:
Speed of Man = 8 kmph
Speed of stream = 3 kmph
Speed in DownStream = 11 kmph
Speed in UpStream = 5 kmph
Average Speed = (2 x 11 x 5)/16 = 6.8 kmph.
Answer: E
Answer: (E) 6.8 kmph
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 25% solution?
(A) A)6.7
(B) B)1.3
(C) C)9.6
(D) D)20
(E) E)7.9
Rationale: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=25/100
40+4x=100+x
3x = 60
x = 20
Answer is D
Answer: (D) D)20
Question: In the equation A + B + C + D + E = FG where FG is the two digit number whose value is 10F + G and letters A, B , C , D , E, F and G each represent different digits. If FG is as large as possible. What is the value of G?
(A) 9
(B) 2
(C) 3
(D) 45
(E) 6
Rationale: FG is as large as possible and all the 7 numbers should be different.
By trial and Error method,
9 + 8 + 7 + 6 + 5 = 35…5 is getting repeated twice.
9 + 8 + 7 + 6 + 4 = 34…4 is getting repeated
9 + 8 + 7 + 5 + 4 = 33…3 repeats
9 + 8 + 6 + 5 + 4 = 32
None of the numbers repeat in the above case and 32 is the maximum number FG can have. The value of G is 2.
Ans: B
Answer: (B) 2
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 6
(B) 4
(C) 5
(D) 1
(E) 2
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.
Answer:C
Answer: (C) 5
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 7
(C) 4
(D) 2
(E) 1
Rationale: US = 25
DS = 35
M = (35 - 25)/2
= 5
Answer: A
Answer: (A) 5
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 3 : 7. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
(A) s 1200
(B) s 1500
(C) s 1600
(D) s 2000
(E) s 1700
Rationale: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 3x and R = 7x.
Then, 5x = 1500 ? x = 500. P=1500,Q=1500 and R = 3500.
Hence, (R - p) = (3500 - 1500) = 2000
Answer : D
Answer: (D) s 2000
Question: A train 110m long is running at 50kmph. In how much time will it pass a platform 210m long?
(A) 14.15 seconds
(B) 15.24 seconds
(C) 16.28 seconds
(D) 13.30 seconds
(E) 10.24 seconds
Rationale: Distance travelled = 110 + 210m = 320mSpeed = 50 * 5/8 = 125/4mTime = 320 * 4/125 = 10.24 SecondsAnswer : E.
Answer: (E) 10.24 seconds
Question: A man sitting in a train which is traveling at 80 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
(A) 32 kmph
(B) 58 kmph
(C) 62 kmph
(D) 65 kmph
(E) 75 kmph
Rationale: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 80) kmph = 32 kmph.
Answer : A
Answer: (A) 32 kmph
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
(A) 51
(B) 52
(C) 59
(D) 55
(E) 56
Rationale: For 40 hrs = 40*16=640
Excess = 976-640=336
For extra hours =.75(16)=12+16=28
Number of extra hrs =336/28=12
Total hrs =40+12=52
Answer B
Answer: (B) 52
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
(A) 12
(B) 14
(C) 27
(D) 53
(E) None of these
Rationale: Explanation:
In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
Answer: Option B
Answer: (B) 14
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 288
(B) 279
(C) 277
(D) 272
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer: E
Answer: (E) 150
Question: In 2008, a certain factory produced 40% more widgets than it did in 2007, and its production in 2009 was 130% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?
(A) 33.9%
(B) 36.7%
(C) 39.5%
(D) 42.3%
(E) 45.1%
Rationale: Let P be the original level of production in 2007.
Let x be the rate of production in 2010 compared to 2009.
x*1.3*1.4*P = P
x = 1/1.82 = 0.549 which is a decrease of 45.1%.
The answer is E.
Answer: (E) 45.1%
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
(A) 4/17
(B) 4/16
(C) 4/15
(D) 4/13
(E) 4/12
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer:D
Answer: (D) 4/13
Question: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error.
(A) 64%
(B) 65%
(C) 66%
(D) 67%
(E) None of these
Rationale: Explanation:
Let the number be x,
then,
5/3−3/5=16/15x
Error% =
(16/15x∗3/5∗100)
Option A
Answer: (A) 64%
Question: Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 40% more than Bert had in savings, and separately, the same price was also 75% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
(A) 1:4
(B) 4:1
(C) 2:3
(D) 3:2
(E) 5:4
Rationale: Suppose bert had 100 so price becomes 140 , this 140 = 1.75 times R's saving .. so R's saving becomes 80
So required ratio is 100:80=5:4
ANSWER:E
Answer: (E) 5:4
Question: If population of certain city increases at the rate of 3%. If population in 1981 was 138915, then population in 1980 was?
(A) 134869
(B) 130000
(C) 261000
(D) 627000
(E) 12690
Rationale: Explanation:
X * (103/100) = 138915
X = 138915/1.157625
X = 134868.93=134869
Answer: Option A
Answer: (A) 134869
Question: The distance between West-Town to East-Town is 15 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
(A) 3.
