divelab/Sys2Bench huggingface dataset:
Question: Three candidates contested an election and received 3834 votes, 7926 votes, and 16240 votes respectively. What percentage of the total votes did the winning candidate receive?
Options:
A)55%
B)56%
C)57%
D)58%
E)59%
Rationale: The total number of votes polled = (3834 + 7926 + 16240) = 28000
The winner's percentage = 16240/28000 * 100 = 58%
The answer is D.
Answer: D
Question: The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 35 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?
Options:
A)20 ft
B)25 ft
C)750 ft
D)900 ft
E)1050 ft
Rationale: Point to note: Both the wheels would have traveled the same distance.
Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).
Equating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 35. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)
Solving this eqn. gives x=30
Sub x=30 either in (x+5)*30 or in x * 35 to get the distance, which is 1050. So the correct choice is E.
Answer: E
Question: If n = (33)^43 + (43)^32 what is the units digit of n?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: First of all, the units digit of (33)^43 is the same as that of 3^43 and the units digit of (43)^32 is the same as that of 3^32. So, we need to find the units digit of 3^43 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:
3^1=3 (the units digit is 3)
3^2=9 (the units digit is 9)
3^3=27 (the units digit is 7)
3^4=81 (the units digit is 1)
3^5=243 (the units digit is 3 again!)
...
Thus:
The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).
The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (33)^43 + (43)^32 is 7 + 5 = 2.
Answer: B.
Answer: B
Question: If x is a whole number, then x2(x2 - 1) is always divisible by
Options:
A)12
B)24
C)12-x
D)multiple of 12
E)NOne
Rationale: Sol.
Putting x = 2, we get 22 (22 - 1) = 12.
So, x2(x2 - 1) is always divisible by 12.
Answer A
Answer: A
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Options:
A)$28
B)$82
C)$110
D)$138
E)$194
Rationale: by the question, the equation would be 150 p - 84*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 194. Answer E for me.
Answer: E
Question: The average of first 12 even numbers is?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Sum of 12 even numbers = 12 * 13 = 156
Average = 156/13 = 13
ANSWER:D
Answer: D
Question: log 3600 is equal to
Options:
A)2log6 +1
B)6log2 + 1
C)2log6 +2
D)6log2 + 2
E)6log2 + 4
Rationale: log 3600=log 36 + log 100=2log 6 + 2.
log 36=log 6^2=2log 6
log 100=2.
-->2log 6+2
ANSWER:C
Answer: C
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)2828
B)2277
C)2797
D)3900
E)1981
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3
= Rs.3900
D
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?
Options:
A)75%
B)67%
C)29%
D)55%
E)45%
Rationale: 600 --- 400
100 --- ? => 67%
Answer: B
Answer: B
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)8
B)10
C)12
D)11
E)15
Rationale: Speed = 120/10 = 12 m/sec
speed of the second train = 120/5 = 8 m/sec
relative speed = 12+8 = 20 m/sec
Req time = 120+120/20 = 12 sec
ANSWER C
Answer: C
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs.605 as interest. What was the value of his total savings before investing in these two bonds?
Options:
A)Rs.5500
B)Rs.11000
C)Rs.22000
D)Rs.2750
E)None
Rationale: Solution:
Explanatory Answer
Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.
The extra interest earned on the compound interest bond = Rs.55
The interest for the first year =550/2 = Rs.275
Therefore, the rate of interest =55/275 * 100 = 20% p.a.
20% interest means that Shawn received 20% of the amount he invested in the bonds as interest.
If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the bonds = 275/20 * 100 = 1375.
As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = Rs.2750.
Answer D
Answer: D
Question: A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)11 seconds
B)38 seconds
C)50 seconds
D)88 seconds
E)19 seconds
Rationale: Speed = 36 Km/hr = 36*(5/18) m/sec = 10 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/10) = 50 seconds
Answer: C
Answer: C
Question: A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 11 members, then what is the exact number of researchers required?
Options:
A)33
B)34
C)36
D)31
E)27
Rationale: 11*3-2( because james is included in all the three teams)
=33-2 =31
D
Answer: D
Question: There are 15 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
Options:
A)10
B)30
C)105
D)60
E)90
Rationale: 15 players are there.
two players play one game with one another.
so 15C2=15x14/2=105
SO OPTION C is correct
Answer: C
Question: Find the odd man out. 10, 20, 30, 40, 50, 60, 72
Options:
A)15
B)72
C)51
D)90
E)115
Rationale: Explanation :
All except 72 are multiples of 10
Answer : Option B
Answer: B
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)28 km/hr
B)17 km/hr
C)60 km/hr
D)16 km/hr
E)15 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train
= 2x m/sec.
