divelab/Sys2Bench huggingface dataset:
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
Options:
A)15 1/3 days
B)13 1/3 days
C)19 1/3 days
D)11 1/3 days
E)12 1/3 days
Rationale: B
13 1/3 days
5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer: B
Question: The largest number that exactly divides each number of the sequence
(15 - 1), (25 - 2), (35 - 3), ...., (n5 - n), ...... is
Options:
A)1
B)15
C)30
D)120
E)None
Rationale: Sol.
Required number = (25 - 2)
= (32 - 2) = 30.
Answer C
Answer: C
Question: f two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
Options:
A)1/9
B)1/2
C)1/1
D)1/5
E)1/8
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
Answer: B
Question: There are 34 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
Options:
A)435
B)367
C)361
D)497
E)561
Rationale: Explanation:
Total number of persons = n = 34
Shake hands involve only 2 persons = r = 2
Number of shake hands = nCr = 34C2
34C2 = (34 * 33) /(2 * 1) = 561
ANSWER:E
Answer: E
Question: Amithab's average expenditure for the January to June is Rs. 4200 and he spends Rs.1200 in January and Rs.1500 in july.The average expenditure for the months of febraury to July is:
Options:
A)Rs.4250
B)Rs.4288
C)Rs.4227
D)Rs.4218
E)Rs.4219
Rationale: Explanation:
Amithab's total expenditure for Jan - June = 4200 x 6 = 25200
Expenditure for Feb - June = 25200-1200 = 24000
Expenditure for the months of Feb - July = 24000 + 1500 =25500
The average expenditure = {25500}{6}=4250
Answer: A
Answer: A
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)6
C)7
D)4
E)32
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
Answer: A
Question: For which of the following values of s is (60+s)/s an integer?
Options:
A)3
B)4
C)9
D)11
E)60
Rationale: This problem has to be solved by checking the options
(60 + s)/s
For this entity to be an integer, 50 + s should be divisible by s
Option A: 63/3 - Not an Integer
Option B: 64/4 - Not an Integer
Option C: 69/9 - Not an integer
Option D: 81/11 - Not an integer
Option E - 120/60 - Integer
Correct Option: E
Answer: E
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 3/5 of its present?
Options:
A)41.66667
B)60.5
C)63.5
D)62.5
E)64.5
Rationale: Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 3x/5
Hence, number of buckets needed = 25x/(3x/5)=(25×5)/3=41.66667
Answer is A.
Answer: A
Question: The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:
Options:
A)Rs. 960
B)Rs. 760
C)Rs. 840
D)Rs. 1020
E)Rs. 1615
Rationale: T.D = (B.Gx100)/(R/T) = (270X100)/(12X3) = Rs. 750
B.D. = Rs.(750 + 270) = Rs. 1020.
answer :D
Answer: D
Question: The ratio of the volumes of two cubes is 27 : 64. What is the ratio of their total surface areas?
Options:
A)9:12
B)12:18
C)9:16
D)8:2
E)4:2
Rationale: Ratio of the sides = Â³âˆš27 : Â³âˆš64
= 3 : 4
Ratio of surface areas =9:16
Answer: C
Answer: C
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)57%
B)58%
C)60%
D)65%
E)68%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required % =(11628/20400)*100% = 57%
answer :A
Answer: A
Question: What is 82% of 3/4?
Options:
A)6.9
B)69.0
C)0.6845
D)0.6859
E)0.615
Rationale: 82%*(3/4)=0.82*0.75=0.615
Answer :E
Answer: E
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
Options:
A)221
B)287
C)400
D)288
E)171
Rationale: Explanation:
441 = P(21/20)2
P = 400
Answer:C
Answer: C
Question: A bag contains 5 red, 4 blue and 3 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)2/15
B)2/21
C)5/33
D)3/29
E)4/27
Rationale: P(Both are red),
=5C212C2=5C2/12C2
=10/66=5/33
C
Answer: C
Question: City X has a population 6 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
Options:
A)1:8
B)1:4
C)2:1
D)4:1
E)12:1
Rationale: x= 6y, y= 2*z
X : Y , Y : Z
6 : 1 , 2 : 1
12 : 2 , 2 : 1
So, X : Z =12 : 1
(E)
Answer: E
Question: The average of first 10 prime numbers is?
