divelab/Sys2Bench huggingface dataset:
Question: If an amount of Rs 42,900 is distributed equally
amongst 22 persons, how much amount would each
person get?
Options:
A)Rs 1950
B)Rs 2000
C)Rs 745
D)Rs 765
E)None
Rationale: Required amount =42900/22 = Rs 1950
Answer A
Answer: A
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?
Options:
A)1.2 kg
B)1.5 kg
C)1.7 kg
D)1.9 kg
E)None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 85% (100-15).
Therefore 0.5 X Amount of flower-nectar = 0.85 X Amount of honey = 0.85 X 1 kg
Therefore amount of flower-nectar needed =
(0.85/0.51)kg=1.7 kgs
Answer : C
Answer: C
Question: A particular library has 300 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 244 books in the special collection at that time, how many books of the special collection were loaned out during that month?
Options:
A)120
B)140
C)160
D)180
E)200
Rationale: The total number of books is 300.
Let x be the number of books which were loaned out.
65% of books that were loaned out are returned.
35% of books that were loaned out are NOT returned.
Now, there are 244 books, thus the number of un-returned books is 300-244 = 56 books.
0.35x = 56
x = 160
The answer is C.
Answer: C
Question: What least number should be added to 1019, so that the sum is completely divisible by 25?
Options:
A)4
B)3
C)2
D)0
E)6
Rationale: 1019 Ã· 25 = 40 with remainder = 19
19 + 6 = 25.
Hence 6 should be added to 1019 so that the sum will be divisible by 25
Answer: Option E
Answer: E
Question: When N is divided by T, the quotient is S and the remainder is B. Which of the following expressions is equal to N?
Options:
A)ST
B)S + V
C)ST + B
D)T(S+V)
E)T(S – V)
Rationale: Using the rule dividend = Quotient * divisor + remainder =>ST + B C is correct
Answer: C
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran share in the profit?
Options:
A)Rs 9500
B)Rs 10,000
C)Rs 10,500
D)Rs 11,000
E)Rs 14,000
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.24500 x	3/7	= Rs. 10,500.
ANSWER :C
Answer: C
Question: The positive number a is q percent greater than the positive number b, which is p percent less than a itself. If a is increased by p percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
Options:
A)I only
B)II only
C)III only
D)I and II only
E)II and III only
Rationale: a = (1 + q%)b
b = (1-p%)a
a = (1 + q%)*(1-p%)a
So (1 + q%)(1 - p%) = 1 = No change
One easy solution to this would be q = 0 and p = 0. In that case, a = b = c. So statement II can hold.
Assuming p and q are not 0,
(1 + q%)(1 - p%) = 1 = No change
So if you increase something by q% (it becomes bigger) and then decrease it by p% (now you will need to decrease it by a lesser %), there is no change.
Such as, you increase 100 by 25% and it becomes 125. Then you decrease 125 by only 20% and it comes back to 100. (This should remind you of cost price, sale price, profit and margin). So q would be a higher percentage than p.
Now if you increase something by p% (the lower %) and then decrease by q% (the higher %), the value you will obtain will certainly be lower than original.
Say you increase a (100) by p% (20%) to get 120 and then decrease it by q% (25%), you will get c (90). Hence c < a is possible too.
Answer (E)
Answer: E
Question: what is next no. 11 23 47 83 131 191 263 347 443???
Options:
A)171
B)181
C)191
D)551
E)211
Rationale: 11+12*1=23
23+12*2=47
47+12*3=83
83+12*4=131
131+12*5=191
191+ 12*6=263
263+12*7=347
347+12*8=443
443+12*9=551
ANSWER:D
Answer: D
Question: The product of all the prime numbers less than 30 is closest to which of the following powers of 10 ?
Options:
A) 10^9
B) 10^8
C) 10^7
D) 10^6
E) 15*10^5
Rationale: 2*3*5*7*11*13*17*19
2*19*3*17*5*13*7*11
38*51*65*77
By approximation
40*50*70*70
2000*4900
By approximation
3000*5000
1,500,000
E
Answer: E
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5130. What was the number of original inhabitants?
Options:
A)7300
B)7600
C)7900
D)8200
E)8500
Rationale: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 5130
(27/40) * x = 5130
x = 5130 * 40 / 27 = 7600
The answer is B.
Answer: B
Question: A 400 meter long train crosses a platform in 45 seconds while it crosses a signal pole in 30 seconds. What is the length of the platform?
Options:
A)200
B)400
C)350
D)1800
E)45
Rationale: Speed = [400 / 30] m/sec = 40/3 m/sec.
