divelab/Sys2Bench huggingface dataset:
Question: A tank is filled by 3 pipes A,B,C in 4 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
Options:
A)25hr
B)35hr
C)40hr
D)20hr
E)28hr
Rationale: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/4
7/x = 1/4
x = 28 hours
Answer is E
Answer: E
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 300meters, after what time will they meet at the starting point?
Options:
A)20sec
B)15sec
C)30sec
D)50sec
E)1min
Rationale: They meet every 300/7+8 = 20sec
Answer is A
Answer: A
Question: A company’s eight trucks running 3 hrs a day can carry 1,200 packs of produce. The company invested in 4 new trucks and got rid of 2 of the previous ones. The new trucks can carry 0.5% more produce than the old ones. How many produce in total can be delivered within the next 2 days for 4 hours?
Options:
A)4,800
B)9,200
C)4,400
D)3,600
E)800
Rationale: Old trucks can carry (1,200/8)/3 = 50 per hour each.
New trucks carry 1.5*50= 75 per hour each.
In total, 6 old trucks + 2 new trucks is (6*75*4 hours*2 days) + (2*50*4 hours*2 days)= 4,400.
Answer is option C.
Answer: C
Question: Today is Monday. After 30 days, it will be :
Options:
A)Thursday
B)Saturday
C)Monday
D)Sunday
E)Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 28 days, it will be Monday.
After 30 days, it will be Wednesday.
Answer is E
Answer: E
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 15 more blue balls than white balls, and thrice as many red balls as blue balls, how many white balls does The box has ?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 15 more blue balls than white balls...
Equation #2: y = 15 + z
...thrice as many red balls as blue balls...
Equation #3: x = 3y
Solve equation #2 for z: z = y - 15
Now, we can replace both x and z with y in Equation #1
3y + y + (y - 15) = 100
5y - 15 = 100
5y = 115
y = 23
There are 23 blue balls. This is 15 more than the number of white balls, so z = 8. That's the answer. Just as a check, x = 69, and 69 + 23 + 8 = 100.
Answer = 8,(A)
Answer: A
Question: There are 20 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
Options:
A)20
B)25
C)30
D)45
E)60
Rationale: Note that each handshake includes two people.
The total number of handshakes is 20*3/2 = 30
The answer is C.
Answer: C
Question: The food in a camp lasts for 25 men for 40 days. If fifteen more men join, how many days will the food last?
Options:
A)25 days
B)30 days
C)20 days
D)16 days
E)27 days
Rationale: one man can consume the same food in 25*40 = 1000 days.
15 more men join, the total number of men = 40
The number of days the food will last = 1000/40 = 30 days.
Answer:A
Answer: A
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
Options:
A)720
B)730
C)740
D)750
E)800
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
A
Answer: A
Question: What is the sum of the integers from -60 to 65, inclusive?
Options:
A)315
B)215
C)115
D)165
E)765
Rationale: In an arithmetic progression,
the nth term is given by tn=a+(n-1)d
here tn=65, a=-60, d=1
hence, 65=-60+(n-1)
or n=126
Sum of n terms can be calculated by sn=n/2(a+l)
a=first term, l=last term, n=no. of terms
sn=126*(-60+65)/2
sn=126*5/2 = 315
Answer : A
Answer: A
Question: The new swimming pool needs to be filled with water. If the swimming pool is 5m^3, and the speed to fill the swimming pool is 2.5 cm^3/sec (1m^3 = 10^6 cm^3), how long does it take to fill the entire swimming pool?
Options:
A)2*10^3
B)2*10^4
C)2*10^5
D)2*10^6
E)2*10^7
Rationale: From 1 m^3 = 10^6 cm^3, 5m^3 = 5*10^6 cm^3, time = 5*10^6 cm^3 / 2.5cm ^3/sec = 2*10^6 seconds. Correct Option: 2*10^6 Answer: D
Answer: D
Question: A certain bag contains 60 balls — 22 white, 18 green, 17 yellow, 3 red, and 1 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
Options:
A)0.09
B)0.15
C)0.54
D)0.85
E)0.95
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 17)/60 = 57/60 = 0.95.