Relative speed
= ( x + 2x) = 3x m/sec.
(100 + 100)/8
= 3x => x = 25/3.
So, speed of the faster train = 50/3
= 50/3 * 18/5
= 60 km/hr.
Answer: C
Answer: C
Question: Two vessels contains equal number of mixtures milk and water in the ratio 7:2 and 8:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
Options:
A)1:3
B)9:13
C)5:1
D)11:3
E)15:4
Rationale: The ratio of milk and water in the new vessel is = (7/9 + 8/9) : (2/9 + 1/9)
= 15/9 : 3/9 = 5:1
Answer is C
Answer: C
Question: Evaluate:434 - 12*3*2 = ?
Options:
A)426
B)526
C)626
D)726
E)826
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
434 - 12*3*2 = 434 - 8 = 426
correct answer A
Answer: A
Question: When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is :
Options:
A)20 lakh tons
B)80 lakh tons
C)200 lakh tons
D)800 lakh tons
E)None of these
Rationale: Solution
Let the total production be x lakh tons.
Then, 15% of X - 10% of X = (40 - 30) lakh tons
⇔ 5% of x = 10 lakh tons ⇔ x = ( 10x100/5 )= 200 lakh tons.
Answer C
Answer: C
Question: I chose a number and divide it by 4. Then I subtracted 24 from the result and got 10. What was the number I chose?
Options:
A)170
B)700
C)800
D)900
E)None
Rationale: Solution:
Let x be the number I chose, then
x/4âˆ’24=10
x/5=34
x=170
Answer: A
Answer: A
Question: The odds against ram solving the problem are 6 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
Options:
A)1/4
B)5/21
C)16/21
D)23/28
E)13/18
Rationale: Odds against Ram are 6:3 so probability that he will solve the problem is 1/3.
Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12
It will be solved means that either Ram or Krishna or both will be able to solve it.
P(A or B) = P(A) + P(B) - P(A and B) = 1/3 + 7/12 - (1/3)*(7/12) = 13/18
E
Answer: E
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
Options:
A)5/17
B)5/12
C)5/11
D)5/18
E)5/19
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: B
Question: If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/2 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
Options:
A)1/4
B)1/2
C)10/3
D)2
E)4
Rationale: N = 2D/5
J = N/2 = D/5
The average of November and January is (N+J)/2 = 3D/5 / 2 = 3D/10
D is 10/3 times the average of November and January.
The answer is C.
Answer: C
Question: A’s speed is 17/15 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
Options:
A)1/16
B)2/15
C)2/17
D)1/8
E)1/7
Rationale: Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (17v/15) = xD/v
(15/17)*D/v = x*D/v
x = 15/17
B should have a head start of 2/17 of the full distance.
The answer is C.
Answer: C
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.50 km and 1.0 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)48
B)9
C)7
D)60
E)15
Rationale: :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.50 + 1.0 = 2.5 km = 2500 m.
Required time = 2500 * 3/125
= 60 sec.
Answer: D
Answer: D
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)2888
B)3120
C)2877
D)2999
E)1277
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: B
Question: A corporation triples its annual bonus to 50 of its employees. What T percent of the employees’ new bonus is the increase?
Options:
A)50%
B)662⁄3%
C)100%
D)200%
E)300%
Rationale: T of the employees’ new bonus is the increase Hence B.
Answer: B
Question: In order to obtain an income of Rs. 3800 from 70% stock at Rs. 280, one must make an investment of
Options:
A)Rs.16000
B)Rs.15000
C)Rs.15250
D)Rs.15200
E)Rs.15300
Rationale: Explanation :
Market Value = Rs. 280
Required Income = Rs. 3800.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.70 (ie,70% of the face value 100), investment = Rs.280
To obtain Rs.3800, investment = 280/70Ã—3800=Rs.15200
Answer : Option D
Answer: D
Question: the percentage discount offered for"Buy 6 get 1 free is"?