Options:
A)12.7
B)12.2
C)12.9
D)12.1
E)12.6
Rationale: Sum of 10 prime no. = 129
Average = 129/10 = 12.9
Answer: C
Answer: C
Question: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab is even
III. ab > 0
Options:
A)I only
B)II only
C)I and II
D)I and III
E)I, II, and III
Rationale: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
II only.letter B
Answer: B
Question: What is 15 percent of 54?
Options:
A)7.3
B)8.1
C)9.5
D)10.2
E)11.6
Rationale: (15/100) * 54 = 8.1
The answer is B.
Answer: B
Question: What is the remainder when 103 * 505 * 607 is divided by 9
Options:
A)6
B)18
C)2
D)4
E)7
Rationale: 103/9==> Remainder=4
505/9==> Remainder=1
607/9==> Remainder=4
=4*4*1=16/9==> Remainder=7
Answer: E
Answer: E
Question: Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/4 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
Options:
A)7/12
B)29/60
C)17/30
D)19/30
E)11/15
Rationale: Let s assume the platinum card spending limit =x
Gold card spending limit will be =x/2
balance on gold card is =x/2*1/3=x/6
Platinum card unspent limit is= x-1/4x=3/4x
So if gold card balance is transferred then the rest unspent will be
3/4x-x/6=7/12x
So the ans is A
Answer: A
Question: A company selects an employee at his 25th age and offers salary as Rs.40000 per
annum for first 2 years. Afterwards, every year he gets increment of Rs.4000 for
next 15 years and his salary become constant till his retirement. If Rs.80,000 is
his average salary (throughout his career) then at what age he retires?
Options:
A)48
B)49
C)50
D)52
E)53
Rationale: For 1st 2 yrs salary=40,000
After 2 years he get increment of 4000 every year for 15 years
So 15th year salary =44000+14*4000=100000
Now by using arithmetic progression
S15=n/2(a+l)=15/2(44000+100000)=1080000
Now avg salary=80000
80000+10,80000+10,0000x/17+x=80000
By solving
x=10
now 27+15+10=52
so 52 is the age
ANSWER:D
Answer: D
Question: In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence?
Options:
A) 3/5
B) 5/8
C) 8/5
D) 5/3
E) 9/2
Rationale: First term = 1
Second term = (1/1)+1 = 2
Third Term = (1/2)+1 = 3/2
Forth Term = [1/(3/2)]+1 = 5/3
Fifth Term = [1/(5/3)]+1 = 8/5
Answer: Option C
Answer: C
Question: A pipe can empty 2/3rd of a cistern in 12 mins. In 8 mins, what part of the cistern will be empty?
Options:
A)1//3
B)2/3
C)4/9
D)4/7
E)5/9
Rationale: 2/3 ---- 12
? ----- 8 ==> 4/9
C
Answer: C
Question: Nr Books bought Nr of People
1 5
3 2
4 7
6 3
What is the median of books bought per person?
Options:
A)a) 2
B)b) 4
C)c) 6
D)d) 8
E)e) 18
Rationale: 1,1,1,1,1,3,3,4,4,4,4,4,4,4,6,6,6
so you will observer that the median of the list is 4.
Ans B
Answer: B
Question: The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is?
Options:
A)Rs. 2000
B)Rs. 3000
C)Rs. 4000
D)Rs. 4500
E)Rs. 5000
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
M + O = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv)
Subtracting (ii) from (iv), we get M = 4000.
M's monthly income = Rs. 4000
C
Answer: C
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)Rs529
B)Rs527
C)Rs598
D)Rs540
E)Rs516
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 =Rs540
Answer:D
Answer: D
Question: Find the average of all the numbers between 17 and 32 which are divisible by 3.
Options:
A)15
B)18
C)20
D)26
E)None
Rationale: Sol.
Average = (21+ 24+ 27+ 30/ 4) = 102 / 4 = 25.5
Answer D
Answer: D
Question: In a barrel of juice there is 40 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
Options:
A)3:2.
