divelab/Sys2Bench huggingface dataset:
Question: If the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
Options:
A)50
B)52
C)49
D)68
E)74
Rationale: Sum of 5 Integer (a, b, c, d, e) = 5*60 = 300
e - a = 10
i.e. e = a+10
For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers
i.e. a+a+a+a+(a+10) = 300
i.e. 5a = 290
i.e. a = 58
i.e. Largest e = 58+10 = 68
Answer: option D
Answer: D
Question: Ages of two brothers differ by 14 years. If 12 years ago, the elder one was 3 times as old the younger one, find their present age
Options:
A)12,26
B)14,28
C)16,30
D)19,33
E)21,35
Rationale: Explanation:
Let the age of the younger brother be x,
Then the elder brother's age is (x+14)
=> 3(x-12) = (x+14-12) [12 years before]
=> 3x-36 = x+2
=> x = 19.
So the elder brother's age is x + 14 = 33
Answer: Option D
Answer: D
Question: The measure of the side of a square is multiplied by 7. If x represents the perimeter of the original square, what is the value of the new perimeter?
Options:
A)3x
B)4x
C)7x
D)12x
E)27x
Rationale: Original perimeter = x
Hence original side = x/4
New side = 7x/4
New perimeter = 4*7x/4 = 7x
Correct Option: C
Answer: C
Question: The average age of applicants for a new job is 31, with a standard deviation of 6. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
Options:
A)8
B)13
C)15
D)18
E)30
Rationale: within one standard deviation of the average age means 31 +/- 7
25--31--37
number of dif.ages -25 26 27 28 29 30 31 32 33 34 35 36 37
total=13
B
Answer: B
Question: When positive integer n is divided by 2, the remainder is 1. When n is divided by 7, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 10?
Options:
A)1
B)2
C)5
D)19
E)20
Rationale: When positive integer n is divided by 2, the remainder is 1 i.e., n=2x+1
values of n can be one of {1, 3, 5, 7, 9, 11, 13, 15, 17,19,..............31, 33,35..................}
Similarly,
When n is divided by 7, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 12, 19, 26, 33, 40, 47, 54, 61........}
combining both the sets we get
n={19, 52, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 21 or 21x
in case of n=5 p=5
so for min value of p, we take min value of n.
C is the answer.
Answer: C
Question: Find the common factors of 15 and 18.
Options:
A)50
B)55
C)60
D)70
E)90
Rationale: First of all we need to find the prime factors of 15 and 18
15 = 5 x 3
18 = 3x 3 x 2
LCM is the product of highest exponent of all the factors.
LCM (15,18) = 5 x 3^2 x 2
= 90
ANSWER : 90
Answer: E
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 14 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
Options:
A)40.2
B)40.4
C)40.6
D)40.8
E)None of the above
Rationale: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 14 = 406
Hence, new average = 406⁄10 = 40.6
Answer C
Answer: C
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 1 or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following?
Options:
A)1/8
B)1/16
C)1/32
D)1/64
E)1/128
Rationale: There are 8*8 = 64 possibilities.
Bob has 2 chances so the probability is 2/64 = 1/32.
The answer is C.
Answer: C
Question: In a certain accounting class of 100 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 65%, and the students on the make-up date had an average score of 95%, what was the average score for the entire class?
Options:
A)68%
B)70%
C)72%
D)74%
E)77%
Rationale: 70% of the class scored 65% and 30% of the class scored 95%.
The difference between 65% and 95% is 30%.
The average will be 65% + 0.3(30%) = 74%.
The answer is D.
Answer: D
Question: (x +1 )(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d What are the values of a, b, c and d?
Options:
A)2
B)7
C)6
D)1
E)9
Rationale: (x + 1)(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d
6(x + 1)(x - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d
6(x2x2 - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d
⇒6(x3+x2−x−1)⇒6(x3+x2−x−1) = ax3+bx2+cx+dax3+bx2+cx+d
⇒6x3+6x2−6x−6⇒6x3+6x2−6x−6 = ax3+bx2+cx+dax3+bx2+cx+d
Equating the coefficients of like learns on both the sides, a = 6, b = 6, c = -6 and d = -6.
Answer:C
Answer: C
Question: The side of a square is increased by 25% then how much % does its area increases?
Options:
A)56.26
B)56.25
C)56.21
D)56.28
E)56.22
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer: B
Answer: B
Question: Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is Q?