Options:
A)14.29%
B)15.29%
C)17.29%
D)19.29%
E)12.29%
Rationale: Total Items = 7
Discounted = 1
Percentage = 1/7*100
=14.29%
ANSWER:A
Answer: A
Question: The radius of the wheel of a bus is 100 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
Options:
A)175
B)250
C)300
D)330
E)None of these
Rationale: Radius of the wheel of bus = 100 cm. Then,
circumference of wheel = 2Ï€r = 200Ï€ = 628.57 cm
Distance covered by bus in 1 minute
= 66â„60 Ã— 1000 Ã— 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 440 cm
âˆ´ Revolutions per minute = 6600000/60Ã—628.57 = 175
Answer A
Answer: A
Question: The ratio of boys to girls in a school is 9 to 11. After 36 more girls join, the ratio becomes 9 to 13. How many boys are there in the school?
Options:
A)102
B)115
C)132
D)162
E)234
Rationale: Boys : Girls
9 : 11
let the boys be 9x and the girls be 11x. Now, 36 more girls are added -------> 9:13(new ratio).
so,
9x/(11x+36) =9/13.
solving,
We get : x=18
so No. of boys in the school are :9x= 9*18= 162
hence (D)
Answer: D
Question: In how many ways letters of the word REPEAT be arranged?
Options:
A)360
B)120
C)240
D)180
E)169
Rationale: REPEAT has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 360ways
A
Answer: A
Question: The least number, which when divided by 12, 15, 20 and 63 leaves in each case a remainder of 8 is:
Options:
A)448
B)488
C)542
D)1268
E)560
Rationale: Required number = (L.C.M. of 12, 15, 20, 63) + 8
= 1260+ 8
= 1268.
answer :D
Answer: D
Question: What will be the cost of building a fence around a square plot with area equal to 25 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)1160
B)2287
C)2977
D)2668
E)1298
Rationale: Let the side of the square plot be a ft.
a2 = 25=> a = 5
Length of the fence = Perimeter of the plot = 4a = 20 ft.
Cost of building the fence = 20 * 58 = Rs. 1160.
Answer:A
Answer: A
Question: In a 1000 m race, A beats B by 100 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Options:
A)A)190m
B)B)829m
C)C)822m
D)D)929m
E)E)132mj
Rationale: By the time A covers 1000 m, B covers (1000 - 100) = 900 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/900 * 1000/900 = 1000/810 So, by the time A covers 1000 m, C covers 810 m.
So in 1000 m race A beats C by 1000 - 810 = 190 m.
Answer:A
Answer: A
Question: The average of first five multiples of 7 is:
Options:
A)9
B)16
C)15
D)8
E)21
Rationale: Explanation :
(7(1+2+3+4+5)/5
= 7x15/5
= 21
Answer : E
Answer: E
Question: If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is
Options:
A)1/2
B)1
C)2
D)4
E)8
Rationale: Given: 5/w + 5/x = 5/ywx=y
Find: (w+x)/2 = ?
5(1/w + 1/x) = 5(1/y) - divide both sides by 5
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A
Answer: A
Question: A car averages 70 mph for the first 4 hours of a trip and averages 60 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Let the time for which car averages 60 mph = t
65*(t+4)= 70*4 + 60 t
=>5 t= 20
=> t = 4
Total duration of the trip = 4+4=8
Answer A
Answer: A
Question: If p is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of p?
Options:
A)51
B)54
C)162
D)72
E)50!+2
Rationale: In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.
Answer: C.
Answer: C
Question: A heap of coconuts is divided into groups of 2, 5 and 9 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
Options:
A)A)31
B)B)41
C)C)51
D)D)61
E)E)91
Rationale: LCM = 90
=> 90 + 1 = 91
ANSWER:E
Answer: E
Question: In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 0.8, then the 3rd term is which of the following?
Options:
A)−1.5
B)−1
C)0
D)0.2
E)2
Rationale: First = 0.8
Second = 2*0.8-1 = 0.6
Second = 2*0.6-1 = 0.2
Answer: option D
Answer: D
Question: If the side of the regular hexagon above is 2, what is the circumference of the inscribed circle?
Options:
A)2∏√3
B)3∏
C)4∏/√3
D)2∏/√3
E)∏√3
Rationale: Now AC will be 1 because circle is touching the midpoints of the circle.
Then we get kite ACBO.
We have AC = 1 and CB = 1, now we need to find BO which is radius
from triplets we get 30:60:90 = 1:√3:2
Now CBO is right angled triangle, then we get BO as √3.
r = √3...circumference is 2∏r is 2∏√3.
Answer :option A.
