divelab/Sys2Bench huggingface dataset:
Question: At a tanning salon, customers are charged $10 for their first visit in a calendar month and $3 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?
Options:
A)$1220
B)$1120
C)$1300
D)$1340
E)$1880
Rationale: I get B. This question seems too straightforward for 600+. Am I missing something?
100 first-time visits --> 100(10) = $1000
30 + 10 = 40 subsequent visits --> 40(3) = $120
Total revenue: 1000+ 120 = $1120
The answer is B.
Answer: B
Question: Maria's grandparents were celebrating their 50th anniversary. Each of the children contributed $100 and the grandchildren each contributed $80. Together, all 15 members the family collected a total of $1,300 dollars for the celebration. How many children did Maria's grandparents have.
Options:
A)3
B)5
C)8
D)9
E)10
Rationale: Let x = the number of children. That means the number of grandchildren = 15 - x.
The amount contributed by the children = 100x. The amount contributed by the grandchildren = 80(15 - x).
This means: 100x + 80(15 - x) = 1300
100x + 1200 - 80x = 1300
100x - 80x = 1300 - 1200
20x = 100
x = 5
Answer: B
Answer: B
Question: What is the speed required for a car to cover a distance of 600 km in 5 hours?
Options:
A)160 kmh
B)140 kmh
C)150 kmh
D)130 kmh
E)120 kmh
Rationale: Speed= Distance / Time
Speed = 600 / 5 = 140
Answer: B
Answer: B
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 54 more than n. What is y in terms of x ?
Options:
A)x-10
B)x-12
C)x+8
D)x+6
E)x+7
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 54 more than 10x+y
10x+y+54=10y+x
10x-x+54=10y-y
9x+54=9y
x+6=y
OR
y=x+6
Answer : D
Answer: D
Question: How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?
Options:
A)420
B)360
C)320
D)210
E)None
Rationale: Solution:
Total number of arrangements = [8! /(4! *2! *2!)]= 420.
Since, there are two 1's and two 0's, the number of arrangements in which the first 1 is before the first 2 is same as the number of arrangement in which the first 2 is before the first 1 and they are each equal to half the total number of arrangements = 210.
Answer: Option D
Answer: D
Question: If 12 men do a work in 80 days, in how many days will 16 men do it?
Options:
A)17 days
B)19 days
C)15 days
D)60 days
E)14 days
Rationale: 12 * 80 = 16 * x
x = 60 days
Answer: D
Answer: D
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $700 (before payroll deductions)?
Options:
A)1220
B)1250
C)1280
D)1310
E)1340
Rationale: total pay = 40*$12.50 + $0.16*x = 700
x = 200 / 0.16 = 1250
The answer is B.
Answer: B
Question: Each of the following equations has at least one solution EXCEPT D. Is it true?
Options:
A)2* -a = (–2)*a
B)(–2)-a = –2-a
C)(–2)a = –2a
D)-2*a = -2-a
E)2*a = (–2)*-a
Rationale: If we put a = 1 then
A. -2
B. -3
C. -2
E. 2
For D -2 = -3 wrong. If we put 0 0=-2 wrong
Answer: D
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 10% sugar. What percentage of the gallon is dye?
Options:
A) 6
B) 6.5
C) 7.5
D) 8
E) 24
Rationale: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/10
=> 4/5 = x/10 => x = 4*10/5 = 8
Answer is D
Answer: D
Question: The price of 24 apples is equal to that of 28 oranges. The price of 45 apples and 60 oranges together is Rs.1350. The total price of 30 apples and 40 oranges is
Options:
A)400
B)200
C)450
D)900
E)1300
Rationale: Price of 45 apples and 60 oranges = Rs.1350
Price of 15 apples and 20 oranges = Rs.1350/3 = Rs.450 (∵ Divided LHS and RHS by 15)
Price of 30 apples and 40 oranges = Rs.450 × 2 = Rs.900 (∵ Multiplied LHS and RHS by 2)
Answer : Option D
Answer: D
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
Options:
A)20
B)25
C)15
D)10
E)30
Rationale: P = (P*5*R)/100
R = 20%
ANSWER A
Answer: A
Question: A jogger running at 9 kmph along side a railway track is 280 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Options:
A)3.6 sec
B)40 sec
C)36 sec
D)72 sec
E)None of these
Rationale: Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (280 + 120) m = 400 m.
