divelab/Sys2Bench huggingface dataset:
Question: A man goes from A to B at a speed of 14 kmph and comes back to A at a speed of 10 kmph. Find his average speed for the entire journey?
Options:
A)11.6 kmph
B)12.9 kmph
C)12.8 kmph
D)11.9 kmph
E)12.6 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/14) + (d/10]
= (2d)/[12d/70) => 11.6 kmph.
Answer:A
Answer: A
Question: In a certain city, 40% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
Options:
A)a) 50%
B)b) 53%
C)c) 54%
D)d) 55%
E)e) 57%
Rationale: Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=55%
D
Answer: D
Question: If the product of 6 integers is negative, at most how many of the integers can be negative?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: product of even number of -ve numbers is positive so it cant be 6 .
ANSWER:D
Answer: D
Question: If n divided by 7 has a remainder of 1, what is the remainder when 3 times n is divided by 7?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: As per question => N=7P+1 for some integer p
hence 3N => 21Q + 3 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 3 => 3 divided by 7 will leave a remainder 3
hence C
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)298m
B)180m
C)287m
D)297m
E)261m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: B
Question: In a particular state, 62% of the counties received some rain on Monday, and 54% of the counties received some rain on Tuesday. No rain fell either day in 28% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
Options:
A)25%
B)44%
C)56%
D)62%
E)70%
Rationale: 62 + 54 + 28 = 144%
The number is 44% above 100% because 44% of the counties were counted twice.
The answer is B.
Answer: B
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)25
B)15
C)65
D)82
E)95
Rationale: Explanation:
A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
ANSWER A
Answer: A
Question: The “s-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^s, where s is the s-number of the result of his die roll, and plots 3^s on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
Options:
A) 3/8
B) 13/36
C) 17/36
D) 19/36
E) 23/36
Rationale: If you calculate 3^s for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: B
Question: Today my car meter reads as 63736 kms. I notes that this is a palindrome. How many minimum kms i need to travel so my car meter find another palindrom.
Options:
A)100 kms
B)115 kms
C)110 kms
D)210 kms
E)120 kms
Rationale: A
100 kms
63736+100 = 63636, a palindrome
Answer: A
Question: The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:
Options:
A)15
B)20
C)30
D)32
E)33
Rationale: Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 ? y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 ? y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 ? 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30
correct answer C
Answer: C
Question: The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability T that 3 of Sam’s 4 funds grew by at least 10% over last year?
Options:
A) 6C3 / 10C4
B) 6C3 * 4C1 / 10C4
C) 6C3 * 4C1 / 10P4
D) 6P3 * 4P1 / 10C4
E) 6P3 * 4P1 / 10P4
Rationale: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.
We know this is a combination, not a permutation. This rules out choices C, DE.
A clearly isn't the answer because T= 6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.
B it is.
Answer: B
Question: Roy is now 8 years older than Julia and half of that amount older than Kelly. If in 2 years, Roy will be twice as old as Julia, then in 2 years what would be Roy’s age multiplied by Kelly’s age?
Options:
A)160
B)168
C)176
D)184
E)192
Rationale: R = J+8 = K+4
R+2 = 2(J+2)
(J+8)+2 = 2J+4
J = 6
R = 14
K = 10
In 2 years (R+2)(K+2) = 16*12 = 192
The answer is E.
Answer: E
Question: Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
Options:
A)7:9
B)7:5
C)7:2
D)7:6
E)7:1
Rationale: Let x be the investment of Ravi in 6% and y be in 7%
x(6)(n)/100
= y(7)(n)/100
=> x/y = 7/6
x : y = 7 : 6
Answer: D
Answer: D
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is?
Options:
A)8
B)8/11
C)8/13
D)8/15
E)None
Rationale: A's 1 day's work =	1	;
15
B's 1 day's work =	1	;
20
(A + B)'s 1 day's work =	(	1	+	1	)	=	7	.
15	20	60
(A + B)'s 4 day's work =	(	7	x 4	)	=	7	.
60	15
Therefore, Remaining work =	(	1 -	7	)	=	8	.
