divelab/Sys2Bench huggingface dataset:
Question: Ram will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
Options:
A)5
B)6
C)9
D)24
E)26
Rationale: Ram will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: A
Question: If w/x = 2/3 and w/y = 3/5, then (x + y)/y =
Options:
A)4/5
B)9/10
C)7/5
D)8/5
E)9/5
Rationale: W/X = 2/3x=>x=3/2w and W/Y = 3/5=>y=5/3w
(X+Y)/Y = (3/2w+5/3w)/(5/3x)=9/10
Correct Option: B
Answer: B
Question: A train 100 m long crosses a platform 125 m long in 10 sec; find the speed of the train?
Options:
A)81
B)77
C)54
D)33
E)99
Rationale: D = 100 + 125 = 225
T = 10
S = 225/10 * 18/5 = 81 kmph
Answer: A
Answer: A
Question: There are 7 non-collinear points. How many triangles can be drawn by joining these points?
Options:
A)22
B)38
C)35
D)29
E)18
Rationale: Explanation:
A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points
The number of triangles formed = \inline {\color{Black} 7C_{3}} = 35
Answer: C) 35
Answer: C
Question: In how many different number of ways 3 boys and 2 girls can sit on a bench?
Options:
A)720
B)730
C)740
D)750
E)120
Rationale: npn = n!
5p5 = 5 × 4 × 3 × 2 × 1 = 120
E
Answer: E
Question: 15, 31, 63, 127, 255, ?
Options:
A)513
B)511
C)523
D)517
E)527
Rationale: Each number is double of the preceding one plus 1.
Answer : B.
Answer: B
Question: The average of 20, 30 and 130 is twice the average of 10, 30, and which of the following ?
Options:
A)1)10
B)2)50
C)3)60
D)4)90
E)5)180
Rationale: 20 30 130 = 130+50 = 180/3 = 60
60/2 = 30
10 30 x = 40+x/3 should be smaller than 30
cross multiply 30*3-40 = 50
B
Answer: B
Question: The jogging track in a sports complex is 594 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
Options:
A)5.29 min
B)4.32 min
C)5.08 min
D)9.28 min
E)5.988 min
Rationale: Clearly, the two will meet when they are 594 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 594 m apart, they take (100/825 * 594/1000) hrs = (594/8250 * 60) min = 4.32 min.
Answer: B
Answer: B
Question: A couple decides to have 2 children. If they succeed in having 2 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 1 girl and 1 boy?
Options:
A)1/2
B)3/4
C)1
D)2
E)3
Rationale: Sample space = 2^2 = 4.
Favourable events = {bg}, {gb},
Probability = 2/4 = 1/2.
Ans (A).
Answer: A
Question: Kanul spent $3000 in buying raw materials, $2000 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
Options:
A)$5555.555
B)$5543.22
C)$5568.000
D)$5366.521
E)$5365.66
Rationale: Let the total amount be x
then, (100-10)% of x = 3000+2000
90% of x = 5000
90x/100 = 5000
x = $50000/9
x = $5555.555
Answer is A
Answer: A
Question: If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is?
Options:
A)250 m
B)112 m
C)117 m
D)125 m
E)123 m
Rationale: A
A = 180 * 5/18 * 5 = 250 m
Answer: A
Question: A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 92, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Options:
A)80
B)75
C)76
D)77
E)78
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 92 + 77*5x) = 260x+552x+385x = 1197x
total number of students = 15x
average = 1197x/15x = 80
A is the answer
Answer: A
Question: 4524 - ? = 2456
Options:
A)2058
B)2069
C)2072
D)2089
E)None of these
Rationale: Explanation:
None of these
Answer: Option E
Answer: E
Question: The average of first ten prime numbers which are odd is?
