divelab/Sys2Bench huggingface dataset:
Question: What is the units digit of the solution to 177^28−133^23?
Options:
A)1
B)3
C)4
D)6
E)9
Rationale: Let's reduce the clutter and make it easy to solve
So, 7^28 - 3^23 will have the same units digit as the big numbers above
Both 7 and 3 have a cyclicity of 4, i.e. their powers repeat the units digit after every 4th power
So , 7^28 has the same units digit as 7^4 ,which is 1
Similarly, 3^23 has the same units digit as 3^3, which is 7
Now, we get
xx...xx1 - xx....xx7 = xx...xx4
Thus, the units digit of the solution to 177^28 - 133^23 is 4
Correct Option : C
Answer: C
Question: What is the square root of 324?
Options:
A)A)18
B)B)9
C)C)45
D)D)62
E)E)81
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
18*18=324
324 divided by x = 18
x=18
(A) 18
Answer: A
Question: A company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price of a box did not change and all boxes are full of juice, by approximately what percent did the price of the juice decrease?
Options:
A)12.00%
B)16.67%
C)18.33%
D)20.00%
E)21.50%
Rationale: suppose when v = 5x10x20 = 1000 cm, the price is $1200
per cm price = $1.2
the price is $1200 if v = 6x10x20 = 1000 cm.
per cm price = $1.0
so the price is decreased by $0.2
so the % price decreased by $0.2/1.20 = 16.67%
ANSWER:B
Answer: B
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 2 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)
Options:
A) 1
B) 6
C) 7
D) 11
E) 10
Rationale: We're told that there are 2 ingredients (we'll call them A, B); we're told that each 'mix' must include AT LEAST 2 ingredients...
2 ingredient blends:
AB
Total blends = 1
A
Answer: A
Question: 70,75, 73,76,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70, 73 and 75.
Answer: C.
Answer: C
Question: How many multiples of 5 are there between 10 and 89, 10 and 89 inclusive?
Options:
A)17
B)16
C)18
D)19
E)20
Rationale: 5 multiples are ...10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,...
,...,
the answer is =16
Answer is B
Answer: B
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6?
Options:
A)12.6.
B)15.8.
C)14.4.
D)16.2.
E)16.4.
Rationale: [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6
= 6*0 + 2*7.2 + 8 - 6.6
= 0 +14.4 +1.4
15.8
Answer B
Answer: B
Question: What is the sum of first 10000 numbers in the series -1,+1,-1,+1,-1.......??
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: -1+1=0
and for 10000 numbers it will form 5000 pairs
so 5000*0 = 0
ANSWER:A
Answer: A
Question: Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years?
Options:
A)30
B)35
C)40
D)50
E)60
Rationale: Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 10 years = (20 + 10) years =30 years.
Answer : A
Answer: A
Question: (4!)^n is a factor of 12!, but (4!)^(n+1) is not factor of 12!. What is the value of n?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 24
Question can be rephrased as how many 24's are there in 12!
12 * 2 = 24
4 * 6 = 24
3 * 8 = 24
Value of n = 3
Answer: C
Answer: C
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $55.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
Options:
A)25.5
B)30.4
C)31.8
D)32.5
E)33.8
Rationale: $69-$55=14$
(14/55)*100=25.5%
ANSWER:A
Answer: A
Question: Bill is golfing with two friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 10 golf tees for each member of his foursome, if he will buy no more than 1 packages of the generic golf tees?
Options:
A)16
B)10
C)9
D)4
E)2
Rationale: At least 10 golf tees for each member of his threesome = total of at least 3*10 = 30 tees.
1 packages of the generic golf tees, that are packaged by the dozen = 1*12 = 12 tees.
So, Bill must by at least 18 Aero tees. They come by the pair, hence he must by at least 18/2 = 9 packages of Aero flight tees.
Answer: C.
Answer: C
Question: If the price of 50 toys is 1000, then what will the price of 20 toys ?
Options:
A)400
B)361
C)117
D)287
E)112
Rationale: One toy price = 1000/50 = 20
20 toy price = 20 * 20 = 400
Answer : A
Answer: A
Question: Arun is traveling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm?
Options:
A)22
B)38
C)12
D)99
E)28
Rationale: Let the distance be x km
if travels at 10 kmph, Arun will reach point A at 2 pm
if travels at 15 kmph, Arun will reach point 12 noon
=> Time taken when traveling at 10 km = Time taken when traveling at 15 km + 2 hours
⇒x10=x15+2⇒x10−x15=2⇒3x−2x=2×30⇒x=60⇒Distance = 60 km
Examine the any statement say, if travels at 10 kmph, Arun will reach point A at 2 pm
⇒Time taken = DistanceSpeed=6010=6 hours⇒He must have started 6 hours back 2 pm, ie, at 8 am⇒Now he wants to reach at 1 pm. ie; time to be taken = 5 hours⇒Speed needed = DistanceTime=605=12 kmph
Answer : C
Answer: C
Question: Out of 450 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
Options:
A)120
B)150
C)100
D)180
E)220
Rationale: n(A)=325,n(B)=175,n(AuB)=450-50=400.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-400=100.