Answer: E.
Answer: E
Question: John invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 2 years and to $ 500 at the end of another 3 years. What was the rate of interest in which he invested his sum?
Options:
A)12%
B)40%
C)6.67%
D)25%
E)33%
Rationale: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 2years the principal P amounts to $300 and after a time of 5years ( question says after another 3years so 2+3) P becomes $500.
Formulating the above data
Amount (A1) at end of 2years
A1= P(1 + 2R/100) = 300
Amount (A2) at end of 8years
A2 = P(1 + 5R/100) = 500
Dividing A2 by A1 we get
(1 + 5R/100)/(1 + 2R/100) = 5/3
after cross multiplication we are left with 5R =100*2 which gives R = 40%
Option: B
Answer: B
Question: 100 men started working to complete a work in 50 days.After working 8hours/day they had completed 1/3rd of the work in 25 days.How many men should be hired so that they will finish the work in time by working 10 hours/day.
Options:
A)30 men
B)60 men
C)90 men
D)100 men
E)120 men
Rationale: Working 8 hours/day, in 25 days, 100 men completes 8*25*100= 20000 men hours which is 1/3 of the work, So remaining 2/3 work to be completed =20000*(2/3)/(1/3)=40000 men hours.
If with 'x' extra men hired ,remaining work is to be completed in 50-25=25 days , working 10 hours/day, then, (100+x)*25*10=40000, 25000+250x=40000, x=60 men
ANSWER:B
Answer: B
Question: What is the total number of integers between 10 and 100 (exclusive)that are divisible by 7?
Options:
A)10
B)13
C)15
D)12
E)11
Rationale: 14, 21, 28, ..., 91,98
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (98 - 14) / (7) + 1 = 12 + 1 = 13
Answer is B
Answer: B
Question: When a 192 meters long rod is cut down into small pieces of length 3.0 meters each. Then how many pieces are available ?
Options:
A)52
B)68
C)62
D)64
E)69
Rationale: Answer
No. of pieces = Total length / Length of each piece
= 192/3.0
= 64
Option: D
Answer: D
Question: If T = 5/9 * (K - 32), and if T = 75, then what is the value of K?
Options:
A)158
B)161
C)164
D)167
E)170
Rationale: K-32=9T/5
K=9T/5 + 32
K=9(75)/5 + 32 = 167
The answer is D.
Answer: D
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Options:
A)12.8
B)12.4
C)12.5
D)16.8
E)92.7
Rationale: 1000*15
= 1200*x
x = 12.5
Answer: C
Answer: C
Question: 320 students are to embark on an excursion. What is the smallest possible number of vans that are needed to transport all 320 students, if a van can carry 18 students only?
Options:
A)18
B)17
C)14
D)12
E)13
Rationale: To find the number of vans, we divide 320 by 22.
320/18 = 17 and remainder = 14
So 17 vans are needed to transport 320 students, and 1 van is needed to transport the 14 remaining students . A total of 18 vans are needed.
correct answer A
Answer: A
Question: Income and expenditure of a person are in the ratio 7 : 6. If the income of the person is Rs. 14000, then find his savings?
Options:
A)500
B)1000
C)1500
D)2000
E)2500
Rationale: Let the income and the expenditure of the person be Rs. 7x and Rs. 6x respectively.
Income, 7x = 14000
=> x = 2000
Savings = Income - expenditure
= 7x - 6x = x
So, savings =Rs.2000.
Answer: D
Answer: D
Question: The price of precious stone is directly proportional to square of its weight. what will be the loss incurred if a stone weighing 28gm and costing 28,000 breaks into two pieces whose weights are in the ratio 15:13?
Options:
A)No loss
B)10,000
C)28,000
D)9,500
E)14,000
Rationale: x=28000/28^2=35.71
cost of 15g=35.71*15^2=8035.714
cost of 13g=35.71*13^2=6035.714
total cost=14071.428
loss=28000-14071.428=13928.5=14000
ANSWER:E
Answer: E
Question: How many times in a day, the hands of a clock are straight?