Options:
A)15.5
B)15.7
C)15.2
D)15.8
E)15.1
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer:D
Answer: D
Question: Matt gets a $1,300 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let, Average Commission = x
No. of items sold = y
Total Commission = xy
New Commission = xy+1300
New Average = (xy+1300) / (y+1) = 150+x
i.e. (xy+1300) = (y+1)* (150+x)
i.e. (xy+1300) = (xy+x+150y+150)
i.e. (1150) = (x+150y)
New Commission = 400 = 150+x
i.e. x=250
i.e. y = 6
New Sales = y+1 = 7
Answer: option D
Answer: D
Question: Solve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346
Options:
A)If x>y
B)If x>=y
C)If x < y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=+5,-5 and Y= +5,-5
Comparing, we get X=Y, XY.
Therefore, no relationship can be established between X and Y.
E
Answer: E
Question: In a certain sequence, the first term is 2, and each successive term is 3 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
Options:
A)360/109
B)421/113
C)488/135
D)584/189
E)821/165
Rationale: let five terms in the sequence be a,b,c,d,e
a=3
b= 3+1/3=10/3
c=3+3/10= 33/10
d= 3+10/33 = 109/33
e= 3+33/109 = 360/109
hence answer should be A.
Answer: A
Question: In how many ways can 7 different object be divided among three persons so that either one or two of them do not get any object?
Options:
A)351
B)361
C)371
D)391
E)381
Rationale: Case 1: Two guys don't get anything. All items go to 1 person. Hence, 3 ways.
Case 2: 1 guy doesn't get anything. Division of 7 items among 2 guys. Lets say they are called A & B.
a) A gets 6. B gets 1. 7 ways.
b) A gets 5. B gets 2. 21 ways.
c) A gets 4. B gets 3. 35 ways.
d) A gets 3. B gets 4. 35 ways.
e) A gets 2. B gets 5. 21 ways.
f) A gets 1. B gets 6. 7 ways.
Total = 126 ways to divide 7 items between A & B.
Total number of ways for case 2 = 126*3 = 378 (Either A, or B, or C don't get anything).
Answer = Case 1 + Case 2 = 3 + 378 = 381
ANSWER:E
Answer: E
Question: A man rows his boat 90 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)5 kmph
B)7 kmph
C)9 kmph
D)8 kmph
E)1 kmph
Rationale: Speed downstream = d/t = 90/(2 1/2) = 36 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (36 - 18)/2 = 9 kmph
Answer:C
Answer: C
Question: Two angles of a triangle have ratio 7:3, and their difference equals the third angle. What is the smallest angle, in degrees, of the triangle?
Options:
A)90/7
B)150/7
C)270/7
D)300/7
E)350/7
Rationale: The angles of the triangle are 7x, 3x, and (7x-3x)=4x for some value x (due to the ratio) [note that 3x is the smallest angle]
the angles of a triangle add up to 180, so
7x+3x+4x=180
14x=180
x=180/14
x=90/7
the smallest angle is 3x so 3*(90/7) = 270/7
C
Answer: C
Question: At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
Options:
A)12 years
B)15 years
C)19 and half
D)21 years
E)22 years
Rationale: Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26 4x = 20
x = 5.
Deepak's age = 3x = 15 years. Answer: Option B
Answer: B
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $250. What is the share of Rahul?
Options:
A)$50
B)$40
C)$60
D)$100
E)$90
Rationale: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 250*2/5 = $100
Answer is D
Answer: D
Question: The H.C.F. of two numbers is 42 and the other two factors of their L.C.M. are 12 and 14. The larger of the two numbers is:
Options:
A)588
B)642
C)567
D)344
E)789
Rationale: Explanation:
Clearly, the numbers are (42 x 12) and (42 x 14).
{\color{Blue} \therefore } Larger number = (42 x 14) = 588.
Answer: A) 588
Answer: A
Question: Square OCAB has an area of 9 square units. Point O is found where the axes meet. What are the coordinates of point A?
Options:
A)(3, 1)
B)(3, 2)
C)(3, 3)
D)(3, 4)
E)None
Rationale: Solution:
If the square has an area of 9 square units, then its side has a length of 3 units. If O is where the axes meet, then points C and B are found on the x- and y-axes and they have the coordinates (3, 0) and (0, 3). Point A is at 3 units from the x-axis and at 3 units from the y-axis and it has the coordinates (3, 3).