15	15
Option D
Answer: D
Question: The greatest number by which the product of three consecutive multiples of 3 is always divisible is
Options:
A)54
B)76
C)152
D)162
E)None of these
Rationale: Solution
Required number	= Product of first three multiplies of 3
= (3 × 6 × 9)= 162.
Answer D
Answer: D
Question: For a drama, Jack need to select 5 dramatist from a team of 8 members. What is the possible way to select dramatist?
Options:
A)60
B)56
C)48
D)25
E)10
Rationale: The question is out of 8 members, john needs 5 members.
So the combination is 8C5.
8C5=8!/3!*5!
=8*7*6*5!/5!*3*2*1
=56 ways to select.
Option B is answer
Answer: B
Question: Evaluate 20% of 450 + 45% of 200
Options:
A)232
B)242
C)252
D)262
E)180
Rationale: Explanation:
= (20/100) * 450 + (45/100) * 200
= 180
Option E
Answer: E
Question: A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
Options:
A)30
B)39
C)87
D)27
E)91
Rationale: Let the side of the square(ABCD) be x meters.
Then, AB + BC = 2x metres.
AC = = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = = 30% (approx)
Answer:A
Answer: A
Question: Convert 150 inches into centimeter?
Options:
A)312cm
B)381cm
C)350cm
D)310cm
E)354cm
Rationale: 1 inch = 2.54cm
150 inches = 110*2.54 = 381cm
Answer is B
Answer: B
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Options:
A)800
B)880
C)720
D)1500
E)1110
Rationale: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).
Hence we can assume total letters as 5 and all these letters are different.
Number of ways to arrange these letters
=5!=5×4×3×2×1=120
All the 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves
=3!=3×2×1=6
Hence, required number of ways
=120×6=720
C
Answer: C
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Options:
A)36 1/3%
B)37 1/3%
C)33 1/3%
D)33 1/8%
E)31 1/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: C
Question: What number comes next in this Number series.
3 4 4 6 9 7 8 ?
*Hint: check calender
Options:
A)8
B)3
C)6
D)1
E)9
Rationale: E
8 (the number of letters in the month December)
May : 3 letters
June : 4 letters
July : 4 letters
August: 6 letters
September : 9 letters
October : 7 letters
November : 8 letters
Answer: A
Question: A chair is bought for Rs. 800/- and sold at a loss of 10% find its selling price
Options:
A)Rs. 720/-
B)Rs. 600/-
C)Rs. 630/-
D)Rs. 820/-
E)Rs. 970
Rationale: Explanation:
100 % ------> 800 (100 * 8 = 800)
90 % ------> 720 (90 * 8 = 720)
Selling price = Rs. 720/-
Answer: Option A
Answer: A
Question: The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area E of that hemisphere?
Options:
A) 6/π
B) 9/π
C) 6
D) 9
E) 12
Rationale: Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !!
Answer: D
Question: A person purchased a TV set for Rs. 1000 and a DVD player for Rs. 650. He sold both the items together for Rs. 2500. What percentage of profit did he make?
Options:
A)51.51%
B)96.96%
C)10.11%
D)15.12%
E)23.32%
Rationale: The total CP = Rs. 1000 + Rs. 650
= Rs. 1650 and SP = Rs. 2500
Profit(%)
= (2500 - 1650)/1650 * 100
= 51.51%
Answer: A
Answer: A
Question: What is the probability of getting a sum 9 from two throws of a dice?
Options:
A)5/5
B)1/9
C)5/1
D)5/7
E)5/2
Rationale: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
The probability = 4/36 = 1/9.
Answer: B
Answer: B
Question: On a ferry, there are 38 cars and 12 trucks. The cars have an average mass of 950 kg and the trucks have an average mass of 3100 kg. What is the average mass of all 50 vehicles on the ferry?
Options:
A)1442
B)1448
C)1454
D)1460
E)1466
Rationale: The total mass of the vehicles is 38*950+12*3100=73300
The average mass is 73300/50=1466
The answer is E.
Answer: E
Question: How long will a boy take to run round a square field of side 20 meters, if he runs at the rate of 12km/hr?
