divelab/Sys2Bench huggingface dataset:
Question: You enter a weight loss challenge game and manage to lose 12% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?
Options:
A)10.24%
B)9.22%
C)9%
D)14%
E)12%
Rationale: (100%-12%)*(100%+2%) = 0.88*1.02 = 10.24%
The weigh in records your weight loss at 10.24%!
The Answer is A
Answer: A
Question: A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 30 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
Options:
A)2
B)8
C)4
D)6
E)5
Rationale: Explanation:
He covered 5 km in 1 hour , so he might cover 30 km in 6 hours.
But he took 10 hours.
He would have saved 10 â€“ 6 = 4 hours.
Answer: C
Answer: C
Question: A worker's daily wage is increased by 40% and the new wage is $28 per day. What was the worker's daily wage before the increase?
Options:
A)$18
B)$20
C)$22
D)$24
E)$25
Rationale: Let x be the daily wage before the increase.
1.4x = $28
x = $20
The answer is B.
Answer: B
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A)10 years
B)40 years
C)30 years
D)50 years
E)20 years
Rationale: Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
Answer: B
Answer: B
Question: The circulation for magazine X in 1981 was 5 times the average (arithmetic mean) yearly circulation for magazine X for the years 1982-1990. What is the ratio of the circulation in 1981 to the total circulation during 1981-1990 for magazine X ?
Options:
A)1/5
B)1/4
C)5/14
D)5/9
E)5/6
Rationale: There are 9 years from 1982-1990, inclusive. Let's say the average circulation every year between 1982-1990 inclusive is x.
So the total circulation is 9x from 1982-1990, inclusive.
In 1981, the circulation is 5x.
So total circulation for 1981-1990 is 5x + 9x = 14x.
Ratio of circulation in 1981 to total circulation during 1981-1990 is 5x to 14x or 5/14.
ANSWER:C
Answer: C
Question: A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min
48 sec. What is the actual speed of the car?
Options:
A)30 km/hr
B)35 km/hr
C)25 km/hr
D)40 km/hr
E)45 km/hr
Rationale: time 1 hr 40 min 48 sec
= 1 hr + 40/60 hr + 48/3600
1 +2/3+1/75=126/75
distance = 42 km
speed = 42 * 75 /126 = 25 km/hr
that is 5/7 of the actual speed = 25
actual speed = 25 * 7/5 = 35 km/hr
ANSWER B
Answer: B
Question: A fort of 400 soldiers has provisions for 10 days. After 2 days some of them left and the food was now enough for the same period of 10 days as before. How many of them left?
Options:
A)80
B)90
C)100
D)110
E)120
Rationale: 2000 ---- 50
400 ---- 8
x ----- 10
x*10 = 400*8
x=320
400
-------
80
Answer: A
Answer: A
Question: A factory produces x widgets per day. The factory's fixed costs are $8420 per day. The price per widget is $80 and the variable costs are $20 per widget. How many widgets need to be produced for profits of $5440 a day?
Options:
A)42.33
B)90.33
C)168
D)231
E)400
Rationale: profits=5440=60x-8420--> x=231
Answer D.
Answer: D
Question: In a group of Hens and Goats, the total number of legs are 28 more than twice the number of heads. Find the total number of Goats.
Options:
A)A)16
B)B)12
C)C)14
D)D)8
E)E)6
Rationale: Explanation :
Let the number of Hens be d
and number of goats be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 28 + 2(c + d)
=> d + 2c = 14 + c + d
=> 2c = 14 + c
=> c = 14
Answer : C
Answer: C
Question: Sum of the numbers from 1 to 35 is
Options:
A)630
B)660
C)670
D)450
E)None of these
Rationale: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2
Substitute n = 35.
So S20=35Ã—36/2=630
Correct Option: A
Answer: A
Question: A basketball coach will select the members of a five-player team from among 12 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?