Answer C
Answer: C
Question: Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 20kmph and Prasanna moves southward at a speed of 30 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
Options:
A)11
B)50
C)28
D)27
E)18
Rationale: Explanation:
We know 60 min = 1 hr
Total northward Laxmi's distance = 20kmph x 1hr = 20 km
Total southward Prasanna's distance = 30kmph x 1hr = 30 km
Total distance between Prasanna and Laxmi is = 20 + 30 = 50 km.
Answer: B
Answer: B
Question: If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many Q digits does this integer consists of?
Options:
A)150
B)339
C)342
D)359
E)362
Rationale: Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer Q= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
Answer: C
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 100000. If the profit at the end of a year is Rs. 108000, then the share of B is?
Options:
A)40000
B)50000
C)70000
D)60000
E)80000
Rationale: Ratio of investments of A and B is (70000 * 12) : (100000 * 6) = 7 : 20
Total profit = Rs. 108000
Share of B = 20/27 (108000) = Rs. 80000
Answer: E
Answer: E
Question: Insert the missing number.
3, 4, 6, 8, 9, 12, 12, 16, 15, (....)
Options:
A)18
B)19
C)20
D)25
E)22
Rationale: Explanation:
There are two series, beginning respectively with 3 and 4. In one 3 is added and in another 4 is added.
The next number is 16 +4 = 20.
Answer: C) 20
Answer: C
Question: One year ago, the ratio of Roonie’s and Ronaldo’s age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Ronaldo ?
Options:
A)32
B)33
C)34
D)35
E)36
Rationale: 7(x-1)=6(y-1)=> 7x-6y-1=0 ----eq1
8(x+4)=7(y+4)=> 8x-7y+4=0 ----eq2
on solving eq1 n eq2
y=36
ANSWER:E
Answer: E
Question: A plane moves from a place 9N 40E to a place 9N 40W taking 8 hours to travel. If the plane had left at 10.00 a.m. then what is the local time of arrival at the destination?
Options:
A)11.40 p.m.
B)12.40 p.m.
C)1.40 p.m.
D)2.40 p.m.
E)4.40 p.m.
Rationale: Time difference between places will be 4*(40+40) minutes = 320 min =
5 hrs 20 min
as change of 1 degree in longitude cause change of 4 minutes in time.
and that change is 80 degrees here.
so when plane land. time will be = 10.00 + 8.00 -5.20 = 12.40 p.m.
ANSWER:B
Answer: B
Question: An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 3 ?
Options:
A)1/9
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: n(n+2) to be divisible by 3 either n or n+2 must be a multiples of 3.
In each following group of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, ..., {97, 98, 99} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3} n can be: 1, or 3. Thus, the overall probability is 2/3.
Answer: D.
Answer: D
Question: On a certain road 12% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
Options:
A)10.5%
B)12.5%
C)15%
D)22%
E)30%
Rationale: Answer is C.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 12%+0,2X
id est X = 15%
Answer: C
Question: Set R has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
Options:
A){18, 20}
B){8, 10}
C){28, 38}
D){6, 10}
E){5, 10}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 9,the values (8,10) are closer than others.
Hence Answer : B
Answer: B
Question: If a2 - b2 = 9 and a*b = 4, find a4 + b4.
Options:
A)32
B)90
C)113
D)92
E)81
Rationale: a2 - b2 = 9 : given
a4 + b4 - 2a2b2 = 92 : square both sides and expand.
a*b = 4 : given
a2b2 = 42 : square both sides.
a4 + b4 - 2(16) = 81 : substitute
a4 + b4 = 113
correct answer C
Answer: C
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 750 responses are needed, what is the minimum number of questionnaires that should be mailed?
Options:
A)1160
B)1190
C)1220
D)1250
E)1280
Rationale: Let x be the minimum number of questionnaires to be mailed.
0.6x = 750
x = 1250
The answer is D.
