divelab/Sys2Bench huggingface dataset:
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 3 on it exactly once?
Options:
A)18/100
B)1/10
C)11/100
D)19/100
E)1/5
Rationale: Probability = No of balls with exactly one 1 / total number of balls
= {3,13, 23, 30,31, 32, 34 to 39, 43,53,63,73,83,93}/100
= 18/100
Answer is A
Answer: A
Question: A cylindrical can has a radius of 3 centimeters and a height of 24 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
Options:
A)16 pi
B)64 pi
C)96 pi
D)144 pi
E)576 pi
Rationale: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*3*24=144 pi
Answer is D.
Answer: D
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 4 hours. If at 6:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
Options:
A)16:00.
B)18:00.
C)20:00.
D)22:00.
E)24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 4 hours
Time taken by both buses to meet again in St. Louis will be LCM of 3 and 4 = 12
If the buses start at 6:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Answer: B
Question: We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let x be the number of canoes.
Then 2x/3 is the number of kayaks.
12x+(2x/3)*18=504
12x+12x=504
24x=504
x=21 (canoes)
2x/3=14 (kayaks)
There were 21-14 = 7 more canoes rented out.
The answer is C.
Answer: C
Question: Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is:
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: Explanation:
Let first number be x.
So,2nd no. = 4x & 3rd no.=8x.
So,x+4x+8x=78 × 3 = 234.
13x = 234
x = 234/13
Hence,smallest Number x=18.
Answer: A
Answer: A
Question: What is the unit digit in 4^100?
Options:
A)0
B)1
C)6
D)3
E)5
Rationale: Unit digit in 4^100 = unit digit in [(4^4)^25 ]But unit digit in 4^4=6unit digit 4^100= 6Answer is C
Answer: C
Question: A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%
Options:
A)Rs 6.56
B)Rs 9.56
C)Rs 10.56
D)Rs 11.56
E)None of these
Rationale: Explanation:
80 : 5 = 105 : x
x= (5×105/80)
= Rs 6.56
Option A
Answer: A
Question: How many integers from 0 to 53, inclusive, have a remainder of 1 when divided by 3 ?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: My ans is also C.17.
Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 52, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so,52 = 1+(n-1)3
or, (n-1)3 = 51
or, n-1 = 17
or, n = 18
D
Answer: D
Question: How many ways are there to select a subcommittee of 8 members from among a committee of 17?
Options:
A)22888
B)24310
C)28791
D)27711
E)12111
Rationale: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,8)= 24310
Answer: B)
Answer: B
Question: The area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot. What will be the length of the diagonal of the square plot?
Options:
A)100m
B)120m
C)95m
D)80m
E)150m
Rationale: Given that the length of the rectangular field l = 90 m and breadth = b = 80 m.
Then its area lb = 90 x 80 sq.m
We know that the area of square = (1/2)x(diagonal)2
from the given question, we have area of square plot = area of rectangular field
That is, 90 x 80 = 1/2 x diagonal2
diagonal^2 = 2 x 7200 = 14400 = (120)2
diagonal = 120 m.hence B
Answer: B
Question: Which of the following is equal to 5^k*7^(k-1)?
Options:
A)5*35^(k-1)
B)5*35^(k-1)
C)35^k
D)5*35^k )
E)35^(2k-1)
Rationale: 5^k*7^(k-1) = 5*5^(k-1)*7^(k-1) = 5*35^(k-1)
The answer is A.
Answer: A
Question: The ratio of the area of a square to that of the square drawn on its diagonal is
Options:
A)1:2
B)1:0
C)1:7
D)1:5
E)1:6
Rationale: Answer: A) 1:2
Answer: A
Question: If x,y ,and z are positive real numbers such that x+y-z = 62, y-z+x =82 , and z-x+y = 100, then find the x+y+z value?
Options:
A)80
B)91
C)62
D)74
E)82
Rationale: x+y-z = 62, ------1)
y-z+x =82 , ------2)
z-x+y = 100------3)
from (1)&(2)
2z=20
z=10
from (2)&(3)
2y = 182
y=91
then x=62-81= -19
x+y+z = 82
correct option is E
Answer: E
Question: A man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream.
Options:
A)2 km/hr
B)3 km/hr
C)7 km/hr
D)9 km/hr
E)5 km/hr
Rationale: Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=18 or x=9.
Rate upstream=9 km/hr,rate downstream=27 km/hr.
Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.
ANSWER D 9 km/hr
Answer: D
Question: Look at this series: 31, 29, 24, 22, 17, ... What number should come next?
