divelab/Sys2Bench huggingface dataset:
Question: Before being simplified, the instructions for computing income tax in country R were to add 4 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 I?
Options:
A)50 + I/200
B)50 + 3I/100
C)50+ I/40
D)100+ I/50
E)50+ 9I/200
Rationale: Income of a person is I
4 percent of ones annual income = 4I/100
100 units of Country R's currency = 100
1 percent of one's annual income = I/100
Average of 100 units and 1 percent annual income = 50 + I/200
Sum of average and 4 percent = 4I/100 + 50 + I/200
= 50 + 9I/200
So answer is E.
Answer: E
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
Options:
A)33
B)66
C)88
D)47
E)88
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D
Answer: D
Question: A rectangular football field is fenced on all four sides. The length of the football field is twice the length of its breadth. The cost of fencing the field was $360. The football management has decided to change the dimensions of field by increasing the breadth by 50% of its original value and reducing the length by 5% of its original value and fence the field again.. What will be the cost of the new fencing?
Options:
A)$360
B)$180
C)$425
D)$408
E)$415
Rationale: Let's take x to be the breadth. Then the length of the football field is 2x.
The perimeter of the old football field is x + 2x + x + 2x = 6x.
Now, for the new football field:
The new breadth = 1.5 times old breadth = 1.5x
The new length is 0.95 times old length = (.95)2x = 1.9x
So the new perimeter is 1.5x + 1.9x + 1.5x + 1.9x = 6.8x.
for old perimeter rate is $360
For new perimeter = (360 * 6.8)/6
= 408
Ans - D
Answer: D
Question: Reeya obtained 65, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average
Options:
A)70
B)75
C)80
D)85
E)90
Rationale: Explanation:
(65+67+76+82+85 / 5)=75
Option B
Answer: B
Question: In a lottery, there are 10 prizes and 35 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/10
B)2/5
C)2/7
D)2/9
E)None
Rationale: Solution
P(getting a prize)	= 10 / (10+35)
‹=› 10 / 45
‹=› 2 / 9.
Answer D
Answer: D
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
Options:
A)8.5%
B)50%
C)x/12%
D)60/x%
E)500/x%
Rationale: total dist = x miles
time take to clear 5 mile section at 30 miles/hr = 5/30 = 1/6 hr
time taken to clear x-5 miles section at 60 miles/hr = x-5/60 hr
Total time = 1/6 + x-5/60 = x+5/60 hr
Total time to clear x miles if he traveled at constant rate of 60 miles/hr = x/60 hr
Extra time = 5/60 = 1/12 hr
Percentage greater = (1/12)/(x/60) * 100% = 500/x %
ANSWER:E
Answer: E
Question: When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
Options:
A)k + 1
B)k -11
C)4k + 2
D)(k-3)/3 +2
E)k/3
Rationale: First, because k/6 leaves a remainder of 3, we know k must be odd.
(k=6x+3 = 3(2x+1) = odd*odd = odd)
Knowing k is odd we can examine the answer choices:
a. k + 1 --> odd + 1 --> must be even
b. k -11 --> odd - odd --> must be even
c. 4k + 1 --> 4*odd + 1 = even + 1 --> must be odd
d. (k-3)/3 +2 --> (6x+3-3)/3 + 2 = 2x + 2 --> must be even
e. k/3 --> (6x+3)/3 = 2x+1 = Must be odd
ANSWER:C
Answer: C
Question: what is the smallest integer that is multiple of 3,5,9
Options:
A)A)70
B)B)45
C)C)200
D)D)280
E)E)140
Rationale: It is the lcm of 3, 5 and 9 which is 45.
The answer is B.
Answer: B
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
Options:
A)36/141
B)36/145
C)24/122
D)20/133
E)21/113
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: B
Question: f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2)
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: f(x) + 3f(8 - x) =f(2) + 3f(6) = 2 : x = 2 above
f(6) + 3f(2) = 6 : x = 6 above
f(6) = 6 - 3f(2) : solve equation C for f(6)
f(2) + 3(6 - 3f(2)) = 2 : substitute
f(2) = 2 : solve above equation
correct answer C
Answer: C
Question: A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is?