∴ Time taken = (400⁄10) sec = 40 sec.
Answer B
Answer: B
Question: Which of the following is not a prime number ?
Options:
A)383
B)389
C)390
D)397
E)401
Rationale: Clearly, 390 is not a prime number.
Answer : C
Answer: C
Question: The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-sixth of its original value. How many amperes of electrical current will flow through the wire?
Options:
A)2/3
B)4
C)16
D)24
E)32
Rationale: Given that, I∝1/R, I*R is a constant value.
I1*R1 = I2*R2
I1*R1 = I2*R1/6
I2 = 6*I1 = 24 amperes
The answer is D.
Answer: D
Question: If A:B = 1/2: 1/5 B:C = 1/2:1/5 then A:B:C?
Options:
A)12:24:36
B)1:2:3
C)25:10:4
D)14:12:16
E)4:
Rationale: A:B = 1/2:1/5 = 5:2
B:C = 1/2:1/5 = 5:2
--------------------
A:B:C = 8:12
Answer: C
Answer: C
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 30-sided polygon have?
Options:
A) 875
B) 405
C) 1425
D) 2025
E) 2500
Rationale: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 30.
Plugging it in, we get 405 diagonals!
Answer (B).
Answer: B
Question: A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?
Options:
A)1:2:7
B)1:2:3
C)1:2:6
D)1:2:4
E)1:2:2
Rationale: WC of A: B = 1:2
B: C = 1:2
---------------------
A: B: C = 1:2:4
Answer: D
Answer: D
Question: From the top of a building, an object is thrown upward with an initial speed of 64 ft/sec. It touches the ground 5 seconds later. What is the height of the bulding
Options:
A)80 feet
B)70 feet
C)60 feet
D)50 feet
E)40 feet
Rationale: The formula for the height H of a projectile thrown upward is given by
H(t) = -(1 / 2) g t 2 + Vo t + Ho
g is a constant and equal to 32. The initial speed Vo is known and also when t = 5 seconds H = 0 (touches the ground). Ho is the initial height or height of the building. Hence we can write
0 = -(1 / 2) (32) (5) 2 + (64) (5) + Ho
Solve the above for Ho to find the height of the building
Ho = 80 feet
Answer A
Answer: A
Question: A shopkeeper forced to sell at cost price, uses a 700 grams weight for a kilogram. What is his gain percent?
Options:
A)10%
B)9%
C)11.11%
D)42.85 %
E)None of these
Rationale: Shopkeeper sells 700g instead of 1000g.
So, his gain = 1000 - 700 = 300g.
Thus, %Gain = (300 *100)/700 = 42.85%.
answer : OPTION D
Answer: D
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,879,277 minutes earlier? (Assume standard time in one location.)
Options:
A)6:22
B)6:24
C)6:27
D)6:30
E)6:32
Rationale: 6:27 minus 2,879,277 in any way must end with 0.
The only answer choice which ends with 0 is D.
The answer is D.
Answer: D
Question: The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 20 homes?
Options:
A)$206,000
B)$210,000
C)$215,000
D)$220,000
E)$230,000
Rationale: IMO the answer has to be D.
5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 20 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 20x=120,000.
x=6,000.
The 20 houses are sold at $6,000 profit or at $206,000. (ANSWER A)
Answer: A
Question: Solve for x: 2x – y = (3/4)x + 6
Options:
A)(y + 6)/5
B)4(y + 6)/5
C)(y + 6)
D)4(y - 6)/5.
E)-4(y-6)/5
Rationale: 2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5.
correct answer B
Answer: B
Question: The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother
Options:
A)40
B)41
C)42
D)43
E)44
Rationale: Option C
Answer: C
Question: How many two-element subsets of <1, 2,3,4,5,6,7,8> are there that do not contain the pair of elements 2 and 4?