Options:
A)1/9
B)1/6
C)2/9
D)5/33
E)1/3
Rationale: you can but that will require more cases and will be time consuming.
straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 10c3
total number of ways of selecting 5 players out of 12 = 12c5
probability = 10c3/12c5 = 5/33
D
Answer: D
Question: A trader wants 10% profit on the selling price of a product whereas his expenses amount to 15% on sales. What should be his rate of mark up on an article costing 9?
Options:
A)20%
B)66 2⁄3%
C)30%
D)100⁄3%
E)None of these
Rationale: Let the SP of the article be x
Expenses = 15% of x = 0.15x
Profit = 10% of x = 0.10x
CP = 9 (given)
Therefore, 9 + 0.15x + 0.1x = x ⇒ x = 12
∴ % increase for marked price = 12−9/9×100=100/3%
Answer D
Answer: D
Question: The average age 15 girls of a class is 15 years. Out of these, the average age of 12 girls is 13 years and that of the other 3 girls is 14 years. The age of the 15th girl is?
Options:
A)35
B)30
C)31
D)28
E)27
Rationale: Age of the 15th girl = 15*15 - (12*13+3*14) = 225-198 = 27 years
Answer is E
Answer: E
Question: If 189*s is a perfect square then s can be which of the following numbers?
Options:
A)21
B)35
C)54
D)105
E)150
Rationale: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 945 are 3 *3 *3 * 7
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice A completes the pairing of 3, 7. It adds a3, a5, and a7to the prime factors of 945 (3*3*3*7) and makes it a perfect square.A
Answer: A
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is -
Options:
A)1/5
B)1/3
C)1/4
D)118/2
E)21/4
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: C
Question: Which of the following set is equivalent to set A= {a,b,c,d,e}
Options:
A)B= {1,2,3,4,5}
B)B= {c,a,b,f}
C)B= {-1,0,2,4}
D)B= {-1,2,4}
E)None of these
Rationale: Number of elements of A= Number of elements of B
ANSWER:A
Answer: A
Question: To which of the following shapes the area can't be calculated if the perimeter is given?
Options:
A)Circle.
B)An isosceles right triangle.
C)Rectangle.
D)A regular Hexagon
E)Square.
Rationale: Except for a rectangle all other geometric shapes are dependent on one variable, and thus we can calculate one unique value of the area if we are provided the perimeter.
A. Circle -> Radius
B. An isosceles right triangle -> One side.
C. Rectangle -> Length and breadth.
D. A regular Hexagon -> Side of the hexagon
E. Square -> Side.
ANSWER:C
Answer: C
Question: A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 7600 a year. What is his average monthly income?
Options:
A)2000
B)2010
C)2100
D)2200
E)2300
Rationale: Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 7600 = Rs. 27600
So, Average monthly income = 27600/12 = Rs. 2300
E
Answer: E
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 53 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week?
Options:
A)48
B)50
C)52
D)54
E)56
Rationale: Annie earned 40x + 13(2x) = 66x
Let H be the number of hours that Harry worked.
Harry earned 30x + 1.5x(H-30) = 66x
(1.5x)(H) = 81x
H = 54 hours
The answer is D.
Answer: D
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 48 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)19.9
D)16.7
E)22.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 48 Paise is given as tax
=> Total tax incurred = 48 Paise = Rs.48/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 48/100
⇒ 6(25 −0.3 −x) = 48
⇒ (25 − 0.3 − x) = 8
⇒ x = 25 − 0.3 − 8 = 16.7
D)
Answer: D
Question: In a room filled with 7 people, 2 people have exactly 1 sibling in the room and 5 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
Options:
A)5/21
B)3/7
C)4/7
D)5/7
E)16/21
Rationale: There are suppose A B C D E F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 5 people who have exactly 2 siblings....(E has F and G as his/her sibling and so on..)
there are now 3 different set of siblings (A and B)
(C and D);(EFG)
Now first selecting 2 people out of 7 is 7C2=21
first sibling pair----(A and B)--selecting 2 people --2C2=1
second sibling pair (C and D)--selecting 2 people--2C2=1
third sibling pair (E F G)--selecting 2 out of 5 --5C2=10
total= 1+1+10=12
but,a/c to formula P(success)-1-p(fail)
here,p(failure)is selecting 2 people who are siblings
=12/21(21 is 7C2)
=1-12/21
=9/21
=3/7 ANS B
Answer: B
Question: The price of a certain bicycle this year is $1325, which is 6 percent greater than the cost of the bicycle last year. What was the price of the bicycle last year?