Answer: D
Question: Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
Options:
A)66
B)70
C)72
D)75
E)78
Rationale: Let the distance one way be x
Time from home to work = x/60
Time from work to home = x/100
Total time = 2 hrs
(x/60) + (x/100)= 2
Solving for x, we get x = 75
Time from home to work in minutes= (75)*60/60 = 75 minutes
Ans= D
Answer: D
Question: Line J has a y-intercept of 8 and passes through point (a,b). What is the slope of Line J in terms of a and b?
Options:
A)(a−6)/b
B)(b-8)/a
C)(6−a)/b
D)(6−b)/a
E)(b−6)/a
Rationale: You know that the line goes through point (a,b) and the y-intercept of 8 tells you that the line also goes through point (0,8).
slope m = (y-y1)/(x-x1) = (b-8)/(a-0)= (b-8)/a
B
Answer: B
Question: Jancy had 100 currency notes in all, some of which are of Rs 70 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 50?
Options:
A)103
B)102
C)100
D)105
E)106
Rationale: Let the number of 50-rupee notes = x
Then, the number of 70-rupee notes = (100 – x)
50x + 70(100 – x) = 5000 : x = 100
ANSWER:C
Answer: C
Question: A reduction of 10% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Options:
A)1.1
B)2.2
C)2.5
D)2.1
E)2.9
Rationale: 100*(10/100) = 10 --- 10
? --- 1 => Rs.1
100 --- 90
? --- 1 => Rs.1.1
Answer: A
Answer: A
Question: A man whose speed is 3 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)7
B)4
C)3
D)9
E)3.6
Rationale: M = 3
S = 1.5
DS = 4.5
US = 3
AS = (2 * 4.5 * 3) /7.5 = 3.6
Answer:E
Answer: E
Question: A number when multiplied by 3 is odd and divisible by 9. This number when multiplied by 4 is 108. What is the original number?
Options:
A)10
B)18
C)13
D)21
E)27
Rationale: Working backward, 108 divided by 4 is 27.
This number fits the rules of Three and Nine, where the digits add up to a sum divisible by nine.
Answer is E.
Answer: E
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)11
B)18
C)12
D)99
E)13
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer:C
Answer: C
Question: How many different positive integers exist between 10^4 and 10^5, the sum of whose digits is equal to 2?
Options:
A)6
B)7
C)5
D)8
E)18
Rationale: So, the numbers should be from 10,000 to 100,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
10,001
10,010
10,100
11,000
4 numbers.
2. One 2 and the rest are 0's:
20,000
1 number.
Total = 5 numbers.
Answer: C
Answer: C
Question: A class of 60 students has an average height of 200 cm. Six students whose average height is 120 cm, left the class and six others whose average height is 134 cm, joined. Calculate the new average height of the students of the class (in cm) is?
Options:
A)231.4 cm
B)301.4 cm
C)201.4 cm
D)221.4 cm
E)101.4 cm
Rationale: Total height = 200 * 60 = 12000 cm.
Total height of those who left = 120 * 6 = 720
Total height of those who joined = 134 * 6 = 804
New average
= [12000 - 720 + 804 ] / 60 = 12084/60 cm.
= 201.4
Answer:C
Answer: C
Question: A store owner estimates that the average price of type A products will increase by 35% next year and that the price of type B products will increase by 15% next year. This year, the total amount paid for type A products was $4000 and the total price paid for type B products was $5300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
Options:
A)$14,755
B)$11,495
C)$16,000
D)$16,225
E)$17,155
Rationale: cost of type A products next year = 1.35 * 4000 = 5400
cost of type B products next year = 1.15* 5300 = 6095
total 5400 + 6095 = 11495
ANSWER:B
Answer: B
Question: If n = 3^6 – 2^8 which of the following is NOT a factor of n?
Options:
A)11
B)43
C)1
D)43
E)5
Rationale: 3^6 - 2^8
= (3^3)^2 - (2^4)^2
=(3^3 + 2^4)(3^3 - 2^4)
=(27+16)(27-16)
=43*11
Therefore, 5 is Not a factor of n.