B)2:1.
C)3:1.
D)4:3.
E)3:4.
Rationale: Juice barrel : beer Barrel = 40:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 4/8 costs 3/4, ie 4J / 8B = 3/4.
Solving for J/B, we get 3:2
Answer A.
Answer: A
Question: The average weight of 8 person's increases by 6 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person?
Options:
A)80 kg
B)85 kg
C)90 kg
D)88 kg
E)110 kg
Rationale: Total weight increased = (8 x 6) kg = 48 kg.
Weight of new person = (40 + 48) kg = 88 kg.
Answer : D
Answer: D
Question: In a company the manager wants to give some gifts to all of the workers. In each block there are about 100 workers are there. The total amount for giving the gifts for all the workers is $4000. The worth of the gift is $4. How many blocks are there in the company?
Options:
A)12
B)10
C)15
D)17
E)20
Rationale: Each employee will get a gift worth of = $4
total employees = 4000/4 = 1000
total blocks = 1000/100 = 10
correct option is B
Answer: B
Question: Mary can do a piece of work in 28 days. Rosy is 40% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?
Options:
A)22
B)24
C)20
D)25
E)27
Rationale: Ratio of times taken by Mary and Rosy = 140:100 = 14:10
Suppose Rosy takes x days to do the work.
14:10 :: 28:x => x= 20 days.
Hence, Rosy takes 20 days to complete the work.
Answer: C
Answer: C
Question: A certain restaurant offers 6 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
Options:
A)260
B)388
C)436
D)504
E)520
Rationale: The number of possible choices for desserts is 7C2 = 21
The number of possible meals is 6*4*21 = 504
The answer is D.
Answer: D
Question: In how many ways can Nicole distribute 20 chocolates among Ben, Kate, Mark and Tom so that each receives at least one?
Options:
A)20C4
B)19C3
C)21C4
D)21C3
E)None of the answers is correct
Rationale: The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is n−1Cr−1
Thus the answer is 19C3.
Answer: B.
Answer: B
Question: 8k8
+ k88
--------
1,6r6
If k and r represent non-zero digits within the integers above, what is r?
Options:
A)6
B)7
C)8
D)9
E)17
Rationale: 8k8
k88
--------
16r6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and r=6.
Answer: A.
Answer: A
Question: A and B started a partnership business investing some amount in the ratio of 2 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Options:
A)4 : 10 : 5
B)5 : 7 : 4
C)6 : 10 : 5
D)7 : 9: 4
E)5 : 4 : 8
Rationale: Let the initial investments of A and B be 2x and 5x.
A : B : C = (2x x 12) : (5x x 12) : (5x x 6) = 24 : 60 : 30
= 4 : 10 : 5.
ANSWER :A
Answer: A
Question: It was raining and a water drop accumulated itself over a leaf. It fell down to another leaf and lost 1/4th of its volume. It then fell off to another leaf losing 1/5th of its volume. After that it fell to another leaf losing 1/6th of its volume. This was process was repeated again and again till the water drop reached the last leaf and lost 1/75th of its volume.
Seeking the facts given in the question, will you be able to determine the accurate percentage of loss in the volume of the water drop when it is on the last leaf from its initial volume?
Options:
A)5%
B)3%
C)8%
D)4%
E)9%
Rationale: D
4%
Suppose that the initial volume of the water drop was p.
p - (1/4) p = (3/4) p
(3/4) p - (1/5) [(3/4) p] = (3/4) p * [1 - (1/5)] = (3/4) p * (4/5) = (3/5) p
(3/75) p = (1/25) p
1/25 = 4%
Therefore, the required percentage is four percent.
Answer: D
Question: Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour?
Options:
A)The average speed is 1/5 miles per hour.
B)The average speed is 1/3 miles per hour.
C)The average speed is 2/5 miles per hour.
D)The average speed is 2/3 miles per hour.
E)The average speed is 3/5 miles per hour.
Rationale: We know the average speed and must find the fraction of time taken at a particular speed.
t1/t2 = (A2 – Aavg)/(Aavg – A1)
t1/t2 = (60 – 50)/(50 – 30) = 1/2
So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3.
