divelab/Sys2Bench huggingface dataset:
Question: Two persons start running simultaneously around a circular track of length 700 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)63
B)10
C)28
D)27
E)12
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 700 / (15 + 25)5/18 = 700* 18 / 40 * 5 = 63 seconds.
Answer: A
Answer: A
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $105, how much more remains to be paid?
Options:
A)$945
B)$965
C)$1025
D)$1050
E)$1105
Rationale: 90% remains to be paid so the remaining amount is 9*105=$945.
The answer is A.
Answer: A
Question: TATA company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
Options:
A) 3,024
B) 4,536
C) 5,040
D) 9,000
E) 10,000
Rationale: TATA company plans to assign identification numbers to its employeeS.The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.
Total = 9*9*8*7 = something with the units digit if 6.
Answer: B.
Answer: B
Question: A first grade teacher uses eight cards, each numbered from 1 to 8, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
Options:
A)70
B)15
C)60
D)45
E)33
Rationale: problem of combination 6C4 = 6!/4!*(6-4)! = 6*5*4!/4!*2! =15
B
Answer: B
Question: How much is 60% of 40 is greater than 4/5 of 25?
Options:
A)4
B)6
C)10
D)8
E)13
Rationale: 60/100) * 40 â€“ (4/5) * 25
24 - 20 = 4
Answer: A
Answer: A
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
Options:
A)10 days
B)5 days
C)6 days
D)24 days
E)18 days
Rationale: Explanation:
B = 1/8 – 1/2 = 1/24 => 24 days
Answer D
Answer: D
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Qâ€™s amount. At the end of the year 32% profit was earned which was equal to 98,000. What was the amount invested by R?
Options:
A)2,10,000
B)1,05,000
C)1,75,000
D)Data inadequate
E)65625
Rationale: Ratio for amount invested by P, Q & R
= 5x Ã— 12 : 6x Ã— 12 : 6x Ã— 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 32% of T
where, T = Total amount
T = 306250
Amount received by
R = 3x /3x+6x+5x(306250)
= 65625
Answer E
Answer: E
Question: Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?
Options:
A)4800
B)6400
C)2280
D)3400
E)3490
Rationale: B
6400
Let the sum invested in Scheme A be x and that in Scheme B be (13900 - x).
Then, (x x 14 x 2)/100 + ((13900 - x) x 11 x 2)/100 = 3508
28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = (13900 - 7500) = 6400.
Answer: B
Question: If P is a prime number greater than 7, what is the remainder when P^2 is divided by 8.
Options:
A)4
B)3
C)1
D)2
E)Cannot be determined
Rationale: take square of any prime number
remainder will be 1
Ans C
Answer: C
Question: For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.35 – 6.35*?
Options:
A)0.35
B)0.5
C)6.25
D)0.25
E)6.0
Rationale: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.35* =6 (the greatest positive even integer less than or equal to 6.35 is 6).
Hence, 6.35 – 6.35* = 6.35 - 6 = 0.35
Answer: A.
Answer: A
Question: Margaret is 9 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages
Options:
A)21yrs
B)20yrs
C)30yrs
D)40yrs
E)50yrs
Rationale: Let, age of son x=12
Margaret is 9 years more than twice the age of his son, y = 9+2(x)
=9+2(12)
=9+24
=33yrs
Difference = 33 - 12
=21yrs
ANSWER:A
Answer: A
Question: The total marks obtained by a student in Mathematics and Physics is 70 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
Options:
A)40
B)45
C)27
D)28
E)22
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 70 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (70 + 20) / 2 = 45.Answer:B
Answer: B
Question: There are 4 people who has to cross a stretch of 300 km. They normally run at a speed of 10 kmph. One of them has a bike that travels at 50 kmph. The bike first takes one person alone and crosses the stretch while the other two keep running. Then he comes back without wasting time and picks up from the way, drives him across the stretch, and does the same for the last person. How long does this whole process take?
Options:
A)24 hrs
B)16 hrs
C)56/3 hrs
D)58/3 hrs
E)48/3 hrs
Rationale: Time taken to carry 2nd person = 300/50 = 6 hrs.