Options:
A)11
B)22
C)24
D)25
E)27
Rationale: 8C2 - 1 = 27 Answer is E
Answer: E
Question: x, y, and z are all unique numbers. If x is chosen randomly from the set {6, 7, 8, 9, 10, 11} and y and z are chosen randomly from the set {20, 21, 22, 23}, what is the probability that x and y are prime and z is not?
Options:
A)1/5
B)3/20
C)2/15
D)1/12
E)1/10
Rationale: P(x is prime) = 1/3
P(y is prime) = 1/4
If y is prime, then z is not prime since y and z are unique.
Then the probability is 1/3*1/4 = 1/12
The answer is D.
Answer: D
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 15. Which of the following is NOT a possible value for y + b?
Options:
A)24
B)21
C)20
D)17
E)15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>15 --> y+b>21.
Answer: B.
Answer: B
Question: Which of the following integers does NOT have a divisor bigger than 1 that is the square of an integer?
Options:
A)95
B)125
C)54
D)16
E)48
Rationale: Prime Factorization
95=19*5. There are no perfect squares as factors.
125=5*5*5= 5^2*5. Includes the perfect square of 25.
54=3*3*3*2= 3^2*3*2. Includes the perfect square of 9.
16=2*2*2*2=2^2*2^2. Includes the perfect square of 4.
48=2*2*2*2*3=4^2*3. Includes the perfect square of 16.
All but 95 have a perfect square as a factor so the correct answer is A.
Answer: A
Question: The value of x + x(xx) when x = 3 is:
Options:
A)A)36
B)B)16
C)C)30
D)D)64
E)E)10
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
3 + 3(33)
= 3+ 3(3 × 3)
= 3 + 3(9)
= 3 + 27
= 30
C
Answer: C
Question: Three candidates contested an election and received 3554 votes, 7926 votes, and 16520 votes respectively. What percentage of the total votes did the winning candidate receive?
Options:
A)55%
B)56%
C)57%
D)58%
E)59%
Rationale: The total number of votes polled = (3554 + 7926 + 16520) = 28000
The winner's percentage = 16520/28000 * 100 = 59%
The answer is E.
Answer: E
Question: A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h?
Options:
A)h/ √2
B)h/2
C)h/4
D)(h)^2
E)(h)^2/4
Rationale: IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E
Answer: E
Question: A toy store’s gross profit on a computer game was 10 percent of the cost of the game. If the store increased the selling price of the game from $44 to $46 and the cost of the game remained the same, then the store’s gross profit on the game after the price increase was what percent of the cost of the game?
Options:
A)10.5%
B)11%
C)12.5%
D)13%
E)15%
Rationale: Profit = 10% --> If Cost price = x then Selling price = 1.1x
1.1x = 44 --> x = 40
New Selling Price = 46 --> Profit = 6
Profit percentage = 6/40 = 3/20 = 15%
Answer: E
Answer: E
Question: The average (arithmetic mean) of four distinct positive integers is 6. If the average of the smaller two of these four integers is 6, which of the following represents the maximum possible value of the largest integer?
Options:
A)12
B)6
C)3
D)2
E)4
Rationale: Let the distinct number be A,B,C, and D
Its given A > B > C > D
also A + B + C + D =24 and A + B = 6 means C + D = 18
Since the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 12
Answer : A
Answer: A
Question: A train running at the speed of 30 km/hr crosses a pole in 24 seconds. What is the length of the train?
Options:
A)200 m
B)250 m
C)300 m
D)350 m
E)400 m
Rationale: Speed=(30 * 5/18) m/sec
= (25/3) m/sec Length of the train
= (Speed x Time)
= (25/3 * 24) m = 200 m.
Answer:A
Answer: A
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ?