Options:
A)22
B)34
C)44
D)54
E)76
Rationale: In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer:C
Answer: C
Question: A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?
Options:
A)130 m
B)140 m
C)150 m
D)170 m
E)190 m
Rationale: Let the length of the train e x meter, and let the speed of train be y km/h, then
\inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1)
and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2)
From eq (1) and (2), we get
\inline (y+3)\times 36 = ( y+6)\times 30
y = 12 km/h
\inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36
x= 150 m
C
Answer: C
Question: Which of the following is the sum of all the even numbers between 1 and 95, inclusive?
Options:
A)2550
B)2448
C)2600
D)2499
E)2652
Rationale: This question can be solved withbunching.
We're asked for the SUM of all of the EVEN integers from 1 to 95, so we really want the sum of 2, 4, 6, 8.....98.
If you take the next smallest and next biggest numbers, you have...
6+94 = 100
This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...
44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.
Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-2 = 2448
Final Answer:
B
Answer: B
Question: In State X, all vehicle license plates have 1 letter from the 26 letters of the alphabet followed by 4 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
Options:
A)23,400
B)60,840
C)67,600
D)608,400
E)260,000
Rationale: The choices give us the answer without any calculations--
4 one digits places can take 10*10*10*10 ways..
1 letter places can be filled up in 26 ways
ans= 26*10*10*10*10=260000
ans E
Answer: E
Question: It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?
Options:
A)13 minutes
B)14 minutes
C)15 minutes
D)16 minutes
E)17 minutes
Rationale: Solution:
Fifteen Minutes.
After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.
Answer C
Answer: C
Question: An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 60% is a passing grade, what is the probability that Brian passes?
Options:
A)1/16
B)37/256
C)1/2
D)35/256
E)15/16
Rationale: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.
If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.
So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.
The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 35/256.
D
Answer: D
Question: The ratio of numbers is 4:5 and their H.C.F is 4. Their L.C.M is:
Options:
A)80
B)16
C)24
D)48
E)98
Rationale: Let the numbers be 4x and 5x.
Then their H.C.F = x. So, x = 4.
So, the numbers are 16 and 20.
L.C.M of 16 and 20 = 80.
ANSWER:A
Answer: A
Question: If the wheel is 21 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)8
B)27
C)10
D)7
E)19
Rationale: 2 * 22/7 * 21 * x = 1056
=> x = 8
Answer: A
Answer: A
Question: A fruit seller had some oranges. He sells 40% oranges and still has 300 oranges. How many oranges he had originally?
Options:
A)700
B)710
C)720
D)500
E)740
Rationale: 60% of oranges = 300
100% of oranges =(300×100)/6=500
total oranges = 500
ANSWER : D
Answer: D
Question: A rectangular surface have length 15m and breadth 8m.calculate its area and diagonal.
Options:
A)120,18
B)120,17
C)115,17
D)115,18
E)120,18
Rationale: area=length*breadth=15*8=120 sq.m
Diagonal=√(15)^2+(8)^2=√289=17 m
Answer B
Answer: B
Question: Three unbiased coins are tossed. What is the probability of getting at least 2 tails?
Options:
A)0.75
B)0.5
C)0.25
D)0.2
E)0.3
Rationale: EXPLANATION:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
E = {HTT, THT, TTH, TTT}
n(S) = 8
n(E) = 4
P(E) =n(E) / n(S) = 4/8 = 0.5
ANSWER IS B
Answer: B
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Options:
A)20
B)30
C)50
D)10
E)40
Rationale: There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children 120 men.
50 children (120/200)	* 50 = 30 men
Answer is B.
Answer: B
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)3484
B)3467
C)3567
D)4567
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: If 4 (A's capital) = 6 (B's capital) = 8 (C's capital). Then the ratio of their capitals is?