Options:
A)50+Q/200
B)50+3Q/100
C)50+Q/40
D)100+Q/50
E)100+3Q/100
Rationale: 50+Q/40=C
Answer: C
Question: Running 3/4th of his usual rate, a man is 14min late. Find his usual time in hours ?
Options:
A)6/4 hrs
B)3/4 hrs
C)9/4 hrs
D)3/4 hrs
E)7/10 hrs
Rationale: Explanation:
Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time
so 1/3rd of the usual time = 14min
or usual time = 3 x 14 = 42min = 45/60 hrs = 7/10 hrs.
Answer: E
Answer: E
Question: If the average (arithmetic mean) of the four numbers 3, 25, 52, and (N + 1) is 50, then N =
Options:
A) 119
B) 120
C) 121
D) 122
E) 129
Rationale: 3+25+52+N+1= 50 x 4 = 200
=>N +81 = 200
=>N=119
Answer A
Answer: A
Question: If log 27 = 1.431, then the value of log 9 is
Options:
A)0.754
B)0.854
C)0.654
D)0.554
E)0.954
Rationale: log 27 = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = Log 3square = 2 log 3 = (2 x 0.477) = 0.954
answer :E
Answer: E
Question: Set S = {1, 2, 3, 4, 5, 6, 7, x}
If x is an integer, which of the following could be the median of Set S?
Options:
A)3.75
B)4.25
C)4.5
D)5
E)5.25
Rationale: Median = 4+5/2 = 4.5
Hence, Answer will be (C) 4.5
Answer: C
Question: What is the sum of the different positive prime factors of 450?
Options:
A)10
B)11
C)15
D)16
E)18
Rationale: 450
45*10 --> 5*3*3*2*5 --> 5+3+2=10. Remember its asking for the DIFFERENT positive prime factors of 450.
A
Answer: A
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 63 = x?
Options:
A)1
B)5
C)3
D)6
E)7
Rationale: C) 3
Answer: C
Question: The average age of students in section A of 122 students is 28 years and the average age of students in section B of 180 students is 35 years. Find the average age of students in both sections taken together?
Options:
A)26 years
B)30years
C)15years
D)25years
E)32years
Rationale: The required average = (122*28+180*35)/122+180 = 32 years
Answer is E
Answer: E
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 750 grams per kg, what is his percent?
Options:
A)25%
B)33%
C)29%
D)55%
E)45%
Rationale: 750 --- 250
100 --- ? => 33.33%
Answer: B
Answer: B
Question: A tradesman by means of his false balance defrauds to the extent of 45%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)110.25%
B)99.5%
C)84.5%
D)24.75%
E)45%
Rationale: g% = 45 + 45 + (45*45)/100
= 110.25%
Answer: A
Answer: A
Question: The ratio between the length and the breadth of a rectangular park is 2 : 3 If a man cycling along the boundary of the park at the speed of 10 km/hr completes one round in 18 min, then the area of the park (in sq. m) is?
Options:
A)3000 m
B)9000 m
C)540000 m
D)10000 m
E)54000 m
Rationale: Perimeter = Distance covered in 8 min. = (10000 x 18)/60 m = 3000 m.
Let length = 2x metres and breadth =3x metres.
Then, 2(2x + 3x) = 3000 or x = 300.
Length = 600 m and Breadth = 900m.
Area = (600 x 900) m2 = 540000 m
C
Answer: C
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
Options:
A)10
B)99
C)88
D)66
E)12
Rationale: 1/6 – 1/15 = 1/10 => 10
Answer:A
Answer: A
Question: At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:50. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?
Options:
A)80
B)81
C)82
D)83
E)84
Rationale: (5/3)*50=83 plus remainder
The answer is D.
Answer: D
Question: If point A coordinates are (-7, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
Options:
A)(-2, - 2/3)
B)(2, -2/3)
C)(2/3, -2)
D)(0, 2)
E)(2, 2/3)
Rationale: coordinates of A (-7; -3)
coordinates of B (8; 4)
since, line AB consists of three equal segments:
-7 + 3m = 8 hence, m = 5
-3 + 3n = 4 hence, n = 7/3
x-coordinate of C = x-coordinate of A + m = -7 + 5 = -2
y-coordinate of C = y-coordinate of A + n = - 3 + 7/3 = - 2/3
Answer A
Answer: A
Question: If a, b, and c are consecutive odd positive integers and a<b<c, which of the following must be true?