Let the length of the platform be x meters.
Then, x + 400 / 45= 40/3
3(x + 400) = 1800 è x = 200 m. Answer: A
Answer: A
Question: If 5^5 × 5^x = (125)^4 , then what is the value of x?
Options:
A)2
B)3
C)5
D)6
E)7
Rationale: 5^5 × 5^x = (125)^4
5^(5+x) = 5^12
Since they have the same base we can just set the exponents equal to each other: (5+x) = 12
x=7
Ans. E) 7
Answer: E
Question: Aravamudhan, Balakrishnan and Chinnan work in a developing software company in starting level positions. However their salaries are different. Aravamudhan's salary to Balakrishnan's salary and Balakrishnan's salary to Chinnan's salary are in the ratio 4:3. If the total salary of all the three employees is Rs.29230, what is the salary of Chinnan?
Options:
A)Rs.12640
B)Rs.9480
C)Rs.7110
D)Rs.8660
E)Rs.9660
Rationale: making them in equal proportion of Aravind:Bala:Cinnana=16:12:9
and given total salary 37*x=29230
x=790
Chinnana salary is 9*790=7110
ANSWER:C
Answer: C
Question: Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day G on which the buses leave at the same time.
Options:
A)G=Tuesday
B)G=Wednesday
C)G=Thursday
D)G=Sunday
E)G=The busses will never leave at the same time
Rationale: The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.
Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E
Answer: E
Question: There are two positive integers a and b.What is the probability that a+b is odd/
Options:
A)3/2
B)6/7
C)1/2
D)7/2
E)4/5
Rationale: s=adding two numbers is (even+even),(even+odd),(odd+odd),(odd+even)
n(s)=4
e=(even+odd),(odd+even) are the points in the event.
n(e)=2
p(e)=n(e)/n(s)
=2/4
=1/2
Answer is option C
Answer: C
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?
Options:
A)6, 8 and 12
B)12, 8 and 6
C)8, 6 and 12
D)12, 6 and 8
E)6, 12 and 8
Rationale: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2, respectively. So
x+2x+x+2=26
4x=24
x=6
Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.
So answer is E.
Answer: E
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)31/32
B)31/36
C)31/27
D)31/28
E)31/18
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T)
= 1 - 1/32
= 31/32
Answer: A
Answer: A
Question: If 70 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Options:
A)45%
B)40%
C)35%
D)30%
E)25%
Rationale: 70% answered the first question correctly and 20% answered neither correctly.
Then 10% missed the first question but answered the second question correctly.
Then the percent who answered both correctly is 55% - 10% = 45%.
The answer is A.
Answer: A
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 4 men and 5 women will do that task.
Options:
A)13/14
B)13/10
C)13/18
D)13/16
E)13/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
4 m + 5 w =13 w
Answer is 13/14
Answer: A
Answer: A
Question: Find the surface area of a 12 cm x 4 cm x 3 cm brick.
Options:
A)84 cu cm.
B)124 cu cm.
C)164 cu cm.
D)192 cu cm.
E)None
Rationale: Sol.
Surface area = [2(12 x 4 + 4 x 3 + 12 x 3)]
= (2 x 96)
= 192 cu cm.
Answer D
Answer: D
Question: 1397 x 1397=?
Options:
A)1951609
B)1981709
C)18362619
D)2031719
E)None of them
Rationale: =(1397)^2
=(1400 - 3)^2
=(1400)^2+3^2-2 x 1400 x 3
=1960000+9-8400
=1960009-8400
=1951609
Answer is A
Answer: A
Question: A merchant marks his goods up by 40% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
Options:
A)21%
B)26%
C)69%
D)31%
E)19%
Rationale: Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 10% on 140.
Profit=126-100
26%
answer B
Answer: B
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)33
B)289
C)48
D)77
E)12
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: C
Answer: C
Question: The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Options:
A)276
B)299
C)322
D)345
E)280
Rationale: Clearly, the numbers are (20 x 13) and (20 x 14).
Larger number = (20 x 14) = 280. Answer: Option E
Answer: E
Question: A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i
Options:
A)8 km / hr
B)9 km / hr
C)10 km / hr
D)12.5 km / hr
E)None
Rationale: Sol.
Man's rate in still in water = (12- 2) km / hr = 10km / hr.
Man's rate against the current = (10 - 2) km / hr = 8 km / hr.
Answer A
Answer: A
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is
Options:
A)20 years
B)21 years
C)22 years
D)24 years
E)26 years
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22
Answer: Option C
Answer: C
Question: If f(x)=4x−1 and g(x)=2x+1 for all integers, which of the following is a possible value of g(f(x))?