Answer is C
Answer: C
Question: Pipe A can fill a tank in 15 hours, pipe B in 30 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)2.5
C)3
D)8
E)None
Rationale: Sol.
Part filled by (A + B + C) in 1 hour = (1/15 + 1/30 + 1/40) = 1/8.
âˆ´ All the three pipes together will fill the tank in 8 hours.
Answer D
Answer: D
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
Options:
A)6620
B)2277
C)2677
D)2688
E)26711
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: A
Question: Let C be defined as the sum of all prime numbers between 0 and 23. What is C/3
Options:
A)155
B)129
C)61
D)25.3
E)43
Rationale: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19
Sum,C = 77
C/3 = 25.3
Answer D
Answer: D
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)22
B)190
C)277
D)18
E)12
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: In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, 23, ?, 47
Options:
A)31
B)34
C)36
D)31
E)33
Rationale: B
34
The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Missing Number = 23 + 11 = 34.
Answer: B
Question: A work crew of 6 Men takes 9 days to complete one-half of a job. If 12 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?
Options:
A)2
B)3
C)3 1/3
D)4
E)4 4/5
Rationale: Suppose 1 man can do work in X days..
so 6 men will do in ..
6/X=1/9*1/2 as half job is done
X=108
now 12 more are added then
18/108=1/2*1/d for remaining half job
d=3 Number of days
B
Answer: B
Question: When 28 is divided by the positive integer r, the remainder is 1. What is the sum of all the possible values of r for which this is true?
Options:
A)2
B)3
C)9
D)30
E)39
Rationale: The only possible values of the form 28=rp+1 are 3,9 or 27
The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: E
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
Options:
A)32
B)86
C)44
D)22
E)55
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer:Option B
Answer: B
Question: A man can row 8 km/hr in still water. If the river is running at 3 km/hr, it takes 3 hours more in upstream than to go downstream for the same distance. How far is the place?
Options:
A)32.5 km
B)25 km
C)27.5 km
D)22.5 km
E)None of these
Rationale: Explanation :
Let the speed downstream = x and speed updstream = y
Then
(x+y)/2=8
=> x + y = 16 ---(Equation 1)
(x−y)/2=3
=> x - y = 6 ---(Equation 2)
(Equation 1 + Equation 2) = > 2x = 22
=> x = 11 km/hr
(Equation 1 - Equation 2) = > 2y = 10
=>y = 5 km/hr
Time taken to travel upstream = Time taken to travel downstream + 3
Let distance be x km
Then
x/5 = (x/11) + 3
=> 11x = 5x + 165
=> 6x = 165
=> 2x = 55
=> x = 27.5. Answer : Option C
Answer: C
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 180 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Options:
A)55
B)65
C)75
D)85
E)90
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 180 + P
C + M = 180
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 180/2 = 90.
ANSWER:E
Answer: E
Question: Find the value of 72519 x 9999 = m?
Options:
A)345434667
B)246465757
C)465767867
D)725117481
E)645354643
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: If the personal income tax rate is lowered from 46% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $36000?
Options:
A)$3500
B)$5040
C)$3150
D)$7000
E)$10000
Rationale: Saving = (46-32)% of 36000 = 5040.
Answer:B
Answer: B
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 7 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
Options:
A)8 minutes, 10.4 seconds
B)5 minutes, 21.8 seconds
C)5 minutes, 43.56 seconds
D)5 minutes, 44.44 seconds
E)5 minutes, 17.6 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 7 minutes, 44 seconds. The only number is 8 minutes, 10.4 seconds.
Another approach:
11/25 close to 30 second when added to the 7 minutes, 44 seconds, it means it passes 8 minute.
Answer: A
Answer: A
Question: A man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water?
Options:
A)11
B)77
C)30
D)88
E)35
Rationale: US = 25
DS = 45
M = (45 + 25)/2 = 35
Answer:E
Answer: E
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)5,14
B)6,4
C)12,7
D)7,5
E)4,7
Rationale: Answer: Option C
x â€“ y = 5
4x â€“ 6y = 6
x = 12 y = 7
Answer: C
Question: In a village there are 20 men and 25 women. In how many ways can a man and a woman be selected?
Options:
A)200
B)300
C)500
D)600
E)650
Rationale: We can select one men from 20 women in 20 ways.