Options:
A)870m3
B)277m3
C)270m3
D)220m3
E)170m3
Rationale: Volume will be length * breadth * height, but in this case two heights are given so we will take average,
Volume=(12∗9∗(1+42))m312∗9∗2.5m3=270m3
Answer: C
Answer: C
Question: A little old lady lives in a house with only her children and the children each have pets. She has twice as many sons as daughters. Each son has a dog, and each daughter has a cat. If the total number of pets and children living with her are Y, then how many dogs live in the house, in terms of Y
Options:
A)Y/8
B)Y/2
C)2*Y
D)3*Y
E)Y/3
Rationale: Since Y is the total of all children and pets, Y = Boys + Girls + Dogs + Cats
Since each boy has a dog then, Boys = Dogs. Since each Girl has a Cat then, Girls = Cats
Thus Y = 2*Boys + 2*Girls
Since there are twice as many boys as girls, Girls = Boys/2.
Thus Y = 2*Boys + 2*(Boys/2) Which simplifies to Y = 2*Boys + 1*Boy, or Y = 3*Boys
Since Boys = Dogs ... Y=3*Dogs
Which converts to Dogs = Y/3
Answer: E
Answer: E
Question: A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 20 men leave the bus and ten women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
Options:
A)15
B)90
C)36
D)45
E)46
Rationale: Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 20) = (x + 10) or x = 30.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 90.
Answer: B
Answer: B
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 39
Options:
A)11
B)13
C)15
D)17
E)19
Rationale: P Ã· 44 = 432
=> P = 432 * 44 = 19008
P / 39 = 19008 / 39 = 487, remainder = 15
C
Answer: C
Question: The average height of 35 boys in a class was calculated as 183cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
Options:
A)178.27 cm
B)181.29 cm
C)978.29 cm
D)178.89 cm
E)176.29 cm
Rationale: Calculated average height of 35 boys = 183 cm.
Wrong total height of 35 boys = 183 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 183 cm - (166 cm - 106 cm)/35
= 183 cm - 60 /35 cm
= 183 cm - 1.71 cm = 181.29 cm.
Answer: B
Answer: B
Question: If Y < X and XM >YM, what must be true?
Options:
A)M < X.
B)M < Y.
C)X < 0.
D)M > 0.
E)Y < 0.
Rationale: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when ve is multiplied on both sides. That means M is ve
D is the answer
Answer: D
Question: The banker's discount on Rs.1650 due a certain time hence is Rs.165. Find the true discount and the banker's gain.
Options:
A)12
B)15
C)18
D)21
E)None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1650 / 165
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.165,
T.D	= Rs.(10 / 11 x 165)
= Rs.150.
And, B.G	= Rs(165 - 150)
= Rs.15.
Answer B
Answer: B
Question: In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 7 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?
Options:
A)27/343
B)3/7
C)27/125
D)341/422
E)9/125
Rationale: Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.
chances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel
chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33*21/32*20/31*19/30*18/29=81/422
chances that at least 1 customer bought a coffee and a bagel= 1 - 81/422 = 341/422
Answer D.
Answer: D
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 6 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
Options:
A)64
B)65
C)67
D)68
E)70
Rationale: Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:
Assuming x motorcycles were sold every month initially.
(568000/x + 1000)(x-6) = 594000
(568/x + 1)(x-6) = 594
Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 6 = 65 bikes this month
Answer (B)
Answer: B
Question: An article is bought for Rs.695 and sold for Rs.900, find the gain percent?
Options:
A)30 1/3%
B)33 1/3%
C)23 1/3%
D)35 1/3%
E)29 69/139%
Rationale: E
29 69/139%
695 ---- 205
100 ---- ? => 29 69/139%
Answer: E
Question: Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 1,20,000 earned at the end of 3 years from the start of the business in 2010?