Options:
A)-23
B)-17
C)0
D)8
E)20
Rationale: g(f(x)) = 2*f(x)+1 = 2*(4x-1)+1 = 8x-1
Of these five options, only -17 has the form 8x-1.
The answer is B.
Answer: B
Question: In a tree, 1/5 of the birds are robins while the rest are bluejays. If 1/2 of the robins are female and 2/5 of the bluejays are female, what fraction of the birds in the tree are male?
Options:
A)9/25
B)12/25
C)17/25
D)29/50
E)33/50
Rationale: The fraction of birds that are male robins is (1/2)(1/5)=1/10.
The fraction of birds that are male bluejays is (3/5)(4/5)=12/25.
The total fraction of male birds is 1/10 + 12/25 = 29/50.
The answer is D.
Answer: D
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
Options:
A)12 a.m
B)13 a.m
C)14 a.m
D)11 a.m
E)16 a.m
Rationale: D
11 a.m
Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75(x - 1) = 330 => x = 3
So, they meet at (8 + 3) i.e., 11 a.m.
Answer: D
Question: A man can row his boat with the stream at 36 km/h and against the stream in 8 km/h. The man's rate is?
Options:
A)1 kmph
B)6 kmph
C)7 kmph
D)14 kmph
E)9 kmph
Rationale: Explanation:
DS = 36
US = 8
S = ?
S = (36 - 8)/2 =14 kmph
Answer: D
Answer: D
Question: The avg weight of A,B & C is 50 kg. If D joins the group, the avg weight of the group becomes 53 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 51 kg. What is the weight of A?
Options:
A)56
B)65
C)73
D)89
E)90
Rationale: A + B + C = 3 *50 = 150
A + B + C + D = 4 * 53 = 212 ---- (i)
So, D = 62& E = 62 + 3 = 65
B + C + D +E = 51 * 4 = 204 --- (ii)
From Eq. (i) & (ii)
A-E = 212 – 204 = 8
A = E +8 = 65 + 8 = 73
Answer : C
Answer: C
Question: Ifaequals the sum of the even integers from 2 to 120, inclusive, andbequals the sum of the odd integers from 1 to 119, inclusive, what is the value of a - b ?
Options:
A)60
B)10
C)19
D)20
E)21
Rationale: This is a solution from Beatthegmat:
even numbers:
(120-2)/2 + 1 = 60 even integers.
(120+2)/2 = 61 is the average of the even set.
sum = avg*(#of elements) = 61*60 =3660 = a
odd numbers:
(119-1)/2 + 1 = 60 odd integers.
(119+1)/2 = 60 is the average of the odd set.
sum = avg*(#of elements) = 60*60 = 3600 = b
a-b = 3660 - 3600 = 60. Answer : A
Answer: A
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
Options:
A)288
B)1900
C)1287
D)1271
E)2788
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: B
Question: Rebecca's annual income is $15,000 and Jimmy's annual income is $18,000. By how much must Rebecca's annual income increase so that it constitutes 50% of Rebecca and Jimmy's combined income?
Options:
A)7000
B)6000
C)5000
D)4000
E)3000
Rationale: total rebecca = x+15000; total = x+15000+18000
x+15000/x+33000 = 50/100 therefore x =3000
E
Answer: E
Question: 48 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Options:
A)66
B)26
C)42
D)27
E)21
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 48 = 21
Answer: E
Answer: E
Question: If x, y and z are three different positive integers whose sum is prime, which of the following statements could be true?
Options:
A)x + y = z
B)Each of x + 3, y + 3, and z + 3 is prime.
C)Each of x + y, x + z, and y + z is prime.
D)The average (arithmetic mean) of x, y, and z is prime.
E)Each of x, y, and z is prime.
Rationale: the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that E is the answer.
Answer: E
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
Options:
A)Rs.19
B)Rs.29
C)Rs.15
D)Rs.10
E)Rs.13
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20
= Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people
= 140 - 50 = Rs. 90
The average amount with them = 90/6
= Rs.15.
Answer:C
Answer: C
Question: Solve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0
Options:
A)If x>y
B)If x>=y
C)If x<y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=+1,-1 and Y= -1,-3
Comparing we get X>=Y
B
Answer: B
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)7 sec
B)6 sec
C)4 sec
D)5 sec
E)9 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer:B
Answer: B
Question: AB + CD = RRR, where AB and CD are two-digit numbers and RRR is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
Options:
A) 1
B) 3
C) 7
D) 9
E) Cannot be determined
Rationale: AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of RRR it's 111.