I. at least one of the three numbers is prime
II. ab>c
III. a + b + c = 3b
Options:
A)III only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: The Case 91,93,95 where there are no prime nos. is tested here.
as their is only one prime number between 90 to 99 ie 97.
And hence option A
Answer: A
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 5% per first year and 6% for the second year?
Options:
A)3377
B)2678
C)5565
D)1976
E)1671
Rationale: 5000 * 105/100 * 106/100 => 5565
Answer: C
Answer: C
Question: There are two numbers. If 50% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Options:
A)A)3/7
B)B)5/8
C)C)6
D)D)1/2
E)E)7
Rationale: Let the two numbers be x and y.
50/100 * x + y = 5/4y
=> 1/2 x = 1/4 y => x/y = 1/2
D)
Answer: D
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 12 km in stationary water
Options:
A)40 min
B)3hr
C)1hr 15 min
D)1hr 30 min
E)4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(12/4)=3 Hr
Answer(B)
Answer: B
Question: A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/4. What is the sum of the numerator and denominator of the original fraction?
Options:
A) 49
B) 35
C) 56
D) 26
E) 21
Rationale: x/y = 2/5 -> 1
(x+4)/2y = 1/4 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 8/5
=> 5x = 4x + 16
=> x = 16
=> y = 5/2 *16 = 40
so x + y = 56
The answer is C
Answer: C
Question: A certain number when divided by 95 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Explanation:
95 + 25 = 120/15 = 8 (Remainder)
D
Answer: D
Question: There are 200 questions on a 3 hrexamination.Among these questions are 50 mathematics problems.It is suggestedthat twice as much time be spent on each maths problem as for each otherquestion.How many minutes should be spent on mathematics problems
Options:
A)71min
B)72min
C)73min
D)74min
E)75min
Rationale: taking the time in min so convert time into min=60*3=180
x= time spent on maths question
2x=time spent on maths question
x(200-50)+2x(50)=180
150x+100x=180
250x=180
x=0.72
now time spent on maths questions=2*0.72*50=72min
ANSWER:B
Answer: B
Question: The workforce of Company X is 50% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?
Options:
A)225
B)220
C)230
D)235
E)240
Rationale: let x be the total worker then 0.5x =female worker and 0.5x is male worker then 20 male worker added
05x/(0.5x +20) = 50/100 or 50x = 50*( 0.5x+100) = 25x+ 5000 or 25x = 5000 , x = 5000/25=200
total worker = 200 +20= 220
B
Answer: B
Question: If $20,000 interest is invested in x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
Options:
A)10,000(x^n)
B)20,000n(x/100)
C)20,000(x/100)^n
D)10,000(1 + x/100)^n
E)10,000n(1 + x/100)
Rationale: Principal * no.of years * percentage of interest
Answer : B
Answer: B
Question: The letters O,L and T are rearranged to form the word 'Lot'. Find its probability.
Options:
A)1/18
B)1/12
C)1/4
D)1/8
E)1/6
Rationale: Explanation :
There are total 3 letters. The probability that O gets the first position is 1/3.
Likewise, probability for L and T are 1/2 and 1/1.
Hence, the required probability is:-
=> (1/3) x (1/2) x 1.
=> 1/6.
Answer : E
Answer: E
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
Options:
A)22
B)98
C)99
D)36
E)12
Rationale: (9*12)/3 = 36
Answer: D
Answer: D
Question: Average of 6 numbers is zero. At most how many numbers may be greater than zero
Options:
A)0
B)1
C)5
D)9
E)10
Rationale: Answer: Option C
Answer: C
Question: 20-3*4^2+53 = ?
Options:
A)25
B)-13
C)-73
D)13
E)None
Rationale: 20-3*4^2+53= 20-3*16+53=20-48+53=25..
A
Answer: A
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 130 mph. On the way home, I flew 88 mph. What was my average speed for the trip?
Options:
A)198 mph
B)110 mph
C)88 mph
D)100 mph
E)109 mph
Rationale: (130 mph +88 mph)/2= 109 mph
Correct answer is: E
Answer: E
Question: In 10 years,A will be six times as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :
Options:
A)15.8 Years
B)29 Years
C)39 Years
D)49 Years
E)59 Years
Rationale: Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
âˆ´ (x + 9)+ 10 = 6 (x - 10) â‡” x + 19 = 6x- 60 â‡”5 x = 79
x=15.8 .Answer A
Answer: A
Question: The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is?