Time taken to meet 3rd person =(300-6*10)/(50+10) = 4 hrs
Time taken to carry 3rd person = 4 hours
Time taken to meet 4th person = (300 –140)/60 = 8/3
Total time = 6+4+4+8/3+8/3 = 58/3 hours
ANSWER:D
Answer: D
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
Options:
A)8 1/7
B)8 1/1
C)8 1/4
D)8 1/2
E)8 3/7
Rationale: 3/12 + (3 + x)/15 = 1
x = 8 1/4
Answer: C
Answer: C
Question: A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $340 million, approximately what was the percent increase in sales?
Options:
A)2%
B)17%
C)20%
D)65%
E)13%
Rationale: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 385 million
February sales last year = 340 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 385 million and the old value = 340 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(385 – 340)/340] x 100
65/340 x 100
≈ 13%.
The answer is E.
Answer: E
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
Options:
A)3 days
B)4 days
C)6 days
D)7 days
E)8 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself
A)
Answer: A
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations W of soloists can appear in the liner notes?
Options:
A)5!
B)10!/(5!5!)
C)10!/5!
D)10!
E)10!*5!
Rationale: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations W of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Answer: B
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 45% are drinking beer, 30% are drinking mixed drinks, and 25% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
Options:
A)2/5
B)4/7
C)11/18
D)17/24
E)17/10
Rationale: Suppose there are 100 students
Group A : 40% = 40 students
45% drink beer = 18
30% mixed = 12
25% both = 10
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 18+18 =36 and both = 20
thus 22/36 = 11/18
Hence C
Answer: C
Question: Two employees X and Y are paid a total of Rs. 770 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)s.150
B)s.200
C)s.250
D)s.350
E)s.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 770
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 770
â‡’ y[12/10 + 1] = 770
â‡’ 22y/10 = 770
â‡’ 22y = 7700
â‡’ y = 700/22 = 700/2 = Rs.350
D)
Answer: D
Question: How many arrangements of the letters of the word ORANGES can be made, without changing the place of the vowels in the word?
Options:
A)22
B)29
C)24
D)28
E)30
Rationale: O,A,E fixed. Consonants can be arrangements in 4P4 = 4! = 24 ways
Option 'C'
Answer: C
Question: A single discount % equal to three successive discounts of 30%, 20% and 10%.
Options:
A)49.8
B)49.5
C)49.3
D)49.6
E)49.1
Rationale: Explanation:
Let the initial price be 100.
30% discount on 100 is 30
(100 – 30) = 70
20% discount on the 70 is 14
(70 – 14) = 56
10%discount on the 56 is 5.6
So the answer is 30 + 14 + 5.6 = 49.6
Answer: D
Answer: D
Question: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?
Options:
A)30 days
B)40 days
C)50 days
D)60 days
E)70 days
Rationale: Explanation:
Let 1 man's 1 day work = x
and 1 woman's 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]
10 women 1 day work = 10/400 = 1/40
10 women will finish the work in 40 days
Option B
Answer: B
Question: A cube is divided into 64 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
Options:
A)12
B)16
C)20
D)24
E)30
Rationale: Each side of the cube has 4 x 4 = 16 cubelets.
Only the interior cubelets are painted one colour.
On each side, 2 x 2 = 4 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*4 = 24
The answer is D.
Answer: D
Question: In a college the ratio of the numbers of boys to the girls is 5:7. If there are 140 girls, the total number of students in the college is?
Options:
A)200
B)240
C)160
D)250
E)310
Rationale: Let the number of boys and girls be 5x and 7x
Then , 7x = 140
x= 20
Total number of students = 12x = 12*20 = 240
Answer is B
Answer: B
Question: 32 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
Options:
A)2√2
B)2√5
C)5
D)4√2
E)8
Rationale: Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 32
=> x/360*2*pi*r +2r= 32
=> 2A/r+2r=32
=> A= r16-r^2
= r16-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 16-2r=0
r=8
E
Answer: E
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 240 meters long
Options:
A)6 ½ sec
B)7 ½ sec
C)12 sec
D)8 ½ sec
E)9 sec
Rationale: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (200 + 240) m = 440 m.
Time taken =440×(3/110) sec =12 sec
Answer: Option C
Answer: C
Question: It takes 2 workers a total of 12 hours to build a giant machine with each worker working at the same rate. If 3 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 2:00 PM, at what time will the machine be complete?
Options:
A)4:30
B)4:45
C)5:00
D)5:15
E)5:30
Rationale: 2 workers build 1/12 of a machine in one hour.
1 worker builds 1/24 of a machine in one hour.