We select one woman from 25 women in 25 ways
We select a Men and women in 20 * 25 ways i.e., = 500 ways.
C
Answer: C
Question: A and B can do a work in 5 days, B and C in 15 days and C and A in 25 days. In how many days will the work be completed, if all three of them work together?
Options:
A)26/18
B)42/15
C)48/63
D)12/36
E)150/23
Rationale: One day work of A and B = 1/5
One day work of B and C = 1/15
One day work of C and A = 1/25
2(A + B + C) = 1/5+ 1/15 + 1/25
2(A + B + C) = 23/75
(A + B + C) = 23/150
Number of days required = 150/23 days.
Answer: E
Answer: E
Question: Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $19.20, how many discounted tickets did he buy?
Options:
A)3
B)4
C)5
D)6
E)2
Rationale: Let x be the number of tickets he bought at $2 per ticket.
then 2 x + (10-x)1.6 = 19.2
0.4x = 3.2 => x = 8
discounted tickets = 10 -x = 2
Ans : E
Answer: E
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be $84 more. What is the cost price?
Options:
A)$900
B)$1200
C)$1500
D)$1800
E)$2100
Rationale: 7% * cost price = $84
1% * cost price = $84 / 7 = $12
The cost price is $1200.
The answer is B.
Answer: B
Question: In a survey of 350 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?
Options:
A)7/12
B)8/41
C)9/348
D)1/8
E)41/70
Rationale: ---------UI----------------NUI-------Total
PT----(12.5/100)*104 = 13----------- --54
NPT---104-13-------------- x--------296
Total--104----------------------------350
we have to find not part time and not uninsured . in other words not part time and insured = x/350 = (296-104+13)/350
= 41/70
Answer is E.
Answer: E
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 80 km/hr. When will he overtake the thief?
Options:
A)6:30 p.m
B)9:30 p.m
C)4:30 p.m
D)2:30 p.m
E)1:30 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 80(x - 1/2) => x = 2 hrs.
So, the thief is overtaken at 4:30 p.m.'
Answer: C
Answer: C
Question: The 540 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT
Options:
A) 4
B) 20
C) 30
D) 60
E) 90
Rationale: Obviously the number of rows must be a factor of 540. The only option which is not a factor of 540 is A (4).
Answer: A.
Answer: A
Question: If Josh, Doug, and Brad have a total of $68 between them, and Josh has two times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have?
Options:
A)$8
B)$9
C)$27
D)$32
E)$36
Rationale: Josh+Doug+Brad = 68 ; Josh = 2 Brad, Josh =3/4 Doug
Josh+1/2 Josh+ 4/3 Josh = 68 (substituted the given values)
Josh = 24. 24= 3/4 Doug => Doug =32
Answer is D.
Answer: D
Question: A rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 96 inches and the width is 72 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches?
Options:
A)a 64
B)b 22
C)c 27
D)d 40
E)e 50
Rationale: l = 96 /12 = 8 ft
w = 72 / 12 = 6 ft
Area of paper = 48
Area of cube = 8 * side^2
side of cube = 4
V of cube = 64
Answer: A
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
Options:
A)242
B)297
C)648
D)267
E)108
Rationale: Number of shares = 4455 = 540.
8.25
Face value = Rs. (540 x 10) = Rs. 5400.
Annual income = Rs. 12	x 5400 = Rs. 648.
100
Answer: C
Answer: C
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)5 sec
B)6 sec
C)7 sec
D)10 sec
E)12 sec
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
ANSWER:B
Answer: B
Question: In a partnership between A, B and C. A's capital is Rs.8000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)19878
B)12798
C)26908
D)11750
E)18800
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 8000
470 ---- ? => 18800
Answer: E
Answer: E
Question: If two sides of a triangle are 6 and 10, respectively, which of the following could NOT be the area of this triangle?
Options:
A)1
B)6
C)17
D)38
E)29
Rationale: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 6 and 10.
We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)10 * 6 -or- (.5)6 * 10 will result in a maximum area of 30 for the triangle; therefore, the triangle could never have an area of 38.
D
Answer: D
Question: What is the area of a triangle with the following vertices L(2, 3), M(5, 1), and N(3, 5) ?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.
Though if you make a diagram minimum simple calculations will be needed:
Answer: B.