Options:
A)15
B)14
C)13
D)12
E)11
Rationale: Explanation: This is a simple alternating subtraction series, which subtracts 2, then 5.
Answer: Option A
Answer: A
Question: At 3:40, the hour hand and the minute hand of a clock form an angle of
Options:
A)10º
B)75º
C)90º
D)130º
E)180º
Rationale: Hence the angle
=30(40/5-3)-40/2
=30(8-3)-20
=30 X5-20=130 °
Answer D
Answer: D
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
Options:
A)1509
B)1528
C)1500
D)1598
E)1512
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500.Answer:C
Answer: C
Question: A train 75 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)28
B)50
C)88
D)22
E)32
Rationale: Speed of the train relative to man = (75/10) m/sec = (15/2) m/sec. [(15/2) * (18/5)] km/hr = 27 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 27 ==> x
= 32 km/hr.Answer:E
Answer: E
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)22.9
B)10.8
C)17.2
D)21.1
E)12.6
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.Answer: B
Answer: B
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
Options:
A)0
B)8
C)3
D)7
E)1
Rationale: Explanation:
Average of 20 numbers = 0.
Sum of 20 numbers = (0 * 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).
Answer: A
Answer: A
Question: A cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?
Options:
A)4.5 hrs
B)5 hrs
C)6.5 hrs
D)7.25 hrs
E)11.25 hrs
Rationale: Net part filled in 1 hour= 1/5 -1/9= 4/45
Therefore the cistern will be filled in 45/4 hours or 11.25 hours.
ANSWER:E
Answer: E
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 58?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: four wheeler=14*4=56(max)
2 wheel=1
so no of 4 wheeler=14
ANSWER:D
Answer: D
Question: A, B and C start a business each investing 10,000. After 6 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 34,200 was recorded. Find the share of B.
Options:
A)9,600
B)21,200
C)28,200
D)20,500
E)None of these
Rationale: Ratio of the capitals of A, B and C
= 10000 Ã— 6 + 5000 Ã— 6 : 10000 Ã— 6 + 6000 Ã— 6 : 10000 Ã— 6 + 16000 Ã— 6
=90000 : 96000 : 156000 = 90 : 96 : 156
Bâ€™s share = (34200 Ã— 96â„342) = 9600
Answer A
Answer: A
Question: If yesterday was Monday, when will Wednesday be?
Options:
A)The day after tomorrow
B)Two days before today
C)Today
D)Tomorrow
E)none
Rationale: Explanation:
Yesterday was Monday
=>Today is Tuesday
=> Tomorrow is a Wednesday
Answer: Option D
Answer: D
Question: An unbiased die is tossed. Find the probability of getting a multiple of 5
Options:
A)1/4
B)1/6
C)2/5
D)5/6
E)3/7
Rationale: Here S = {1,2,3,4,5,6}
E = event of getting a multiple of 5
E = {5}
P(E) = 1/6
Answer is B
Answer: B
Question: A man can row with a speed of 30 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?
Options:
A)22
B)28
C)20
D)41
E)34
Rationale: M = 30
S = 11
DS = 30 + 11 = 41.Answer:D
Answer: D
Question: The distance from Steve's house to work is 20 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
Options:
A)5.
B)10.
C)14.
D)15.
E)20.
Rationale: Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 20km => Speed = 10kmph
B
Answer: B
Question: At a dinner party, 6 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
Options:
A)5
B)10
C)24
D)32
E)120
Rationale: Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.
Thus if one person's position is fixed, the others can be arranged in 5! =120 ways.
Ans is E.
Answer: E
Question: In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?
Options:
A)33
B)25
C)77
D)28
E)29
Rationale: Explanation:
The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2, 2, 1
b. 3, 1, 1
Case a. Number of ways of achieving the first option 2 - 2 - 1
Two toys out of the 5 can be selected in \inline {\color{Black} 5C_{2}} ways. Another 2 out of the remaining 3 can be selected in \inline {\color{Black} 3C_{2}} ways and the last toy can be selected in \inline {\color{Black} 1C_{1}} way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2
Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways \inline {\color{Black} 5C_{2}\times 3C_{2}}= 15 ways
Case b. Number of ways of achieving the second option 3 - 1 - 1
Three toys out of the 5 can be selected in \inline {\color{Black} 5C_{3}} ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3 - 1 - 1 option is \inline {\color{Black} 5C_{3}} = 10 = 10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
= number of ways of achieving Case a + number of ways of achieving Case b
= 15 + 10 = 25 ways.