Options:
A)4729
B)4329
C)4320
D)4372
E)9032
Rationale: x Not younger
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!) = 4320
Answer:C
Answer: C
Question: Insert the missing number
2, 4, ..., 16, 32, 64, 128, 256
Options:
A)6
B)5
C)4
D)3
E)8
Rationale: series is 2* Previous Number.
ANSWER:E
Answer: E
Question: Two numbers N and 16 have LCM = 48 and GCF = 18. Find N.
Options:
A)24
B)34
C)44
D)54
E)64
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16 × N = 48 × 18
N = 48 × 18 / 16 = 54
correct answer D
Answer: D
Question: Solve the following quadratic equation by factoring.
x^2+15x=-50
Options:
A)(5,10)
B)(2,4)
C)(-5,-10)
D)(9,0)
E)(4,5)
Rationale: Now all we need to do is use the zero factor property to get,
x+5=0
x=-5
x+10=0
x=-10
(-5,-10)
Ans: C
Answer: C
Question: A car was driving at 72 Km/h for 20 minutes, and then at 81 Km/h for another 40 minutes. What was its average speed?
Options:
A)76.
B)77.
C)78.
D)79.
E)80.
Rationale: driving at 72 Km/h for 20 minutes ,distance covered = 72*1/3=24 km
driving at 90 km/h for 40 minutes ,distance covered = 81*2/3=54 km
average speed = total distance/total time = 78/1 = 78 km/h
Answer: A
Answer: A
Question: I am three times as old as my son. Five year later, I shall be two and half times as old as my son. How old am I and how old is my son ?
Options:
A)45 year and 15 year
B)40 year and 10 year
C)42 year and 12 year
D)41 year and 11 year
E)None of these
Rationale: Let my age is x years and my son’s age is y years, Then,
x = 3y
Five years later, my age will be (x + 5) years and my son’s age will be
(y + 5) years
Thus, (x + 5) = 5/2 (y + 5)
=> 2x - 5 y - 15 =0
putting x = 3y, we get
6y - 5y - 15 = 0
=> y = 15
Thus, x = 45
Hence, my present age is 45 years and my son’s present age is 15 years.
ANSWER:A
Answer: A
Question: Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: (248$ / 7children) = 35.42
Took the lowest number = 35 * 7 children = $245
$248 - $245 = staying $3
Correct option: C) 3$
Answer: C
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph, and 18 kmph respectively. What is the ratio of the time taken by B to than taken by D?
Options:
A)5:16
B)5:17
C)9:8
D)8:9
E)None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D = 18 : 16 = 9 : 8.
Answer : C
Answer: C
Question: Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
Options:
A)88
B)77
C)88
D)18
E)72
Rationale: Explanation:
93 + 123 + 153 = a3 => a = 18
Answer: Option D
Answer: D
Question: 25% students of a class failed in Chemistry and 40% failed in Physics where 10% did not pass in any of the two subjects. If 30 students passed in only Physics, how many of them passed in both the subjects.
Options:
A)60
B)70
C)80
D)90
E)100
Rationale: n(C)=75% , n(P)=60% , n(PUC)= 90% => n(PnC)= 75% + 60% - 90% = 45%. given n(P) - n(PnC)= 30 , 60% - 45% = 30 => 15% = 30 => 1% = 2 . n(PnC) = 45% = 90
ANSWER:D
Answer: D
Question: Which number can you put to fill in the sequence?
23 1 3 25 16 20 6 9 20 ?
Options:
A)11
B)13
C)15
D)17
E)19
Rationale: E
19
Position of first letter of the words in the question in alphabets.
Answer: E
Question: Goldenrod and No Hope are in a horse race with 4 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
Options:
A)720
B)360
C)12
D)24
E)21
Rationale: All 4 horses can finish the race in 4! way (assuming no tie).
If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 4!/2=12 different arrangements of finishes where No Hope always finishes before Goldenrod.
Answer: C.
Answer: C
Question: An oil cylinder was 3/4th full. When FIVE bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold?
Options:
A)120
B)115
C)140
D)130
E)100
Rationale: (4/5 -3/4) cylinder is filled by 5 bottles
0.8 -0.75 = 0.05 cylinder is filled by 5 bottles
1 cylinder is filled by 5/0.05 = 100 bottles
ANSWER:E
Answer: E
Question: A class of 10 students is having an average age of 15, another group of 4 students whose average age is 12 has been added to them. What is the average of the new group formed?