ANSWER (B)
Answer: B
Question: If x is negative and y is positive, which of the following cannot be positive?
Options:
A)-xy
B)x^2/y
C)x^4/y
D)-x^3*y
E)-x/-y
Rationale: - * - = +
+ / - = -
-x/-y is negative.
Answer : E
Answer: E
Question: A quiz has one mcq question with a,b and c as options. and two questions with true/false answers. what is the probability of giving all 3 answers correct?
Options:
A)1/12
B)1/3
C)1/4
D)1/2
E)1/6
Rationale: probability of getting mcq answer correct = 1/3
probability of getting one true/false answer correct = 1/2
probability of getting all 3 answers correct = 1/3 * 1/2 *1/2
=1/12
ANSWER:A
Answer: A
Question: If -6 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?
Options:
A)-42 < xy < 21
B)-42 < xy < 24
C)-28 < xy < 18
D)-42 < xy < 36
E)-24 < xy < 24
Rationale: The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-6)*(-6)=36.
Therefore -42 < xy < 36.
Answer: D.
Answer: D
Question: Convert 0.34 in to a vulgar fraction ?
Options:
A)18/50
B)16/50
C)17/50
D)19/50
E)None
Rationale: Answer
0.34 = 34/100 = 17/50
Correct Option: C
Answer: C
Question: The difference between simple and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is?
Options:
A)8
B)3
C)9
D)3
E)2
Rationale: S.I. = (1200 * 10 * 1)/100 = Rs. 120
C.I. = [1200 * (1 + 5/100)2 - 1200]
= Rs. 123 Difference = (123 - 120)
= Rs.3.
Answer:B
Answer: B
Question: There are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
Options:
A)31
B)32
C)35
D)30
E)45
Rationale: Explanation:
HCF (408, 312) = 24
The number of boys or girls that can be placed in a section = 24.
Thus the total number of sections is given by
408/24+312/24 =17+13 = 30
Answer: D
Answer: D
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability E that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
Options:
A)15/64
B)30/64
C)1/2
D)1/4
E)52/64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days E= 15/64
Ans A it is.
Answer: A
Question: When positive integer N is divided by positive integer J, the remainder is 18. If N/J = 204.03, what is value of J?
Options:
A)600
B)200
C)400
D)800
E)1000
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 204.03
Here 204 is the quotient.
Given that Remainder = 18
So, 204.03= 204 + 18/J
So, J = 600
Answer: A
Answer: A
Question: A bucket full of nuts was discovered by the crow living in the basement. The crow eats a fifth of the total number of nuts in 8 hours. How many hours in total will it take the crow to finish a quarter of the nuts?
Options:
A)9
B)10
C)11
D)12
E)14
Rationale: In one hour, the crow eats 1/40 of the nuts.
(1/4) / (1/40) = 10 hours
The answer is B.
Answer: B
Question: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values are within three standard deviations of the mean?
Options:
A)0
B)1
C)3
D)6
E)7
Rationale: Mean = -1
Standard Deviation = 1/8
1 unit of standard deviation BELOW the mean = -1 - 1/8 = -1 1/8
2 units of standard deviation BELOW the mean = -1 - 1/8 - 1/8 = -1 2/8
2 units of standard deviation BELOW the mean = -1 - 1/8 - 1/8 - 1/8 = -1 3/8
1 unit of standard deviation ABOVE the mean = -1 + 1/8 = -7/8
2 units of standard deviation ABOVE the mean = -1 + 1/8 + 1/8= -6/8
3 units of standard deviation ABOVE the mean = -1 + 1/8 + 1/8 + 1/8= -5/8
So, all values from -1 3/8 to -5/8 are within 3 standard deviations of the mean.
Within this range, there is only 1 integer value: -1
Answer:C
Answer: C
Question: Tough and Tricky questions: Distance/Rate.
On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 300 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?
Options:
A)20
B)40
C)60
D)80
E)50
Rationale: Say, if speed is 60, 300/50 = 6 hrs and 300/60 = 5 hrs (a reduction of 1 hr -> Correct answer)
Answer (E)
Answer: E
Question: What is the value of 26^2 + 27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2+ 34^2?