E
Answer: E
Question: Company KW is being sold, and both Company A and Company B were considering the purchase. The price of Company KW is 20% more than Company A has in assets, and this same price is also 100% more than Company B has in assets. If Companies A and B were to merge and combine their assets, the price of Company KW would be approximately what percent of these combined assets?
Options:
A)66%
B)75%
C)86%
D)116%
E)150%
Rationale: Let the price of Company A's assets be 100
Price of assets of KW is 20% more than company A's assets which is 120
Price of assets of KW is 100% more than company B's assets which means price of Company B's assets is half the price of KW = 60
A+B = 160
KW = 120
KW/(A+B)*100 = 120/160*100 = 75% B
Answer: B
Question: if 5 men take an hour to dig a ditch, then how long should 12 men take a dig to ditch of the same type?
Options:
A)25 min
B)30 min
C)28 min
D)20 min
E)10 min
Rationale: if 5 men take an hour to dig a ditch, then
12 men will take 5*60/12 = 25 mins to dig a ditch of the same type.
ANSWER:A
Answer: A
Question: 47% of the students in a class of 42 students has glasses or contacts. How many students in the class have either glasses or contacts?
Options:
A)15
B)16
C)17
D)18
E)20
Rationale: a=r⋅b
47%=0.47a
=0.47⋅42
a≈20
Option E is correct.
Answer: E
Question: A certain industrial loom weaves 0.132 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?
Options:
A)114
B)115
C)116
D)117
E)118
Rationale: Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
(cloth) 0.132 : 15 :: 1 : x
=>0.132*x=15
=>x=15/0.132
=>x=114
ANSWER:A
Answer: A
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)10
B)12
C)13
D)14
E)15
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: Option B
Answer: B
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 54 kmph, find the speed of the stream?
Options:
A)16 kmph
B)19 kmph
C)14 kmph
D)11 kmph
E)18 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 54/3 = 18 kmph.
Answer: E
Answer: E
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
Options:
A)300 kmph
B)360 kmph
C)600 kmph
D)720 kmph
E)400 kmph
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1(2/3) hours as 5/3 hours]
Required speed =1200 x3/5km/hr= 720 km/hr.
Answer:D
Answer: D
Question: Bob travels at an average speed of 12km/h, to the school and then return to the home he travels at an average speed of 10km/h. Which of the following is the closest approximation of Bob's average speed, in kilometers per hour, for the trip?
Options:
A)6.3
B)2.9
C)15.2
D)10.9
E)9.1
Rationale: Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 12 km/hour and 10 km/hour, using a multiple of both 12 and 10 would make the math easiest.
Let's set the Distance up the hill at 60 km.
So, going school, we have....
D = (R)(T)
60 = (5)(T)
60/12 = 5 = T
5 hours to go school
Going home, we have....
D = (R)(T)
60 = (10)(T)
60/10 = 6 = T
6 hours to go home
Total Distance = 120 km
Total Time = 5+6 = 11 hours
Average Speed = 120/11 = 10.9 km/hour
D
Answer: D
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
Options:
A)5
B)6
C)8
D)9
E)2
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B
Answer: B
Question: What least value must be assigned to * so that the number 197*5462 is r 9 ?
Options:
A)2
B)4
C)6
D)8
E)5
Rationale: Let the missing digit be x.
Sum of digits = (1 + 9 + 7 + x + 5 + 4 + 6 +»2) = (34 + x).
For (34 + x) to be divisible by 9, x must be replaced by 2 .
Hence, the digit in place of * must be 2.
Answer is A.
Answer: A
Question: If 20 men can build a water fountain 56 metres long in 6 days, what length of a similar water fountain can be built by 35 men in 3 days?
Options:
A)40 m
B)44 m
C)47 m
D)49 m
E)50 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Answer : D
Answer: D
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
Options:
A)26
B)87
C)86
D)36
E)73
Rationale: (9*12)/3
= 36
Answer: D
Answer: D
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
Options:
A)28,002
B)28,027
C)28,028
D)28,000
E)28,0012
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer:D
Answer: D