Options:
A)6:4:5
B)6:4:3
C)6:4:2
D)6:2:3
E)6:5:3
Rationale: 4A = 6B = 8 C
A:B:C = 1/4:1/6:1/8
= 6:4:3
Answer: B
Answer: B
Question: An bus covers a certain distance at aspeed of 150 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
Options:
A)560 km/h
B)450 km/h
C)779 km/h
D)723 km/h
E)720 km/h
Rationale: Distance = (150 x 5) = 750 km.
Speed = Distance/Time
Speed = 750/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 750 x 3/5 km/hr = 450 km/hr.
B
Answer: B
Question: Prizes totaling $45,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
Options:
A)(a) $5,000
B)(b) $10,000
C)(c) $17,000
D)(d) $55,000
E)(e) $65,000
Rationale: The highest prize cannot possibly be less than 1/3rd of 45,000 (because in this case the sum of 3 prizes would be less than 45,000) and cannot be more than 45,000.
Answer: C.
Answer: C
Question: The average age of 20 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
Options:
A)79
B)86
C)95
D)72
E)80
Rationale: Age of the 15th student = 20*15 - (14*5+16*9) =300-214 = 86 years
Answer is B
Answer: B
Question: The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 3200 meters per second, what was the speed, in meters per second, when the stopwatch was started?
Options:
A)25/3
B)25/4
C)25/8
D)25/16
E)25/32
Rationale: Let x be the original speed when the stopwatch was started.
In 90 seconds, the speed doubled 9 times.
2^9 * x = 3200
x = (2^7 * 25) / 2^9 = 25/4
The answer is B.
Answer: B
Question: In Township K, 1/4 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
Options:
A)23/30
B)11/15
C)7/10
D)1/6
E)2/15
Rationale: 1/4 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/4) = 1/12
therefore only video cassette recorder = 1/10 - 1/12 = 1/60
Total = 1/4+1/60+neither cable tv nor videocassette recorders
1 = 4/15 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-4/15 = 11/15
Hence B.
Answer: B
Question: In 1982 and 1983, Company B’s operating expenses were $11.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
Options:
A)3%
B)16 2/3%
C)25%
D)4 1/3%
E)60%
Rationale: Profit in 1982 = 15.6 - 11 = 4.6 million $
Profit in 1983 = 18.8 - 14 = 4.8 million $
Percentage increase in profit = (4.8-4.6)/4.6 * 100 %
= 4 1/3%
Answer D
Answer: D
Question: How many even multiples of 55 are there between 549 and 1101?
Options:
A)5
B)6
C)9
D)10
E)11
Rationale: 550 = 10*55
1100 = 20*55
The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Answer: B
Question: The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...?
Options:
A)3:2
B)5:4
C)7:6
D)9:8
E)11:10
Rationale: Polly : Sandy = 5:6
Sandy : Willy = 3:2 = 6:4
Polly : Sandy : Willy = 5:6:4
Polly : Willy = 5:4
The answer is B.
Answer: B
Question: The speed of a railway engine is 63 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
Options:
A)19
B)18
C)16
D)17
E)23
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached
Does reduction mean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.
Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.
In other words, if S = speed, and N = number of compartments, then
S = 63 - k*sqrt(N)
where k is a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.
If N = 9, then S = 24
24 = 63 - k*sqrt(9) = 63 - 3k
k = 13
Now, we need to know: what value of N makes S go to zero?
0 = 63 - 13*sqrt(N)
13*sqrt(N) =63
n = 23
With 24 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 23 is the maximum number of cars the engine can pull and still move.
E
Answer: E
Question: A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)Rs.1090
B)Rs.1020
C)Rs.1190
D)Rs.1202
E)NONE
Rationale: Solution
S.P	= 85% of Rs.1200
= Rs.(85/100×1200)
Rs.1020.
Answer B
Answer: B
Question: An angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the Chariot driver of Bheeshm. With one arrow each he knocked down respectively the Chariot, the flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious on an arrow bed. Find the total number of arrows Arjun had.