In the first 3 hours, 3 workers build 3*(1/24)*3=9/24 of a machine
From 2:00 to 3:00, 4 workers build another 4/24. The total is 13/24.
From 3:00 to 4:00, 5 workers build another 5/24. The total is 18/24.
From 4:00 to 5:00, 6 workers build another 6/24. The total is 24/24.
The machine is complete at 5:00.
The answer is C.
Answer: C
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
Options:
A)420
B)776
C)288
D)268
E)198
Rationale: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer:B
Answer: B
Question: The distance between West-Town to East-Town is 10 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
Options:
A)3.
B)8.
C)10.
D)12.
E)15.
Rationale: Time taken by the birds to meet = 10/(4 + 1) = 2 mins
Distance traveled by the bird traveling from West-Town = 4 * 2 = 8
Answer: B
Answer: B
Question: A vessel of capacity 2 litre has 16% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
Options:
A)31%.
B)71%.
C)49%.
D)27.2%.
E)51%.
Rationale: 16% of 2 litres = 0.32 litres
40% of 6 litres = 2.4 litres
Therefore, total quantity of alcohol is 2.72 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 27.2%
ANSWER:D
Answer: D
Question: 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
Options:
A)1:2
B)1:3
C)2:1
D)2:3
E)None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 5x + 2y = 4(x+y)
=> x = 2y
=> x/y = 2/1
=> x:y = 2:1
Option C
Answer: C
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:5
B)3:4
C)3:1
D)3:2
E)3:9
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4
Answer:B
Answer: B
Question: A group of ants, each 1/3 centimeters in length, crosses a sidewalk in single file, each right behind the next, at a speed of 30 cm/min. If the sidewalk is 1.5 meters wide, how long does it take for 30 ants to all make it across?
Options:
A)2 min
B)3 min
C)4 min
D)5 min
E)6 min
Rationale: E
6 min
d = 30 * 1/3 cm + 150 cm = 180 cm
T = 180 cm / 30 cm/min = 6 min
Answer: E
Question: In a certain match all the teams were to play with each other. If there are 7 teams, how many matches will have to be played?
Options:
A)40
B)21
C)24
D)25
E)None of the above
Rationale: 7c2
=21
ANSWER:B
Answer: B
Question: How many possible integer values are there for x if |5x - 3| < 6 ?
Options:
A)One
B)Two
C)Three
D)Four
E)Five
Rationale: Solution: |5x-3| < 6
let 5x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =5x ==> -3<5x<9
dividing all values by +4 we have -0.6<x < 1.8
Now question says Integer values (not rational ) therefore we have 0,1
Hence 2 B
Answer: B
Question: The number 523dbc is divisible by 7,8,9. Then what is the value of d*b*c
Options:
A)504
B)532
C)210
D)180
E)280
Rationale: LCM of 7, 8 and 9 is 504, thus 523dbc must be divisible by 504.
523dbc=523000+dbc
523000 divided by 504 gives a remainder of 352.
Hence, 352+dbc=k*504.
k=1 dbc=152 --> d*b*c=10
k=2 dbc=656 --> d*b*c=180
As dbc is three digit number k can not be more than 2.
Two answers? Well only one is listed in answer choices, so D.
Answer: D.
Answer: D
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)2655
B)3527
C)2500
D)2567
E)2571
Rationale: A:B:C = 2/3:1/6:1/6
= 4:1:1
x * 2/100 * 2/3
= 200
B capital = 15000*1/6
= 2500
Answer: C
Answer: C
Question: A company D has 15 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have?
Options:
A)200
B)125
C)180
D)152
E)250
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 45%
% of of employees other than secretaries and salespeople = 100 - 60 = 40%
But this number is given as 50
so 40% of x = 50
x = 125
Therefore there a total of 125 employees in the company D
Correct answer - B
Answer: B
Question: If m is a positive integer and m^2 is divisible by 33, then the largest positive integer that must divide m is?
Options:
A) 3
B) 6
C) 8
D) 11
E) 16
Rationale: M^2 is divisible by 33 so M^2 must be multiple of 48.
If the value of M is Multiples of 11 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is D but if M = 33 then answer should be 16.
Is the question right? Or am i missing some thing?
D
Answer: D
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?
Options:
A)72
B)80
C)120
D)150
E)100
Rationale: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 48 + 2/3 of 48
80/100x = 80
x = 100.