So, A=1. 1B+CD=111
Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if CD<90 meaning C<9 CD+1B<111) --> C=9
Answer: D.
Answer: D
Question: Working together, printer A and printer B would finish the task in 40 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 4 pages a minute more than printer A ?
Options:
A)250
B)375
C)450
D)480
E)500
Rationale: 40*A + 40*B = x pages
in 40 mins printer A will print = 40/60 * x pages = 2/3*x pages
thus in 40 mins printer printer B will print x - 2/3*x = 1/3*x pages
Also it is given that printer B prints 4 more pages per min that printer A. In 40 mins printer B will print 160 more pages than printer A
thus 2/3*x - 1/3*x = 160 => x = 480 pages
Answer: D
Answer: D
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Options:
A)65
B)24
C)52
D)77
E)82
Rationale: Explanation:
Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
Answer: B
Answer: B
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
Options:
A)6 ½ sec
B)6 ½ sec
C)9 ½ sec
D)8 ½ sec
E)7 ½ sec
Rationale: D
8 ½ sec
D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 ½ sec
Answer: D
Question: Walking at 8KMPH From Point W to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point W to Railway station?
Options:
A)A)9KM
B)B)6.66KM
C)C)7.25KM
D)D)12.40KM
E)E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point W and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point W and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: B
Question: A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 22 inches, how many inches of framing material does the carpenter need to frame the painting?
Options:
A)12
B)22 1/2
C)37 1/2
D)50
E)28
Rationale: (22/2) ( 2+3) * 2 = 28 =E
Answer: E
Question: The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked the second cow in the second year?
Options:
A)4730 lt
B)4356 lt
C)7665 lt
D)2314 lt
E)6545 lt
Rationale: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15% or 10%
So 8100+15/100⋅x+10/100⋅(8100−x)=9100
Therefore 8100+320x+110(8100−x)=9100
120x=190
x=3800
Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, respectively.
correct answer A
Answer: A
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Options:
A)7
B)6
C)3
D)4
E)None of these
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
ANSWER:E
Answer: E
Question: The surface of a cube is 96sq cm. Find its volume?
Options:
A)8cc
B)9cc
C)2cc
D)4cc
E)64cc
Rationale: 6a2 = 96 = 6*16
a = 4 => a3 = 64cc
Answer: E
Answer: E
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Options:
A)3
B)8
C)2
D)1
E)9
Rationale: E
9
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x <-> 14 x x = 6 x 21
x = (6 x 21)/14
x = 9
Answer: E
Question: It takes 3 workers a total of 12 hours to build a giant machine with each worker working at the same rate. If 4 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 3:00 PM, at what time will the machine be complete?
Options:
A)5:30
B)5:45
C)6:00
D)6:15
E)6:30
Rationale: 3 workers build 1/12 of a machine in one hour.
1 worker builds 1/36 of a machine in one hour.
In the first 4 hours, 4 workers build 4*(1/36)*4=16/36 of a machine
From 3:00 to 4:00, 5 workers build another 5/36. The total is 21/36.
From 4:00 to 5:00, 6 workers build another 6/36. The total is 27/36.
From 5:00 to 6:00, 7 workers build another 7/36. The total is 34/36.
To build another 2/36, 8 workers need (2/8)*60 minutes which is 15 minutes.
The machine is complete at 6:15.
The answer is D.
Answer: D
Question: A meal cost $ 35.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
Options:
A)40-42
B)39-41
C)38-40
D)37-39
E)36-37
Rationale: 10%(35.5) = 3.55
15%(35.5) = 5.325
total amount could have been 35.5+3.55 and 35.5+5.325
=> could have been between 39.05 and 40.625
=> approximately between 39 and 41
Answer is B.
Answer: B
Question: Which one of the following is the common factor of (47^43 + 43^43) and (47^47 + 43^47) ?
Options:
A)(2+56)
B)(47+43)
C)(3+7)
D)(4+9)
E)(12+19)
Rationale: Explanation:
When n is odd, (x^ + a^n) is always divisible by (x + a).
Each one of (47^43 + 43^43) and (47^47 + 43^47) is divisible by (47 + 43).
B
Answer: B
Question: Eight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $290. If one of the friends had a coupon for 29% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
Options:
A)$90
B)$70
C)$45
D)$37
E)$25
Rationale: 290 * 0,29 = 84
290 - 84 = 206
206 / 8 = 25
Answer E
Answer: E