Options:
A)$1150
B)$1175
C)$1200
D)$1225
E)$1250
Rationale: The price of the bicycle last year was $1325/1.06=$1250
The answer is E.
Answer: E
Question: If (x - 1)^2 = 289, which of the following could be the value of x - 3?
Options:
A)18
B)16
C)14
D)-17
E)-19
Rationale: (x - 1)^2 = 289
(x - 1) = 17 or -17
x = 18 or -16
x - 3 = 15 or -19
The answer is E.
Answer: E
Question: Rajiv can do a piece of work in 10 days , Venky in 12 days and Ravi in 15 days. They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed. In how many days is the work completed ?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: (Rajiv +venky+ravi) 2 days work= 2(1/10+1/12+1/15)=1/2
ravi works alone for last 3 days = 3*1/15=1/5
total work 1/2+1/5=7/10
remaining work=1-7/10=3/10
(venky+ravi) 1 days work=1/12+1/15=9/60=3/20
3/10 work will be done by venky and ravi in 3/10*20/3=2 days
total days is the work completed= 2+3+2=7 days
ANSWER:A
Answer: A
Question: If the sides of a triangle are 20 cm, 12 cm and 16 cm, what is its area?
Options:
A)70
B)79
C)85
D)96
E)92
Rationale: The triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm.
Area of the triangle = 1/2 * 12 * 16 = 96 cm2
Answer: Option D
Answer: D
Question: A dishonest milkman sells a 50 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?
Options:
A)2:5
B)13:12
C)2:3
D)3:2
E)5:3
Rationale: ............................... Milk ............... Water ....................... Total
Initial ...................... 30 .................... 20 .............................. 50
20 Lts mix. taken out 30-12 ............... 20-8 ........................... 50-20
20 Lts milk added..... 18+20 ................ 12 ..............................50
20 Lts mix. taken out 38-12 ............... 12-8 ........................... 50-20
20 Lts water added..... 26 ................ 4+20 .............................. 50
New ratio = 26:24 = 13:12
B
Answer: B
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
Options:
A)420
B)840
C)1260
D)2520
E)5040
Rationale: The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.
Answer: A.
Answer: A
Question: John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 3 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
Options:
A) 4y
B) 17y/3
C) 6y
D) 8y
E) 9y
Rationale: Let $x be the advance that both receive = 3x
Amount earned per hour by John and Mary = x/10 and x/7
Mary gives $y to John to make the wages earned equal
Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/7
Solve (x+y)10 = (x-y)/7
7x + 7y = 10x -10y
3x = 17y
x = 9y
Ans. B
Answer: B
Question: In a function they are distributing noble prize. In how many ways can 2 prizes be distributed among 9 boys when a boy gets any no. of prizes?
Options:
A)36
B)42
C)81
D)69
E)70
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the 2 prizes can be given in 9 ways, i.e. (9 x 9) ways = 92 ways = 81 ways Or nr ways = 92 ways = 81 ways
Answer: C
Question: Allen and Drake were born on consecutive years on the same date. What could be their ages if teh sum of their age is 23 years?
Options:
A)11 and 12 years
B)9 and 10 years
C)8 and 9 years
D)12 and 13 years
E)All of these
Rationale: Let the age of Allen and Drake be x and x+1
x + x+1 + 23
x = 11
The age of Allen and Drake is 11 and 12 years.
Answer : A
Answer: A
Question: Which number is the odd one out under the list of numbers?