Answer: B) 25
Answer: B
Question: The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Options:
A)11.73
B)12
C)13.8
D)14
E)15.87
Rationale: x -> Price without Gratuity
207 = x + 0.15x
=> x = 207/1.15 = 180
So average price per person,excluding the gratuity = 180/15 = 12
The answer is B.
Answer: B
Question: Given that E and F are events such that P(E) = 15, P(F) = 10 and P(E n F) = 15,
find P (E|F) and P(F|E)
Options:
A)3/2
B)4/5
C)6/2
D)8/5
E)8/9
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 15/5 = 1
P(F|E) = P(EnF)/P(E) = 15/10 = 3/2.
A)
Answer: A
Question: Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 52 yr. How old is E?
Options:
A)25 yr
B)62 yr
C)45yr
D)64 yr
E)NOne
Rationale: Solution:
Total present age of A, B, C and D,
= (45*4)+(4*5) = 200 yr;
Total age present age of A, B, C, D and E,
= 52*5 = 262 yr.
So, age of E = 62 yr.
Answer: Option B
Answer: B
Question: Kevin plants corn and cotton. Once he harvests the crops, he has 30 pounds of corn and x
pounds of cotton. Corn sells for $5 per pound and cotton sells for $10 per pound. If Kevin sells
all his corn and cotton for a total of $640, then compute x.
Options:
A)39
B)49
C)59
D)69
E)79
Rationale: Kevin sells his corn for 305 dollars and his cotton for x10 dollars. Thus 30-5+x*10 =
640, so x = 640-30*5/10 = 490/10 = 49 .
correct answer B
Answer: B
Question: A batsman in his 9th inning makes a score of 75 and their by increasing his average by 7. What is his average after the 9th inning?
Options:
A)12
B)19
C)26
D)33
E)40
Rationale: 8x + 75 = 9(x + 7)
x = 12 + 7 = 19
Answer:B
Answer: B
Question: P runs 20% faster than Q so P gives Q a 300 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?
Options:
A)1500
B)1600
C)1700
D)1800
E)1900
Rationale: Let D be the race distance that P ran.
Let T be the time it took to complete the race.
Let V be Q's speed.
T = D/1.2V = (D-300) / V
D=1.2D-360
0.2D=360
D=1800 meters.
The answer is D.
Answer: D
Question: How many positive integers between 1 and 100 are there such that they are multiples of 13?
Options:
A)6
B)5
C)4
D)7
E)3
Rationale: Multiples of 13 = 13,26,39,-----91
Number of multiples of 13 => 13*7= 91
Answer is D
Answer: D
Question: Of the 75 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department?
Options:
A)15
B)20
C)30
D)40
E)50
Rationale: This is ratio problem solving question.
I will prefer to use RMV box.
R M V
Sales 2 25 50
Other 1 25 25
Total 3 25 75
Answer is 50. i.e E
Answer: E
Question: Which is the following is divisible by 11
Options:
A)A)3052
B)B)4825
C)C)4805
D)D)4905
E)E)4906
Rationale: Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 8 natural numbers = 7(7+ 1)//2 = 7 x 4 = 28
Sum of first 88 natural numbers = 77(77 + 1)//2 = 77 x 40 = 3080
3080 - 28= 3052
Answer: Option A
Answer: A
Question: In how many different number of ways a combination of 3 men and 2 children can be selected from 6 men and 5 children ?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: 6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
A)
Answer: A
Question: If A,B,C are three integers and AB+C is even ; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even
Options:
A)Only C
B)Both A and B
C)Both B and C
D)All of them
E)None of them
Rationale: Case 1:-
AB+C= Even
E+E= E
O*E + E= E
E*O +E= E
Case 2:-
AB+C= Even
O+O= E
O*O +O= E
A)A+C is even- Only possible with Case 2
B)B+C is even- Only Possible with Case 2
C)ABC is even- Only Possible with case 1
No option is 'MUST BE TRUE'
E is the answer
Answer: E
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?
Options:
A)1 : 2
B)2 : 3
C)2 : 5
D)3 : 5
E)3 : 7
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
Answer: A
Question: Ayesha's father was 28 years of age when she was born while her mother was 15 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)12 years
B)17 years
C)16 years
D)18 years
E)10 years
Rationale: Explanation:
Mother's age when Ayesha's brother was born = 15 years.
Father's age when Ayesha's brother was born = (28 + 4) years = 32 years.