Answer: A
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 39 . The largest number is:
Options:
A)28
B)32
C)36
D)42
E)46.8
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 39
15x = 117
x = 7.8
Largest number = 6x = 46.8.
ANSWER E
Answer: E
Question: Out of 12 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
A)5/55
B)21/55
C)51/55
D)41/55
E)31/55
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 8C₃/12C₃ = 1 - (8 * 7 * 6)/(10 * 11 *12)
= 41/55
Answer: D
Answer: D
Question: The speed of a railway engine is 74 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)49
B)18
C)16
D)17
E)19
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached
Doesreductionmean 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 = 74 - k*sqrt(N)
wherekis 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 = 74 - k*sqrt(9) = 74 - 3k
k = 16.67
Now, we need to know: what value of N makes S go to zero?
0 = 74 - 16.67*sqrt(N)
16.67*sqrt(N) = 74
sqrt(N) = 4.44
n = 4.44^2 > 19
With 20 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 19 is the maximum number of cars the engine can pull and still move.
E
Answer: E
Question: If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
Options:
A)20
B)10
C)15
D)25
E)30
Rationale: 100
125
-----
125 ----- 25
100 ------ ? => 20%
ANSWER A
Answer: A
Question: A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 70 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
Options:
A)28%
B)30%
C)32%
D)34%
E)36%
Rationale: 1. 20% of 400=80 pounds of decaffeinated coffee
2. 70% of 100=70 pounds of decaffeinated coffee
3. Wt have 150 pounds of decaffeinated out of 500 pounds, that means 150/500*100%=30%. The correct answer is B.
Answer: B
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)180 sec
B)190 sec
C)290 sec
D)490 sec
E)390 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50
= 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer:B
Answer: B
Question: If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
Options:
A)Wednesday
B)Tuesday
C)Sunday
D)Monday
E)Friday
Rationale: The year 2004 is a leap year. So, it has 2 odd days.
Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday
Answer: C
Answer: C
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)1/3
B)1/9
C)2/8
D)6/4
E)5/7
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: A
Question: If it is 7:19 in the evening on a certain day, what time in the morning was it exactly 2,880,705 minutes earlier? (Assume standard time in one location.)
Options:
A)7:25
B)7:34
C)7:43
D)7:47
E)7:52
Rationale: 7:19 minus 2,880,705 must end with 4, the only answer choice which ends with 4 is B.
Answer : B.
Answer: B
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 16 minutes earlier. How far is the office from his house?
Options:
A)4 4/5 Km
B)4 1/7 Km
C)3 1/5 Km
D)3 1/7 Km
E)3 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 24/6
= 24/2 * 24/60
= 12 * 2/5
= 24/5 = 4 4/5 Km
A)
Answer: A
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be
Options:
A)45 min
B)60 min
C)55 min
D)70 min
E)75 min
Rationale: Time = 50/60 hr = 5/6hr
Speed = 48mph
distance = S*T = 48 * 5/6 = 40km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 kmph = 60kmph
Answer : B
Answer: B
Question: Given that a is the average (arithmetic mean) of the first five positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
Options:
A)3:4
B)6:13
C)5:6
D)13:10
E)4:3
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}
Both sets are evenly spaced, thus their median=mean:
a=18 and b=(36+42)/2=39 --> a/b=18/39=6/13.
Answer: B.
Answer: B
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 5 girls and 7 guys. Assuming girls go on dates with guys, how many possible ways can these 10 medical interns date each other?
Options:
A) 10
B) 25
C) 60
D) 2520
E) 2320
Rationale: 1st girl can go with 7 guys
2nd girl can go with remaining 6
3rd girl can go with remaining 5 and so on
so the total ways are 7 * 6 * 5 * 4 * 3
D should be the answer
Answer: D
Question: If the numbers 1 to 95 are written on 95 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
Options:
A)1/50
B)1/25
C)1/95
D)1
E)2
Rationale: There are 25 primes, 69 composite numbers from 1 to 95. The number
which is neither prime nor composite is 1.
Therefore, required probability = 1/95.
ANSWER:C
Answer: C
Question: 852.68 − 4.5 + 108.98 = ? − 2132.54
Options:
A)6078.58
B)5225.9
C)6258.58
D)6088.58
E)None
Rationale: Option 'A'
Answer: A
Question: If 10 crates have 99 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
A)5
B)10
C)15
D)20
E)0
Rationale: Each crate requires 1 apples and totally there are 10 crates so required apples = 10 * 1 = 10
Answer: B
Answer: B