Options:
A)Rs.40000
B)Rs.50000
C)Rs.60000
D)Rs.70000
E)None of these
Rationale: Explanation :
Aish : Roshan : Atul
= (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1
Roshan's share = Rs. 120000 x 2/6
= Rs. 40000.
Answer : A
Answer: A
Question: Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Options:
A)4
B)7
C)9
D)13
E)12
Rationale: Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
ANSWER IS A
Answer: A
Question: A,B worker are doing a job. Worker A takes 8 hours to do a job. B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.
Options:
A)4 4/9
B)3 3/9
C)3 2/9
D)5 2/9
E)6 4/9
Rationale: In this type of questions, first we need to calculate 1 hours work, then their collective work as,
A's 1 hour work is 1/8
B's 1 hour work is 1/10
(A+B)'s 1 hour work = 1/8 + 1/10
= 9/40
So both will finish the work in 40/9 hours
= 4 4/9
ANSWER A
Answer: A
Question: A shopkeeper sold an article at $100 with 40% profit. Then find its cost price?
Options:
A)$120
B)$100
C)$91
D)$71
E)$69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/140 = $71(approximately)
Answer is D
Answer: D
Question: An investment of d dollars at k percent simple annual interest yields $200 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period?
Options:
A)(2d)/3
B)(3d)/4
C)(4d)/3
D)(3d)/2
E)8d
Rationale: 200 dollars in 2 years means 100 dollars in 1 year.
To get 2400 dollars' it will take 24 years.
To get 2400 in 3 years, we need 24/3 =8 times money. Answer is E.
Answer: E
Question: In a match, awards are given to each of 11 members of the team and a trophy to the team. In all winning team gets 2.75kg weight awards. If the weight of match wining trophy is 1.275kg, what the weight of each player giving weight of trophy ?
Options:
A)134.09 gms
B)144.09 gms
C)154.09 gms
D)164.09 gms
E)174.09 gms
Rationale: Total weight of all the awards for winning team is 2.75kg = 2750gms
trophy weight is 1.275 kg=1275gms
now rest weight = 2750-1275= 1475gms
rest weight divided in 11 players is = 1475/11 = 134.09 gms
ANSWER:A
Answer: A
Question: 10^25 - 760 is divisible by all of the following except:
Options:
A)A.12
B)B.8
C)C.5
D)D.4
E)E.7
Rationale: The last three digits ( 1000 - 760 ) 240
240 is divisible by 12,4,8,5
240 is not evenly divisible by 7 so the answer is E) 7
Answer: E
Question: If N = 16 × 10^(-p) and −4 < p < 4, how many different integer values of p will make N a perfect square?
Options:
A)0
B)2
C)3
D)5
E)7
Rationale: I think the answer should be C.
Thoose are P-Values that satisfy given restriction: -2, 0, 2 (note, a fraction can be also a perfect square) --> 16*100, 16*1, 16/100
Answer: C
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
Options:
A)9:38
B)9:31
C)9:390
D)9:36
E)9:33
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: B
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Options:
A)109620
B)106920
C)109260
D)102960
E)120960
Rationale: In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8!/(2!)(2!)= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =4!/2!	= 12.
Therefore, Required number of words = (10080 x 12) = 120960.
Answer is E.
Answer: E
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is
Options:
A)0.8904
B)0.5904
C)0.5909
D)0.8904
E)0.5984
Rationale: Explanation:
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: Option B
Answer: B
Question: In a certain code '13' means 'stop smoking' and '59' means 'injurious habit'. What is the meaning of '9' and '5' respectively in that code ?