Required difference = (32 - 15) years = 17 years.
Answer: B
Answer: B
Question: Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time ,the rate of interest being the same ?
Options:
A)Rs. 10
B)Rs. 10.40
C)Rs. 15.20
D)Rs. 13
E)None of these
Rationale: Solution
S.I. on Rs. (260-20) for a given time =Rs. 7.34.
S.I. on Rs. 240 for half the time = Rs.10.
T.D. on Rs. 250 = Rs. 10.
∴ T.D. on Rs. 260 = Rs. ( 10/250 x260 ) = Rs. 10.40.
Answer B
Answer: B
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was
Options:
A)13years
B)14years
C)15years
D)16years
E)17years
Rationale: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
D)
Answer: D
Question: An article is bought for Rs.675 and sold for Rs.1200, find the gain percent?
Options:
A)87%
B)88%
C)78%
D)75%
E)73%
Rationale: 675 ---- 525
100 ---- ? =>
=78%
Answer:C
Answer: C
Question: Working in a North Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
Options:
A) 3 and 1/3 weeks
B) 3 weeks
C) 2 and 1/2 weeks
D) 2 and 1/3 weeks
E) 2 weeks
Rationale: VERITAS PREPOFFICIAL SOLUTION:
Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:
Working in a North Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.
Rate (K) = 1 album / 5 weeks
Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.
Rate (C) = 1 album / x weeks
If the two emcees work together…
I’m adding these rates, so their combined rate is 1/5 + 1/x
…they can drop a full-length platinum compilation LP in 2 weeks.
And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2
Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
I’m using that equation to solve for Common’s time, so I’m solving for x.
Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:
1/5 + 1/x = 1/2, so let’s get the x term on its own:
1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:
1/x = 5/10 – 2/10
1/x = 3/10, and from here you have options but let’s cross multiply:
10 = 3x, so divide both sides by 3 to get x alone:
10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice A.
Answer: A
Question: One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?
Options:
A)10 km
B)12 km
C)16 km
D)17 km
E)18 km
Rationale: Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9
4 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
C
Answer: C
Question: Which number can we add to 425897 to get a number exactly divisible by 456?
Options:
A)3
B)5
C)7
D)9
E)11
Rationale: 425897 / 456 = 933 with a remainder of 449.
We need to add 456 - 449 = 7
The answer is C.
Answer: C
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'U', then how many triangles can be determined with the 15 points that contain the point U?
Options:
A)182
B)105
C)185
D)210
E)455
Rationale: Fist point is U which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=A
Answer: A
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 750 m long?
Options:
A)78sec
B)83sec
C)95sec
D)99sec
E)100sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 750)/10 = 99 sec.
Answer:D
Answer: D
Question: If x is a positive integer such that (x-1)(x-3)(x-5)....(x-93) < 0, how many values can x take?
Options:
A)47
B)23
C)46
D)21
E)22
Rationale: Solution
If x takes any value greater than 93, the expression will definitely be positive.
Therefore, the set of values that x takes should be from the set of positive integers upto 93
The expression(x-1)(x-3)(x-5)....(x-93) has a total of 47 terms.
When x = 1, 3, 5,7 ....93 the value of the express will be zero. i.e., for odd values of x, the expression will be zero.
We need to evaluate whether the expression will be negative for all even numbers upto 93
Let x = 2; first term (x-1) > 0; remaining 46 terms < 0.
The product of one positive number and 46 negative numbers will be positive (product of even number of negative terms will be positive).
So, x = 2 does not satisfy the condition.
Let x = 4; (x-1) and (x-3) are positive; the remaining 45 terms < 0.
The product of two positive numbers and 45 negative numbers will be negative. So, x = 4 satisfies the condition.
Let x = 6; first 3 terms (x-1), (x-3), and (x-5) are positive and the remaining 44 terms are negative.
Their product > 0. So, x = 6 does not satisfy the condition.
Let x = 8; first 4 terms positive; remaining 43 terms < 0. Their product < 0. x = 8 satisfies the condition.
Extrapolating what we have oberved with these 4 terms, we could see a pattern.
The expression takes negative values when x = 4, 8, 12, 16 ..... 92 (multiples of 4)
92, the last value that x can take is the 23rd multiple of 4. Hence, number of such values of x = 23
Answer B
Answer: B
Question: Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station?
Options:
A)A)9KM
B)B)6.66KM
C)C)7.25KM
D)D)12.40KM
E)E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point E and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point E and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: B