Options:
A)84129
B)47232
C)84123
D)67626
E)72927
Rationale: B
47632
All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.
Answer is B
Answer: B
Question: Two trains 250 m and 500 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.6
B)10.9
C)10.4
D)27
E)10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 250 + 500 = 750 m.
Required time = 750 * 9/250 = 27 sec
Answer: D
Answer: D
Question: A package contains 8 black and 11 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)3/5
B)11/19
C)6/8
D)7/9
E)1/3
Rationale: Let number of balls = (8+11) = 19.
Number of white balls = 11.
P (drawing a white ball) =	11/19
B
Answer: B
Question: A train running at the speed of 110 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)298 m
B)275m
C)208 m
D)988 m
E)299 m
Rationale: Speed = 110 * 5/18 = 275/9 m/sec
Length of the train = speed * time =275/9 * 9
= 275 m
Answer:B
Answer: B
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 2 km/hr in the direction of the moving train if the speed of the train is 56 km/hr?
Options:
A)30
B)54
C)40
D)36
E)31
Rationale: Speed of train relative to man = 56 - 2= 54 km/hr.
=54 * 5/18 = 15 m/sec.
Time taken to pass the man = 600 *1/15 =40 sec.
Answer: C
Answer: C
Question: If x and y are integers and 3^(x+4) = 3^(y+2), what is y in terms of x?
Options:
A)x - 6
B)x - 5
C)x - 2
D)x + 2
E)x + 6
Rationale: Answer: A
3^(x+4) = 3^(y+2)
Since the base is the same, I isolated the equations and solved for y.
x+4 = y+2
y=x+2
Ans : D
Answer: D
Question: 23 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
Options:
A)19
B)20
C)21
D)22
E)23
Rationale: in case of cycle no of handshakes = no of persons
hence ans = 23
ANSWER:E
Answer: E
Question: How many integers from 101 to 600, inclusive, remains the value unchanged when the digits were reversed?
Options:
A) 50
B) 60
C) 70
D) 80
E) 90
Rationale: question is asking for palindrome
first digit possibilities - 1 through 5 = 5
6 is not possible here because it would result in a number greater than 6 (i.e 606 , 616..)
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 5 *10 = 50
Answer is A.
Answer: A
Question: If k^3 is divisible by 162, what is the least possible value of integer k?
Options:
A)12
B)15
C)18
D)24
E)36
Rationale: k^3 = 162*x = 2*3^4*x
The factors of k must at minimum include 2*3^2 = 18.
The answer is C.
Answer: C
Question: My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age of my father when my brother was born?
Options:
A)35years
B)34years
C)33years
D)32years
E)31years
Rationale: Let my age =x
My brother's age =x+3
My mother's age =x+26
My sister's age =(x+3)+4=x+7
=(x+3)+4=x+7
My father's age =(x+7)+28=x+35
Age of my father when my brother was born
=x+35−(x+3)=32 Answer: Option D
Answer: D
Question: A store sold cherries in the afternoon twice as many as in the morning. Throughout the day were sold 360 kg. How many kilograms were sold in the afternoon?
Options:
A)140 kg.
B)240 kg.
C)340 kg.
D)440 kg.
E)None
Rationale: Solution:
Let's suppose that х kg. were sold in the morning then 2x were sold in the afternoon. x + 2x = 360 <=>
3x = 360 <=> x = 120. In the afternoon were sold 2x = 240 kg.
Answer B
Answer: B
Question: How many ways can 5 different colored marbles be placed in 3 distinct pockets such that any pocket contains at least 1 marble?
Options:
A)60
B)90
C)120
D)150
E)180
Rationale: With 3,1,1 distribution:
# of ways to select 3 from 5
5!/3!2! = 10
# of ways to select 1 ball from 2
2!/1! = 2
# of ways to select 1 ball from 1
1!/1! = 1
How many ways to distribute 3,1 and 1 to 3 boxes? 3!/2! = 3
10*2*3 = 60
With 2,2,1 distribution:
How many ways to select 2 from 5?