Options:
A)500
B)600
C)450
D)550
E)None of these
Rationale: Explanation:
Let the lent at 5% be 'A'
(A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85
5A/100 + 90 â€“ 6A/100 = 85
A/100 = 5
=> A = 500
ANSWER IS A
Answer: A
Question: P is 60% more efficient than Q. P can complete a work in 26 days. If P and Q work together, how many days will it take to complete the same work?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: The work done by P in 1 day = 1/26
Let work done by Q in 1 day = q
q × (160/100) = 1/26
q = 100/(26×160) = 10/(26×16)
The work done by P and Q in 1 day = 1/26 + 10/(26×16) = 26/(26×16)= 1/16
P and Q together can do the work in 16 days.
The answer is C.
Answer: C
Question: A man & his wife appear in an interview for 2 vacancies in the same post.The probability of husband's selection is (1/7) & probability of wife's selection is (1/5). what is the probability that only one of them is selected?
Options:
A)4/5
B)2/7
C)8/15
D)4/7
E)2/5
Rationale: (6/7)*(1/5)+(1/7)*(4/5) = (6/35)+(4/35)= 10/35 = 2/7
ANSWER:B
Answer: B
Question: Virginia, Adrienne, and Dennis have taught history for a combined total of 75 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
Options:
A) 23
B) 34
C) 35
D) 41
E) 44
Rationale: Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D
V+A+D = 75
V= A+9
=>A = V-9
V= D-9
=> A = (D-9)-9 = D-18
D-9 + D-18 + D = 96
=> 3D = 75+ 27 = 102
=> D = 34
Answer B
Answer: B
Question: What will be the difference between simple and compound interest @20% per annum on a sum of $500 after 2 years?
Options:
A)$10
B)$20
C)$25
D)$30
E)$40
Rationale: S.I. = 500*20*2/100 = $200
C.I. = 500 * (1 + 20/100)^2 - 500 = $220
Difference = 220-200 = $20
Answer is B
Answer: B
Question: One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 7 parts soda. Compare the strength of the wine.
Options:
A)35;36
B)7 : 8
C)7 : 4
D)10 : 9
E)None of these
Rationale: 5/8 : 9/16
LCM of 8,16 = 16
(5/8)*16 : (9/16)*16
10:9
Answer is D.
Answer: D
Question: five mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?
Options:
A)6
B)24
C)120
D)60
E)720
Rationale: Arrangement of 5=5!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 5!/2=60.
Answer: D (60)
Answer: D
Question: Sales price is $60, gross profit is 140% of cost, what is the value of gross profit?
Options:
A)32
B)33
C)39
D)35
E)42
Rationale: Cost + Profit = Sales
Cost + (140/100)Cost = 60
Cost = 25
Profit = 60 - 25 = 35
Answer (D)
Answer: D
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 6/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
Options:
A)2/35
B)2/3
C)6/35
D)5/7
E)7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 6/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 6/7 x 1/5 = 6/35
ANSWER:C
Answer: C
Question: If a/b= 1.25, then b is what percent of a?
Options:
A)0.008
B)0.08
C)0.8
D)8
E)80
Rationale: You are given , a/b=1.25 ---> b< a but only 'just'. This eliminates A-C as you are asked % and as such these values will be further reduced by 1/100, making them even smaller.
Also, as b iscloseto 'c', eliminate D and mark E as the correct answer.
Alternatively, 1.25 = 5/4 ---> a/b=5/4 --> b= 4/5 (b) = 0.8a ---> b= 80% of a. E is the correct answer.
Answer: E
Question: Find the length of the longest pole that can be placed in a room 12 m long, 8 m broad and 9 m high.
Options:
A)10 m
B)12 m
C)17 m
D)19 m
E)None
Rationale: Solution
Length of longest pole = Length of the diagonal of the room
=√(12)2 + 82 + 92
‹=›√289
= 17 m.
Answer C
Answer: C
Question: If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.
Options:
A)127 cm^2
B)125 cm^2
C)120 cm^2
D)102 cm^2
E)None of them
Rationale: Let length = x and breadth = y. Then,
2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289.
Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120
Area = xy = 120 cm^2
Answer is C.