Options:
A)8160
B)8108
C)8118
D)8128
E)8138
Rationale: This is what I did, all the nos are close to 30, and squared, so 30^2 plus there are 9 numbers, so (30)^2 x 9 =8100,
now squaring the last digits of each no individually comes up to (16+9+4+1+0+1+4+9+16) = 60.
when you add the 2 up it gives you a (8100+60) =8160,
Answer is A
Answer: A
Question: In what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)8 sec
B)7 sec
C)5 sec
D)6 sec
E)9 sec
Rationale: T = 50/36 * 18/5
= 5 sec
Answer:C
Answer: C
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A?
Options:
A)Rs. 420000
B)Rs. 180000
C)Rs. 201600
D)Rs. 504000
E)None of these
Rationale: B's monthly income = 15000 * 112/100 = Rs. 16800
B's monthly income = 2 parts ----> Rs. 16800
A's monthly income = 5 parts = 5/2 * 16800 = Rs. 42000
A's annual income = Rs. 42000 * 12 = Rs. 504000
ANSWER:D
Answer: D
Question: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options:
A)16.5%
B)20%
C)35%
D)55%
E)65%
Rationale: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);
On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.055*fringe benefit costs;
So, 35(S+F)=30S+55F --> S=4F --> F/S=1/4 --> F/(S+F)=1/(1+4)=1/5=0.2.
Answer: B.
Answer: B
Question: Abhinav and Bhupathi together have Rs. 1210. If 4/15 of Abhinav's amount is equal to 2/5 of Bhupathi's amount, how much amount does Bhupathi have?
Options:
A)Rs 460
B)Rs 484
C)Rs 550
D)Rs 664
E)None of these
Rationale: Explanation :
Let A = Abhinav, B = Bhupathi.
4/15A=2/5B
=> A=(2/515/4)B
=> A=3/2B
=> A/B=3/2
=> A : B = 3:2
B's share = Rs. (12102/5)= Rs. 484.
Answer : B
Answer: B
Question: Reduce
368575
to the lowest terms
Options:
A)3025
B)2829
C)2829
D)1625
E)None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 575 which is 23
Step2: Divide both by 23, we will get the answer 16/25
Answer: Option D
Answer: D
Question: On a journey across Bombay, a tourist bus averages 10 km/h for 20% of the distance, 30 km/h for 60% of it and 20 km/h for the remainder. The average speed for the whole journey was
Options:
A)10 km/h
B)30 km/h
C)5 km/h
D)20 kilometre per hour
E)None of these
Rationale: Let the average speed be x km/h.
and Total distance = y km. Then,
0.2⁄10y + 0.6⁄30y + 0.2⁄20y = y⁄x
⇒ x = 1⁄0.05 = 20 km/h
Answer D
Answer: D
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
Options:
A)65 years
B)35 years
C)55 years
D)44 years
E)11 years
Rationale: Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years.
Answer: B
Answer: B
Question: Given the two equations 5r - 5s = 15 and 2r - 2s = 6, by how much does r exceed s?
Options:
A)3
B)2
C)11
D)4
E)7
Rationale: Solve by Simultaneous Equations.
My Answer is A.
r=6
s=3
Answer: A
Question: The unit digit in the product 1258*6754*4512*9783 is?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Unit digit in the given product = unit digit in 8*4*2*3 = 2
Answer is C
Answer: C
Question: A bowl contains pecans, cashews, and almonds in a ratio of 11 : 20 : 30, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10
Options:
A)I,III only
B)I only
C)III only
D)II only
E)I,II only
Rationale: i. The ratio 2 : 3 is the same as the given ratio 20 : 30. If one pecan were removed, the new ratio would be 10 : 20 : 30, or 1 : 2 : 3.
ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.
iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.
Answer : B
Answer: B
Question: John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 : 1/4 : 1/5 . What is the minimum no. of pencils that the person should have?
Options:
A)56
B)65
C)75
D)77
E)81
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.
D)
Answer: D