Options:
A)52sec
B)45sec
C)60sec
D)24sec
E)39sec
Rationale: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec
Distance = 20*4 = 80m
Time taken = 80*3/10 = 24sec
Answer is D
Answer: D
Question: In a party every person shakes hands with every other person. If there were a total of 105 handshakes in the party then what is the number of persons present in the party ?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: Explanation :
Let the number of persons be n
âˆ´ total handshakes = nC2 = 105
n(n-1)/2 = 105 âˆ´ n = 15
Answer : A
Answer: A
Question: A collection of books went on sale, and 2/3 of them were sold for $3.50 each. If none of the 40 remaining books were sold, what was the total amount received for the books that were sold?
Options:
A)$180
B)$250
C)$260
D)$280
E)$300
Rationale: If 40 books constitute 1/3rd of the total, then 2/3rd of the total = 80 books
Amount received for sold books = 80 * 3.5 = $280
Answer :D
Answer: D
Question: Of the three-digit integers greater than 500, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A) 90
B) 82
C) 80
D) 45
E) 36
Rationale: To satify the given condition,
required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,
number greater than 700;
total numbers = 1*10*10 = 100
numbers with all digits different = 1*9*8 = 72
numbers when all three digits are same (777) = 1
req. = 100- 72 - 1 = 27
considering the numbers between 700999 = 27*3=46
Answer is 80 ('cause 700 can't be included)
Answer (D).
Answer: D
Question: 8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 12th and the 20th terms?
Options:
A)324
B)335
C)346
D)357
E)368
Rationale: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 12th term is 12 × 11 – 3 = 129
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 346.
The correct answer is choice (C).
Answer: C
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39?
Options:
A)3
B)8
C)12
D)32
E)35
Rationale: n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 39m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 8 more to make it
39m + 39
Answer - B
Answer: B
Question: The avearge score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 45. Then find the average for the last four matches?
Options:
A)33.25
B)33.5
C)34.25
D)29.75
E)none
Rationale: Solution
Required average	=(38.9 x 10)-(45 x 6)/ 4
= 119 / 4.
= 29.75
Answer D
Answer: D
Question: In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 2 metres then what will be the area of the square so formed?
Options:
A)133 cm2
B)276 cm2
C)2500 cm2
D)576 cm2
E)None of these
Rationale: Let the side of the square be x m.
∴ Perimeter of the square = 48 × 2 = 4x ∴ x = 24 m
∴ Area = (24)2 = 576 m2
Answer D
Answer: D
Question: While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 7° east of north, in what direction was it originally flying?
Options:
A)(a) 30° west of north
B)(b) 30° east of north
C)(c) 18° west of north
D)(d) 18° east of north
E)(e) 5° west of north
Rationale: After a turn of 25° you are 7°North East, with a 18° turn you would be perfectly pointing at north. So you were, before the turn, 18° to the other side (West).
Answer C)
Answer: C
Question: How many of the positive factors of 45 , 16 and how many common factors are there in numbers?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: factors of 45 - 1, 3, 9, 15 and 45
factors of 16 - 1 , 2, 4, 8 and 16
Comparing both, we have three common factors of 45,16-1
Answer(A)
Answer: A
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Options:
A)Rs. 169
B)Rs. 169.50
C)Rs. 175.50
D)Rs. 180
E)Rs. 180.50
Rationale: Since first and second varieties are mixed in equal proportions.
So, their average price = Rs. 126 + 135 = Rs. 130.50
2
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind
Rs. 130.50	Mean Price
Rs. 153	Rs. x
(x - 153)	22.50
x - 153	= 1
22.50
x - 153 = 22.50
x = 175.50
Option C
Answer: C
Question: A fair die is rolled once and a fair coin is flipped once. What is the probaility that either the die will land on 3 or that the coin will land on heads?
Options:
A)5/12
B)7/12
C)11/12
D)3/4
E)7/4
Rationale: Event A = Fair die is rolled once
Event B = Fair coin is flipped once.
P(A or B) = P(A) + P(B) - P(A and B)
= 1/6 + 1/2 - (1/6)(1/2)
= 7/12
ANSWER B
Answer: B
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 3 second to produce a bolt but 1 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?
Options:
A)1,250 seconds
B)1,500 seconds
C)1,750 seconds
D)2,000 seconds
E)3,000 seconds
Rationale: To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.
Two machines to produce 1,000 bolts will need (1,000*3)/2 = 1500 seconds.