5!/2!3! = 10
# of ways to select 2 from 3
3!/2!1! = 3
# of ways to select 1 from 1
1
How many ways to distribute 2,2,1 to 3 boxes? 3!/2! = 3
10*3*3=90
90+60 = 150
Answer: 150. D
Answer: D
Question: Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an odd number?
Options:
A)3/7
B)4/7
C)3/10
D)7/10
E)2/5
Rationale: There are 7 numbers higher than 3 and 3 of them are odd.
The probability is 3/7.
The answer is A.
Answer: A
Question: What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 160° each?
Options:
A)96 cm
B)108 cm
C)120 cm
D)132 cm
E)270 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 160*n
from here
n = 18
So perimeter becomes 15*18= 270
Answer :E
Answer: E
Question: How many times in a day the hands of a clock are straight?
Options:
A)12
B)322
C)87
D)22
E)771
Rationale: In 12 hours, the hands coincide or are in oppesite direction 22 times.
In 24 hours, they are at right angles 22 times.
Answer: Option 'D'
Answer: D
Question: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 2/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
Options:
A)a) 2/15
B)b) 3/15
C)c) 4/5
D)d) 2/5
E)e)1/5
Rationale: let total homes be 15
termite ridden= 1/3(15)= 5
termite ridden and collapsing = 2/5(5)=2
thus homes that are termite ridden, but not collapsing = 5-2=3
thus required ratio = 3/15=1/5
Answer E
Answer: E
Question: what is the maximum possible remainder when a number 104^n is divided by 51 ? (Assume n be any positive integer)
Options:
A)29
B)32
C)96
D)85
E)78
Rationale: let n=1 then 104/51= 2(rem)
for getting a max rem put n=5, because rem(2)*5= 32 which is less than 51
ANSWER:B
Answer: B
Question: A lady took loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was :
Options:
A)Rs. 15,000
B)Rs. 1,50,000
C)Rs. 1500
D)Rs. 1,62,000
E)None of these
Rationale: Explanation:
Principal = Rs.(100 x 5400)/(12 x 3)= Rs. 15000.
Answer IS A
Answer: A
Question: 5 20 380 144020 ?
Options:
A)20741616380
B)20841616380
C)21741616380
D)22741616380
E)20791616380
Rationale: If number=N, then next number=N*(N-1)
So 5, (5*4=20), (20*19=380), (380*379=144020), (144020*144019=20741616380)
ANSWER:A
Answer: A
Question: Three people have $26, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?
Options:
A)$72
B)$85
C)$98
D)$101
E)$202
Rationale: Solution -
Total money distributed is $196. In order to maximize median, one person has to accept $0 and remaining two people share $98 each. Hence median is $98.
ANS C
Answer: C
Question: Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes.
How much time will it take Roy to consume all the five tablets?
Options:
A)60 minutes
B)50 minutes
C)40 minutes
D)30 minutes
E)None
Rationale: Solution:
60 minutes
Explanation:
Roy will be able to consume all the five tablets in an hour.
Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.
Answer A
Answer: A
Question: The difference between a number and its two-fifth is 510. What is 10% of that number?
Options:
A)58
B)85
C)76
D)68
E)86
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
10% of 850 = 85.
Answer:B
Answer: B
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 11?
Options:
A)7
B)5
C)9
D)4
E)1
Rationale: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4, and 5 then no two numbers out of these 6 add up to 10.
Now, the next, 7th number whatever it'll be (6, 7, 8, or 9) will guarantee that two number WILL add up to 11. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 11.
Answer: A
Answer: A
Question: A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price D per t-shirt that the vendor paid for these purchases?
Options:
A)$12.20
B)$12.50
C)$12.55
D)$12.70
E)$13.00
Rationale: Correct Answer: A
Explanation: The relevant formula for this problem is Average D= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
Answer: A