Options:
A)90
B)100
C)110
D)120
E)130
Rationale: x/2 + 6+3+1+4 sqrt(x) = x
x/2 +10 + 4 sqrt(x) = x
4sqrt(x) = x/2 - 10
squaring on both sides
16x = x²/4 +100 -10x
simplifying x² -104x +400=0
x =100, 4
x=4 is not possible therefore x=100
ANSWER:B
Answer: B
Question: Village P’s population is 800 greater than Village Q's population. If Village Q’s population were reduced by 500 people, then Village P’s population would be 3 times as large as Village Q's population. What is Village Q's current population?
Options:
A)1100
B)1150
C)1200
D)1250
E)1300
Rationale: P = Q+800.
P=3(Q-500).
3(Q-500)=Q+800.
2Q=2300.
Q=1150.
The answer is B.
Answer: B
Question: A 4 digit no may consist of the digits 6,2,7,5 where none of the nos are repeated.Find the possible no of combinations divisible by 36?
Options:
A)18
B)36
C)38
D)48
E)58
Rationale: lcm of 36 = 3 *3 * 4 the four digit number should be divisible by 3 and 4 then it is divisible by 36 adding all the digits 6+2+7+5=20 not divisible by 20 so
any 4 digit number formed by this is not divisible by 36
ANSWER:B
Answer: B
Question: 0, 3, 9, 18, 30, 45, 63, ?What number should replace the question mark?
Options:
A)78
B)74
C)79
D)72
E)84
Rationale: E 84add 3,6,9,12,15,.....
Answer: E
Question: How many X ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
Options:
A)3
B)16
C)28
D)32
E)56
Rationale: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen X= 56 - 24 = 32
Ans: D
Answer: D
Question: A walks at 4 kmph and 4 hours after his start, B cycles after him at 10 kmph. How far from the start does B catch up with A?
Options:
A)25km
B)26.7km
C)30km
D)32.5km
E)31.2km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.
x/4 - x/10 = 4
x = 26.7 km
Answer is B
Answer: B
Question: Machine A and machine B are each used to manufacture 440 sprockets. It takes machine A 10 hours longer to produce 440 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
Options:
A)5
B)6
C)4
D)3
E)2
Rationale: Machine B: Takes x hours to produce 440 sprockets
Machine A: Takes (x+10) hours to produce 440 sprockets
Machine B: In 1 hour, B makes 440/x sprockets
Machine A: In 1 hour, A makes 440/(x+10) sprockets
Equating:
1.1(440/(x+10)) = 440/x
484/(x+10) = 440/x
484x = 440x+4400
44x = 4400
x = 100
A makes 440/(110) = 4 sprockets per hour
Answer : C
Answer: C
Question: It takes Joey the postman 1 hours to run a 4 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?
Options:
A)5
B)12
C)13
D)14
E)15
Rationale: let his speed for one half of the journey be 4 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*4*x/4+x=5
8x=4x+20=>x=5
A
Answer: A
Question: Dacid obtained 90, 92, 85, 87 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)67
B)26
C)88
D)90
E)75
Rationale: Average
= (90+ 92+ 85+ 87+ 85)/5
= 439/5 = 87.8.
Answer: C
Answer: C
Question: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
A)5
B)9
C)10
D)20
E)30
Rationale: 125^10 = (5^3)^10 = 5^30
ANSWER:E
Answer: E
Question: A and B started a business in partnership. A invested Rs. 40000 for 6 months. A received Rs.6000 as his share out of the total profit of Rs. 9000, What was the amount invested by B for the whole year?
Options:
A)Rs. 10000
B)Rs. 10002
C)Rs. 10009
D)Rs. 10007
E)Rs. 122122
Rationale: Explanation:
Profits of A and B are distributed in the same ratio of their investment and period of investments.
Investment of A/ Investment of B = Profit of A/ Profit of B = 6000/3000
(40000*1/2)/X*1 = 2/1
Therefore, X = B's investment amount = Rs. 10,000.
ANSWER:A
Answer: A