Answer: C
Question: Two pipes A and B can fill a tank in 30 and 40 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?
Options:
A)16 1/7
B)17 1/7 mins.
C)15 1/7
D)14 1/7
E)18 1/7
Rationale: Explanation:
In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as
Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/40
Part filled by (A+B) in 1 min = 1/30 + 1/40
= 7/120
So both pipes can fill the tank in 17 1/7 mins.
Option B
Answer: B
Question: John makes $60 a week from his job. He earns a raise and now makes $80 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)18%
D)21%
E)33.33%
Rationale: Increase = (20/60)*100 = 33.33%.
E
Answer: E
Question: ABCD is a square where AB =âˆš4004. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD.
Options:
A)3008
B)2002
C)1008
D)2016
E)3000
Rationale: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is
always
4004/2= 2002 .
correct answer B
Answer: B
Question: A horse is tethered to one corner of a rectangular grassy field 46 m by 20 m with a rope 17 m long. Over how much area of the field can it graze?
Options:
A)154 cm2
B)308 m2
C)227 m2
D)407 m2
E)None of these
Rationale: Area of the shaded portion
= 1⁄4 × π × (17)2 = 227 m2
Answer C
Answer: C
Question: .It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
Options:
A)20 days.
B)23 days.
C)30 days.
D)92 days.
E)97 days.
Rationale: One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)
The total no. of days required to complete the work = (75 * 20) / 50 = 30
Answer:C
Answer: C
Question: The total price of a kilogram each of Shimla apples and Red Delicious apples is 250 rupees more than the total price of a kilogram each of Red Delicious apples and Fuji apples. Fuji apples is how much cheaper than Shimla apples?
Options:
A)250
B)125
C)500
D)100
E)80
Rationale: (Shimla + Red Delicious) - (Red Delicious + Fuji) = 250
Shimla - Fuji = 250
Answer: A
Answer: A
Question: On a class test there are 5 questions. One question has been taken from each of four chapters. The first two chapters have 3 questions each, the last two chapters have 6 questions each. The fourth question can be picked from any of the four chapters. How many different question papers could have been prepared?
A.
B.
C.
D.
E.
Options:
A)540
B)1260
C)2268
D)4000
E)4860
Rationale: nIf 2 questions are picked from the first chapter: C23∗3∗6∗6C32∗3∗6∗6;
If 2 questions are picked from the second chapter: 3∗C23∗6∗63∗C32∗6∗6;
If 2 questions are picked from the third chapter: 3∗3∗C26∗63∗3∗C62∗6;
If 2 questions are picked from the third chapter: 3∗3∗6∗C263∗3∗6∗C62.
Total = 2,268.
ANS:C
Answer: C
Question: In a group of ducks and cows, the total number of legs are 32 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)11
B)12
C)14
D)16
E)18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 32
=> 2x = 32 => x = 16
D
Answer: D
Question: If 16 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?
Options:
A)95
B)90
C)85
D)80
E)64
Rationale: Let x be the number of students in the school. 0.16x students went to the trip and took more than 100$. They compose (100-75)=25% of all students who went to the trip. Therefore the toal of 0.16x/0.25=0.64x students went to the camping which is 64%.
The answer is E
Answer: E
Question: In a box of 11 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
Options:
A)1/25
B)28/55
C)2/35
D)2/55
E)1/75
Rationale: First, there are 9C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 11C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 9C3/11C3=84/165 = 28/55
Answer is B
Answer: B
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 70,000, A receives :
Options:
A)14700
B)24703
C)29400
D)33777
E)34778
Rationale: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (70000 * 21/50 ) = Rs. 29,400.
Answer: C)
Answer: C
Question: Among 600 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
Options:
A)30
B)90
C)120
D)172
E)180
Rationale: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 180
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 264 + 336 - 180 = 420
So, in the image we know that the number of students in the zone with the black boundary = 420
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 600, we can write:
420 +b+w= 600
Or,b+w= 600 - 420 = 180
That is,b= 180 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 180
E
Answer: E