I. '157' means 'stop bad habit'.
II. '839' means 'smoking is injurious'.
Options:
A)If the data in statement I alone are sufficient to answer the question
B)If the data in statement II alone are sufficient answer the question
C)If the data either in I or II alone are sufficient to answer the question;
D)If the data even in both the statements together are not sufficient to answer the question
E)If the data even ether are not sufficient to answer the question
Rationale: Explanation:
'59' means Injurious habit' and '157' means 'stop bad habit' (from I). Thus, the common code number '5' stands for common word 'habit'. So. '9' represents 'injurious'.Hence, I is sufficient.
Also, '59' means Injurious habit' and '839' means 'smoking is injurious'. Thus, the common code number '9' stands for common word 'injurious'. So, '5' represents 'habit'. Thus, II is also sufficient.
Answer: C
Answer: C
Question: How many numbers between 100 and 672 are divisible by 2, 3, and 7 together?
Options:
A)112
B)77
C)267
D)14
E)99
Rationale: Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 672
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 672:
672/42 = 14
Hence, 42*16 = 672 is the last number divisible by 42 within 672
Hence, total numbers divisible by 2, 3, 7 together are (16 â€“ 2) = 14
ANSWER: D
Answer: D
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)28
B)266
C)990
D)20
E)11
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Answer: D
Answer: D
Question: From the word 'JAMIE', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
Options:
A)5
B)8
C)3
D)2
E)1
Rationale: Explanation:
The words formed are
JAM
Answer: E) 1
Answer: E
Question: 15 51 216 1100 ? 46452
Options:
A)6630
B)6650
C)6560
D)6530
E)None of these
Rationale: The format of the series
15*3+6=51
51*4+12=216
216*5+20=1100
1100*6+30=6630
6630*7+42=46452
ANSWER:A
Answer: A
Question: The total number of even prime number is
Options:
A)0
B)1
C)2
D)3
E)None of these
Rationale: Solution
There is only one prime number, namely 2.
Answer C
Answer: C
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Irin bake?
Options:
A)0.125%
B)1.25%
C)12.5%
D)56%
E)0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, irin baked 9*9.18 cookies or 83 cookies (approx)
% share = 83/148 = 56.1 approx
Hence, answer is D
Answer: D
Question: What will be the compound interest on a sum of Rs. 24,500 after 3 years at the rate of 12% p.a.?
Options:
A)s.9920.736
B)s.10823.20
C)s.10123.20
D)s.10123.29
E)s.10123.28
Rationale: Explanation:
Amount = [24500 * (1 + 12/100)3]
= 24500 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (34420.74 - 24500) = Rs. 9920.736
Answer:A
Answer: A
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Options:
A)120
B)720
C)4320
D)2160
E)None
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Option B
Answer: B
Question: The G.C.D. of 1.08, 0.36 and 0.15 is?
Options:
A)0.03
B)0.9
C)0.03
D)0.108
E)none of these
Rationale: Given numbers are 1.08,0.36 and 0.15.
H.C.F of 108, 36 and 15 is 3
H.C.F of given numbers=0.03.
Correct Options:C
Answer: C
Question: If a population of women in a town is 30% of men . What is the population of men as a % of population of women ?
Options:
A)A)333%
B)B)100%
C)C)50%
D)D)65%
E)E)110%
Rationale: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.
IF....
Men = 10
Women = 3
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/3 = 333%
Answer is A
Answer: A
Question: Which of the following is equal to 10^-(-3)^1?
Options:
A)1/(10^5)
B)1/(10^6)
C)1/(10^3)
D)1/(10^8)
E)1/(10^9)
Rationale: 10^-(-3)^1 => 10^-(-3^1) => 10^-(3) = 1/(10^3)
Answer : C
Answer: C
Question: There are 12 red balls, 10 blue balls, 14 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
Options:
A)10
B)23
C)42
D)40
E)16
Rationale: The worst case scenario would be if we pick 11 red balls, 9 blue balls, 13 (?) balls and 8 black balls. In this case we'll have 11+9+13+8=41 balls and still won't have all the balls of one color. The next 42rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: C.
Answer: C
Question: A work can be completed by 12 boys in 24 days and 12 girls in 12 days. In how many days would the 6 boys and 6 girls working together complete the work?