Two machines to produce 1,000 nuts will need (1,000*1)/2 = 500 seconds.
Total = 1500 + 500 = 2000.
Answer: D
Answer: D
Question: A train takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)50 Kmph
B)54 Kmph
C)60 Kmph
D)59 Kmph
E)60 Kmph
Rationale: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
C)
Answer: C
Question: How many seconds will a 400 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 46 km/hr?
Options:
A)25
B)30
C)40
D)45
E)36
Rationale: Explanation :
Speed of train relatively to man = ( 46 - 6)km/hr
= 40 km /hr
= (40 x 5 / 18)m/sec
= 11.11 m/sec
Time taken to pass the man = (400/ 11.11)sec = 36 sec.
Answer : E
Answer: E
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
A)60%
B)50%
C)25%
D)20%
E)10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 55 - {both} + 40
{both} = 20%.
Answer: D.
Answer: D
Question: The volume of water inside a swimming pool doubles every hour. If the pool is filled to its full capacity within 8 hours, in how many hours was it filled to one quarter of its capacity?
Options:
A)2
B)4
C)5
D)6
E)7
Rationale: D
Answer: D
Question: A pair of prime numbers that can be expressed in the form K{p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT
Options:
A) 11
B) 13
C) 17
D) 19
E) 23
Rationale: definetly a sitter.plug in the values for middle term and calculate.We can see clearly that K for 19 , 19+6 gives 25 which is not a prime
therefore correct answer D
Answer: D
Question: While working alone at their respective constant rates, server B uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?
Options:
A) 2 hr
B) 2hr 20 min
C) 2hr 40 min
D) 5 hr 40 min
E) 6hr
Rationale: Server B processes 480/4 files per hour = 120 per hour
Server Y processes 180/8 files per hour = 60 per hour
Total files processed per hour when B and Y work together = 120+60 per hour = 180 files per hour
480/180 = 2 2/3 hours=C
Answer: C
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options:
A)98
B)76
C)23
D)16
E)12
Rationale: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76
Answer B
Answer: B
Question: If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have?
Options:
A)7
B)5
C)6
D)8
E)9
Rationale: take the example of 4...
it has 3 positive divisors (1,2,4)
Now, take the example of 64...
it has only 7 divisors..
so A is the ans
Answer: A
Question: Two employees M and N are paid a total of $605 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
Options:
A)$245
B)$255
C)$265
D)$275
E)$285
Rationale: 1.2N + N = 605
2.2N = 605
N = 275
The answer is D.
Answer: D
Question: When 50 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
Options:
A)3 : 4
B)4 : 5
C)3 : 2
D)Data inadequate
E)None of these
Rationale: Let the first and the second numbers be x and y respect then
y + 50% of x = 140% of y
or, y + 0.5x = 1.4y
or, 0.5x = 0.4y
∴ x : y = 0.4 : 0.5 = 4 : 5
Answer B
Answer: B
Question: A company has 15 managers and 75 associates. The 15 managers have an average salary of $150,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?
Options:
A)$35,000
B)$45,000
C)$50,000
D)$65,000
E)$75,000
Rationale: Another method is to get ratios
Say 30000=a and
We know the # of people are in 1:5 ratio
Average=(5a*1+a*5)/6= 10a/6=50000
Answer is C. $50,000
Answer: C
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many Q hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
Options:
A) 22 hours
B) 30 hours
C) 44 hours
D) 60 hours
E) It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job Q in 44 hours.
Answer: C.
Answer: C
Question: The price of pulses has fallen by 35. How many quintals can be bought for the same amount which was sufficient to buy 24 quintals at the higher price?
Options:
A)20.0
B)22.5
C)25.8
D)36.9
E)32.5
Rationale: 80% of original price can buy = 24 quintals.
Therefore, he can buy ( 24 x 100 )/ 65 = 36.9 quintals at the lower price.
ANSWER:D
Answer: D
Question: A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)3
B)7.5
C)2.25
D)1.5
E)4
Rationale: M = 9
S = x
DS = 9 + x
US = 9 - x
9 + x = (9 - x)2
9 + x = 18 -2x
3x = 9
x = 3
ANSWER:A
Answer: A