(B) 7.
(C) 10.
(D) 12
(E) 15.
Rationale: By end of 1st min: distance covered by 1st bird is 4 km and 2nd is 1 km. Total distance = 5km.
By end of 2nd min: distance covered by 1st bird is 8 km and 2nd is 2 km. Total distance = 10km.
By end of 3rd min: distance covered by 1st bird is 12 km and 2nd is 3 km. Total distance = 15km.
So, meeting point is 12kms from West-Town (from where 1st bird started)
Hence, answer will be D.
Answer: (D) 12
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 2288
(B) 2772
(C) 100
(D) 2771
(E) 2981
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%Answer:C
Answer: (C) 100
Question: What number comes next in this Number series.
7 8 5 5 3 4 4 ?
*Hint: check calende
(A) 6
(B) 3
(C) 6
(D) 1
(E) 8
Rationale: A
6 (the number of letters in the month august)
January : 7 letters
February: 8 letters
March : 5 letters
April : 5 letters
May : 3 letters
June : 4 letters
July : 4 letters
Answer: (A) 6
Question: Find the middle one when The sum of three consecutive even numbers is 57?
(A) 10
(B) 12
(C) 19
(D) 15
(E) 16
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 57.
Hence a = 19.
C
Answer: (C) 19
Question: The actual area of a rectangle is 60 Cm2, but while measuring its length a student decreases it by 20% and the breadth increases by 25%. The percentage error in area, calculated by the student is :
(A) 5%
(B) 15%
(C) 20%
(D) No change
(E) None of these
Rationale: Solution: 100 ---- 25% ↑ ---> 125 ----- 20% ↓ -----> 100.
So there is no change in the area of rectangle.
Alternatively :
Let area be 1.
Area of rectangle,
= l *b
= 0.8 *1.25
= 1.
Answer: Option D
Answer: (D) No change
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.13000 at the end of the year, B's share is
(A) Rs.4000
(B) Rs.4680
(C) Rs.7500
(D) Rs.6600
(E) None
Rationale: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(13000 x 4 / 11)
= Rs.4680.
Answer B
Answer: (B) Rs.4680
Question: The hour hand of a watch rotates 30 degrees every hour. How many complete rotations does the hour hand make in 6 days?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Explanation:
There are 360 degrees in a complete circle, so 360/30 = 12 hours to make one full circle. In 6 days there are 24 hours x 6 = 144 hours total. The total number of rotations will be 144/12 = 12.
Answer :(C)
Answer: (C) 12
Question: A reduction of 30% in the price of oil enables a house wife to obtain 6kgs more for Rs.940, what is the reduced price for kg?
(A) 72
(B) 47
(C) 40
(D) 28
(E) 20
Rationale: 940*(30/100) = 282 ---- 6
? ---- 1 => Rs.47
Answer:B
Answer: (B) 47
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
(A) 287
(B) 219
(C) 168
(D) 140
(E) 779
Rationale: A+B+C = 675
A = 3B
3B+B+B-25 = 675
5B = 700
B = 140
Answer: D
Answer: (D) 140
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
(A) 5 m/s
(B) 8 m/s
(C) 9 m/s
(D) 4 m/s
(E) 2 m/s
Rationale: B
8 m/s
Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer: (B) 8 m/s
Question: A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 65 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
(A) 3,000
(B) 2,700
(C) 4,500
(D) 5,400
(E) 324,000
Rationale: Together the two machines make 35+65=100 copies per minute. So, in half an hour they will make 100*30=3,000 copies.
Answer: A.
Answer: (A) 3,000
Question: A project manager needs to select a group of 3people from a total of 3 men and 3 women. How many possible group combinations exist such that no group has all women?
(A) 72
(B) 19
(C) 74
(D) 82
(E) 48
Rationale: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 6 people in this case.
Where K = the total number of elements to select, 3 people in this case.
The total number of combinations is therefore:
6!/((6-3)!3!) = 20
However, two of these combinations are not valid since they have all members of one gender.
The correct answer is 20-2 = 18. Ans B
Answer: (B) 19
Question: In how many ways can Ram choose a vowel and a constant from the letters of the word ALLAHABAD?
(A) 4
(B) 6
(C) 9
(D) 5
(E) 7
Rationale: Solution
In the letters of the word ALLAHABAD there is only 1 vowel available for selection (A). Note that the fact that A is available 4 times has no impact on this fact.
Also, there are 4 consonants available – viz. L, H, Band D. Thus, the number of ways of selecting a vowel and a consonant would be 1 × 4C1 = 4. Answer A
Answer: (A) 4
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
(A) 227
(B) 266
(C) 800
(D) 277
(E) 261
Rationale: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer: C
Answer: (C) 800
Question: A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 2.9 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 1.6
(B) 1.9
(C) 2.2
(D) 2.5
(E) 2.8
Rationale: 72 km/hr = 1.2 km/min
The total distance is 3 km.
3 / 1.2 = 2.5 minutes
The answer is D.
Answer: (D) 2.5