Options:
A)12
B)13.4
C)14.14
D)15
E)16.25
Rationale: sum of ages of the new group formed= (15x10) + (4x12) = 198
Total number of people in the new group= 10+4= 14
Average of the new group=198/14 = 14.14
Answer: C
Answer: C
Question: There are 2 sections A and B in a class, consisting of 40 and 20 students respectively. If the average weight of section A is 50kg and that of section B is 40kg, Find the average of the whole class?
Options:
A)50.78kg
B)49.32kg
C)46.66kg
D)69.15kg
E)70.89kg
Rationale: Total weight of 40+20 students = 40*50 + 20*40 = 2000+800
Average weight of the class is = 2800/60 = 46.66 kg
Answer is C
Answer: C
Question: Count the numbers between 10 - 99 which yield a remainder of 5 when divided by 8 and also yield a remainder of 1 when divided by 6?
Options:
A)One
B)Three
C)Two
D)Five
E)Four
Rationale: Answer = E) Four
Numbers between 10 - 99 giving remainder 5 when divided by 8 = 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93
The above Numbers giving remainder 1 when divided by 6 = 13, 37, 61, 85 = 4
Answer: E
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water ?
Options:
A)40 minutes
B)1 hour
C)1 hr 15 min
D)1 hr 30 min
E)None of these
Rationale: Solution
Rate downstream =(1/60x60) km/hr = 6 km/hr, Rate upstream = 2 km/hr.
Speed in still water =1/2(6+2) km/hr = 4 km/hr.
∴ Required time = (5/4)hrs = 1 1/4hrs = 1 hr 15 min. Answer C
Answer: C
Question: In a game of 100 points there are three participants A, B, and C. A gives to B 10 points and to C 19 points, then how many points can B give to C
Options:
A)9 points
B)10 points
C)11 points
D)12 points
E)13 points
Rationale: A:B=100:90 (A can give 10 points to B means A is 10 points leads to B and from the problem A=100)
A:C=100:81
for B:C
B:C = (A:C)*(B:A)
= (100/81)*(90/100)
=10/9
= 10:9
multiply and devide by 100
B:C = 100:90
B can give 10 points to C
ANSWER:B
Answer: B
Question: How many seconds will a 400 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)24
B)30
C)40
D)45
E)50
Rationale: Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=400*3/50=24sec
ANSWER:A
Answer: A
Question: Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the greatest of the three numbers is:
Options:
A)180
B)144
C)200
D)212
E)220
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.
The greatest of three number is 8 x 18=144
Answer:B
Answer: B
Question: Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are?
Options:
A)5, 15, 35
B)5, 15, 30
C)5, 15, 25
D)5, 15, 40
E)5, 15, 20
Rationale: Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5.
The numbers are 5, 15, 25.
Answer: C
Answer: C
Question: In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
Options:
A)86 sec
B)80 sec
C)76 sec
D)96 sec
E)None of these
Rationale: runs 45/2m in 6 sec.
B covers 300 m in 6 x	2/45 x 300sec	= 80 sec.
ANSWER:B
Answer: B
Question: When two dice are rolled, what is the probability that the sum of the two numbers is 6?
Options:
A) 1/9
B) 5/36
C) 1/3
D) 2/36
E) None of the above
Rationale: We have 5 outcomes that satisfy the question:
1-5
2-4
3-3
4-2
5-1
the probability is (1/6*1/6)*5= 5/36.
I think the answer is B
Answer: B
Question: Peter read P books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
Options:
A)P > 35N
B)P < N − 35
C)P > N + 35
D)P = N − 35
E)P = N + 35
Rationale: Peter reads 35 more books that Nikki
This translates to
P - N = 35
Or, P = N + 35
Option E
Answer: E
Question: Convert the 15/36 m/s into kilometers per hour?
Options:
A)1.7
B)1.5
C)1.3
D)1.1
E)1.2
Rationale: 15/36 m/s = 15/36 * 18/5 = 3/2
= 1.5 kmph.
Answer: B
Answer: B
Question: When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.?
Options:
A)4.5
B)5
C)5.5
D)5.8
E)6
Rationale: if $x$ is the number, x/6 * 12 = 11
=> 2x = 11
=> x = 5.5
C
Answer: C