Options:
A)12
B)18
C)16
D)20
E)24
Rationale: In 1 day, 12 boys does 1/24 of the total work.
=> In 1 day, 1 boy does 1/(24*12) of the total work
=> In 1 days, 6 boys do 6/(24*12) = 1/48 of the total work
In 1 day, 12 girls do 1/12 of the total work.
=> In 1 day, 1 girl does 1/(12*12) of the total work
=> In 1 day, 6 girls do 6/(12*12) = 1/24 of the total work
In 1 day, 6 boys and 6 girls do 1/48 + 1/24 of the total work
=> In 1 days, 6 boys and 6 girls do 3/48= 1/16 of the total work
So, 6 boys and 6 girls complete all work in 16 days.
Hence, the answer is C
Answer: C
Question: Find the greatest number of five digits to which if 7143 is added, the final number becomes exactly divisible by 18, 24, 30, 32 and 36.
Options:
A)22391
B)81111
C)27999
D)27711
E)99417
Rationale: LCM of 18, 24, 30, 32 and 36 is 1440. 99999 + 7143 = 107142. Dividing 107142 by 1440, the remainder is 582. ∴ Required number = 99999 – 582 = 99417 Alternate Method: Cross check with options.
Answer:E
Answer: E
Question: In the xy-coordinate system, what is the slope of the line that goes through the point (4, 4) and is equidistant from the two points P = (0, 2) and Q = (12, 8)?
Options:
A)0.1
B)0.3
C)0.5
D)0.7
E)0.9
Rationale: First, get the middle coordinate between (0,2) and (12,8)...
x = 0 + (12-0)/2 = 6
y = 2 + (8-2)/2 = 5
Second, get the slope of (6,5) and (4,4). m = 5-4 / 6-4 = 1/2 = 0.5
Answer: C
Answer: C
Question: 10 positive integers are arranged in ascending order. The range of first seven is 25 and last 7 is 30. What will be the difference in minimum range of the set in following 2 cases
1) when 10 integers are distinct.
2) when the integers can be repeated in the set?
Options:
A)3
B)5
C)7
D)25
E)30
Rationale: Let's assume the set starts from 1.
Case 1) when 10 integers are distinct.
1st position = 1
4th position = 4
7th position = 26
10th position = 34
Minimum Range of the set = 33
Case 2) when the integers can be repeated in the set.
1st position = 1
4th position = 1
7th position = 26
10th position = 31
Minimum Range of set = 30
Difference in Minimum Range = 33 - 30 = 3
Answer: A
Answer: A
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.6
B)1.3
C)1.4
D)1.5
E)1.1
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Answer: D
Question: John began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after John?
Options:
A)35
B)55
C)39
D)40
E)60
Rationale: Carla starts 30 minutes later and it takes 3 hr for carla to meet John
So John total time travelled = 3hr + 30 minutes
John distance = 30 * (3 1/2) = 105
so carla need to travle 105 to meet John in 3 hrs
speed of carla = 105/3 = 35 miles per hour
Answer is A
Answer: A
Question: A box contains 6 white, 5 red and 8 white marbles. 5 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
Options:
A)19/11628
B)36/11628
C)613/11628
D)6113/11628
E)63/11628
Rationale: Explanation:
Total marbles in a box = 6 black + 5 red + 8 green marbles = 19 marbles
5 marbles are drawn from 19 marbles at random. Therefore,
n(S) = 19C5 = 11628 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 6C5+ 5C5 + 8C5 = 6 +1+ 56= 63
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 63/11628
ANSWER:E
Answer: E
Question: The cost price of 11 articles is equal to the selling price of 10 articles. What is the profit percent?
Options:
A)5%
B)10%
C)15%
D)20%
E)25%
Rationale: 10*SP = 11*CP
SP = 1.1*CP
The profit percent is 10%.
The answer is B.
Answer: B