Answer: B
Question: The C.P of 17 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)16 2/3%
B)16 2/8%
C)5 5/9%
D)16 2/1%
E)16 1/3%
Rationale: 17 CP = 18 SP
18 --- 1 CP loss
100 --- ? => 5 5/9% loss.Answer: C
Answer: C
Question: 18 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
Options:
A)22
B)66
C)88
D)100
E)281
Rationale: (18 * 8)/30 = (x * 6)/50 => x =40
40 – 18 = 22
Answer: A
Answer: A
Question: Oranges are purchased for $15/bag at the Farmer's Market. A bag weighs 3 lbs. The oranges are peeled and the seeds removed (removing 1/6 of the weight). Then, these oranges are crushed and used for making marmalade. It takes 1 lb of oranges to make 3 cups of crushed oranges. If 4 cups of crushed oranges can make one jar of marmalade, how much money is needed to buy oranges to make x number of jars of marmalade, in dollars?
Options:
A)8x/3
B)4x
C)8x
D)2x
E)3x/2
Rationale: Initial cost for a bag = $15; since 1 bag = 3 lbs, 1 lb = $15/3, but ONLY 5/6 is used.
So the cost of 5/6 lb = $5, or 1 lb = $30/5,
and 1 lb of oranges = 2 cups of crushed oranges, so 2 cups of oranges costs $30/5, but 4 cups are needed for 1 jar, so cost of 4 cups = $(30/5)(4/3) = $120/15 = $8
If 1 jar costs $8, x number of jars will cost $8x.
Answer is C
Answer: C
Question: If two numbers are in the ratio 2:3 and the numerator and denominator are added and subtracted by1 and 2 respectively, then the ratio becomes 6:2, then find the biggest number?
Options:
A)2
B)5
C)3
D)4
E)6
Rationale: 2:3
2x + 1 : 3x - 2 = 3 : 1
[2x + 1] = 3[3x - 2]
2x + 1= 9x -6
9x - 2x = 7
x = 1
Then smallest number is = 3x
3x = 3
C
Answer: C
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 190 m long?
Options:
A)40 sec
B)11 sec
C)88 sec
D)19 sec
E)44 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 190 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer: E
Answer: E
Question: The president of a country and 6 other dignitaries are scheduled to sit in a row on the 7 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?
Options:
A) 720
B) 5
C) 20
D) 24
E) 120
Rationale: IMO A
Given that one chair is taken, i think the remaining 6 dignitaries can be arranged 6!. That is 6*5*4*3*2*1=720.
Answer: A
Question: A man swims downstream 45 km and upstream 25 km taking 5 hours each time, what is the speed of the man in still water?
Options:
A)17
B)24
C)7
D)24
E)20
Rationale: 45--- 5 DS = 9
? ---- 1
25 --- 5 US = 5
? ---- 1 M = ?
M = (9+ 5)/2 = 14/2=7
Answer: C
Answer: C
Question: A person completes half distance of marathon in 20 min including 7 minutes of break time.He runs at 5m/s. Then what is total distance covered if he runs at constant speed and takes only one break in entire marathon.
Options:
A)8km
B)7.8km
C)9km
D)6.1km
E)7km
Rationale: Considering and removing break he runs only for 13 min ie 780 s.So total time =780*2=1560.
Total distance =1560*5=7800m
Thus 7.8km
Answer:B
Answer: B
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan?
Options:
A)288
B)266
C)129
D)300
E)276
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11
=> x
= 300 km
Answer:D
Answer: D
Question: A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
Options:
A)270 m
B)245 m
C)235 m
D)220 m
E)240 m
Rationale: Explanation:
Assume the length of the bridge = x meter
Total distance covered = 130+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (130+x)/30 m/s
=> 45 × (10/36) = (130+x)/30
=> 45 × 10 × 30 /36 = 130+x
=> 45 × 10 × 10 / 12 = 130+x
=> 15 × 10 × 10 / 4 = 130+x
=> 15 × 25 = 130+x = 375
=> x = 375-130 =245
Answer: Option B
Answer: B
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and B leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost?
Options:
A)3 2/3
B)5 2/3
C)6 2/3
D)4 2/3
E)7 2/3
Rationale: x/10 + 2/15 + 4/20 = 1
x = 40/60*10 = 6 2/3
Answer: C
Answer: C
Question: If 4XZ + YW = 5 and XW + YZ = 10, what is the value of the expression (2X + Y)(2Z + W)?
Options:
A)9.
B)12.
C)15.
D)16.
E)25
Rationale: (2x+y)*(2z+w) = 5+2(10) =25
Answer : E
Answer: E
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number Q?
Options:
A)a. 2^96 + 1
B)b. 2^16 - 1
C)c. 2^16 + 1
D)d. 7 * 2^33
E)e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of Q= (a+b) is a factor of (a³ + b³)
Henca A
Answer: A
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 765 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
Options:
A)191
B)192
C)193
D)212
E)213
Rationale: Total movies submitted are 765.
As per question we need to take 1/4 of 765 to be considered for top 10 movies = 191.25
approximate the value we 192.
Answer:option B is the correct answer..
Answer: B