Answer: Option E
Answer: E
Question: In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?
Options:
A)3:1
B)3:5
C)7:8
D)7:9
E)9:11
Rationale: First mixture: milk and water in the ratio of 3x:4x.
Second mixture: milk and water in the ratio 5y:2y.
We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3.
Answer: A.
Answer: A
Question: A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2hours30minutes to cover a distance of 5km upstream. find the speed of the river current in km/hr.
Options:
A)1 km/hr
B)2 km/hr
C)3 km/hr
D)4 km/hr
E)5 km/hr
Rationale: rate downstream=(15/3 Â¾)km/hr=(15*4/15)km/hr=4km/hr.
Rate upstream=(5/2 Â½)km/hr=(5*2/5)km/hr=2km/hr.
Speed of current=1/2(4-2)km/hr=1km/hr
ANSWER A
Answer: A
Question: Two numbers are respectively 17% and 30% more than a third number. The percentage that is first of the second is?
Options:
A)75%
B)80%
C)85%
D)70%
E)90%
Rationale: I II III
117 130 100
130----------117
100-----------? => 90%
Answer:E
Answer: E
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1:2:3. If there are Rs. 30 in all, how many 5 p coins are there?
Options:
A)176
B)167
C)150
D)717
E)154
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x and 3x respectively.
Then, sum of their values
= [25x/100 + (10 * 2x)/100 + (5 * 3x)/100]
= Rs. 60x/100
60x/100 = 30 => x = 50.
Hence, the number of 5 p coins = 3 * 50 = 150.
Answer:C
Answer: C
Question: In one hour, a boat goes 8 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)3 km/hr
B)4 km/hr
C)5 km/hr
D)6 km/hr
E)8 km/hr
Rationale: Upstream relative speed is u + v=8km/hr
Downstream speed is u-v = 2
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =8+2
2u=10
Finally, u=5.
ANSWER : C
Answer: C
Question: Find the value of b from (15)^2 x 9^2 Ã· 356 = b.
Options:
A)53.2
B)52.2
C)51.2
D)8.2
E)54.2
Rationale: Given Exp. =(15)^2 x 9^2 Ã· 356= b
= 225 x 81 Ã· 356
= 51.2
C
Answer: C
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 4:3:2. If there are in all Rs.42, the number of one rupee coins is?
Options:
A)22
B)26
C)18
D)16
E)24
Rationale: 4x 3x 2x
50 25 100
200x + 75x + 200x = 3800
475x = 3800
x = 8 => 2x = 16
Answer: D
Answer: D
Question: A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?
Options:
A)3000
B)Rs. 4056
C)5000
D)5400
E)5600
Rationale: Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
Answer: B
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
Options:
A)176
B)186
C)150
D)179
E)172
Rationale: 1/2 * 15 * 20
= 150
Answer:C
Answer: C
Question: Which of the following is divisible by the first ten positive integer multiples of 11?
(i) 18810
(ii) 263640
(iii) 3011010
Options:
A)None
B)ii only
C)i and ii only
D)i and iii only
E)ii and iii only
Rationale: A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 8*9*5*7*11.
8*9*5*7*11 is less than 70*30*10=21000, (i) cannot possibly be divisible by 8*9*5*7*11.
The integers of 3011010 sum to 6, so 3011010 is divisible by 3, but not 9, so (iii) is not divisible by 8*9*5*7*11.
If (ii) is divisible by 8*9*5*7*11 then 26364 is divisible by 11. So 26364=11y=10y+y for some positive integer y. y must have initial digit 2 and final digit 4. Final and third digit of y must add to 6, so third digit of y is 2. Then similarly, second and third digit add to three, so second digit is 1. But then second and first digit must sum to 6, but first digit is 2, second is 1, so (ii) cannot be divisible by 11.
Answer A
Answer: A
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 70 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
Options:
A)42
B)18
C)20
D)24
E)30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 70 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 70 / 10 = 7 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 7 = 42 kms... Answer - A
Answer: A
Question: A train 100 meters long completely crosses a 300 meters long bridge in 15 seconds. What is the speed of the train is?
Options:
A)32 kmph
B)96 kmph
C)34 kmph
D)43 kmph
E)40 kmph
Rationale: S = (100 + 300)/45
= 400/15 * 18/5
= 96
Answer:B
Answer: B