divelab/Sys2Bench huggingface dataset:
Question: Two brother X and Y appeared for an exam. Let A be the event that X is selected and B is the event that Y
is selected.
The probability of A
is 17 and that of B is 29. Find the probability that both of them are selected.
Options:
A)2/63
B)2/67
C)2
D)3/31
E)4
Rationale: Given, A be the event that X is selected and B is the event that Y
is selected.
P(A)=17
, P(B)=29
.
Let C
be the event that both are selected.
P(C)=P(A)×P(B)
as A and B
are independent events:
=(17)×(29)
= 2/63
Answer is A
Answer: A
Question: At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?
Options:
A)15
B)20
C)25
D)30
E)35
Rationale: Well, first let’s take care of the “totals”. The numbers in the “totals” row must add up. If 90 are females, the other 250 – 90 = 160 must be males. Similarly, the numbers in the “totals” column must add up. If 40 are managers, then the other 250 – 40 = 210 must be associates.
Now, in the “associate” row, 135 + E = 210, which means E = 75 — the other 75 associates must be female.
Now, to find B, which is what the question is asking, we need only look at the sum in the “female” column: B + 75 = 90, which means B = 15. There are fifteen female managers in this company. Thus, the answer = (A).
Answer: A
Question: A train 150 m long running at 72 kmph crosses a platform in 28 sec. What is the length of the platform?
Options:
A)410 m
B)354 m
C)450 m
D)350 m
E)250 m
Rationale: A
410
A = (72 * 5/18)*28-150 = 410
Answer: A
Question: A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^11 and 5^12, respectively, what is the value of A?
Options:
A)-24(5^12)
B)-23(5^12)
C)-23(5^11)
D)23(5^12)
E)24(5^12)
Rationale: Ans : C
Assume that the numbers appear as shown below on the number line
A-----B-----C-----D-----E-----F-----G-----H
(5^12) (5^13)
As the values for G and H are given , we can calculate the difference between any two terms of the series .
Common Difference ,d = (5^13) - (5^12)
= (5^12) *[ 5-1 ]
= (5^12)*(4)
Also F + d = G as the terms are in equidistant and in increasing order.
So F + (5^12)*(4) = (5^12).
That is , F = (5^12) - (5^12)*(4)
= (5^12)[ 1-4]
= (5^12) (-3)
Similarly , E = F - d
= (5^12)[-3-4]
= (5^12)*(-7)
You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD BE (5^12)*(-7-4)= (5^12)*(-11)
Following this pattern , A = (5^11)*(-23)
C
Answer: C
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Options:
A)12
B)9
C)14
D)11
E)16
Rationale: Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps	4:3 :: 8 : x
Days 1:2
:.4 * 1 * x = 3 x 2 x 8
x =	(3 x 2 x 8)/(4)
x = 12.
Answer is A.
Answer: A
Question: Directions(11-15): Study the following arrangement of numbers, letters and symbols carefully and answer the questions given below:
B @ K I 9 D © 5 2 T $ M 4 E J # U R
1 A δ K 5 W 6 % F Q 7 H P 8 Z
How many such symbols are there in the above arrangement, each of which is immediately preceded by a letter but not immediately followed by a letter?
Options:
A)6
B)1
C)8
D)9
E)0
Rationale: Explanation:
Letter Symbol Number/Symbol
There is only one such combination: D © 5
Answer: Option B
Answer: B
Question: In a certain series, each term is m greater than the previous term. If the 12th term is 560 and the 9th term is 500, what is the first term?
Options:
A)140
B)240
C)340
D)540
E)640
Rationale: a + 11m = 560 (12th term)
a + 8m = 500 (9th term)
You get a = 340 and m =
Answer: C
Answer: C
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)2 : 5
B)2 : 6
C)2 : 8
D)2 : 9
E)2 : 3
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
Answer: Option A
Answer: A
Question: 1396 x 1396
Options:
A)1948816
B)1981709
C)18362619
D)2031719
E)None of these
Rationale: 1396 x 1396 = (1396)2
= (1400 - 2)2
= (1400)2 + (4)2 - (4 x 1400 x 4)
= 1948816.
Answer: Option A
Answer: A
Question: A student got 74% in math and 81% in history. To get an overall average of 75%, how much should the student get in the third subject?
Options:
A)66%
B)67%
C)68%
D)69%
E)70%
Rationale: 74 + 81 + x = 3*75
x = 70
The answer is E.
Answer: E
Question: One package of Skittles costs $6.00. There are 5 Skittles in each package. How many Skittles are in 9 packages?
Options:
A)55
B)45
C)15
D)35
E)25
Rationale: 5*9=45.Answer is B.
Answer: B
Question: Winners will be announced the following day at 8 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?
Options:
A)13
B)21
C)23
D)24
E)25
Rationale: The reasoning is as follows:-
B) can't be answer because Y<X
D) can't be answer because it XY x YX will give 4 digit number. Thus wrong
E) can't be answer because it XY x YX will give 4 digit number. Thus wrong
A) can't be answer because it XY x YX will give 3 digit number but the middle digit will not be equal to Y. Thus wrong
C) is the correct answer because Y>xwill give 1 digit numbermiddle digit is Y
C
Answer: C
Question: A batsman makes a score of 88 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
Options:
A)19
B)29
C)40
D)49
E)59
Rationale: let the average after 17th inning =x
Then average after 16th inning=(x-3)
Therefore 16(x-3)+88=17x
Therefore x=40
ANSWER:C
Answer: C
Question: A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?
Options:
A)Rs.60000
B)Rs.60228
C)Rs.62299
D)Rs.60022
E)Rs.60298
Rationale: Explanation:
Answer: A
Answer: A
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 22 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)565
B)444
C)676
D)456
E)663
Rationale: 1h ----- 6
? ------ 60
12 h
RS = 16 + 22 = 38
T = 12
D = 38 * 12 =456
Answer: D
Answer: D
Question: A 100 meter long train crosses a man standing on the platform in 5 sec. What is the speed of the train?
Options:
A)72 kmph
B)108 kmph
C)176 kmph
D)134 kmph
E)161 kmph
Rationale: S = 100/5 * 18/5
= 72 kmph
Answer: A
Answer: A
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 10 years hence?
Options:
A)58
B)59
C)62
D)70
E)80
Rationale: Explanation:
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
10 years, their ages will be 50 and 30.
Sum of their ages = 50 + 30 = 80.
E)
Answer: E
Question: There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 20 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
Options:
A)90.
B)80.
C)50.
D)40.
E)25.
Rationale: STREET-CAT DOMESTIC-Cat
70 130
(20gray+50other) 90gray+40other
Answer:D
Answer: D
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
Options:
A)8!*4!*4! Ways
B)3!*8!*4!*Ways
C)3!*4!*4! Ways
D)4!*4! Ways
E)3!*8!*4!*4! Ways
Rationale: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
Ans E
Answer: E
Question: What is the remainder when 81+82+83……+815 is divided by 6
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: Thus odd powers will have remainder 2 ; and even powers will have remainder 4
Now, 81+82+83……+81581+82+83……+815 will have the following powers -
Odd = 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 ( 8 odd powers ) ; Sum of remainder = 16
Even Powers = 2, 4 , 6 , 8 , 10 , 12 , 14 ( 7 even Powers ) ; Sum of remainder = 28
Total sum of remainder = 44
44/6 = Remainder 2
Hence correct answer will be (C) 2....
Answer: C
Question: Today is Friday. The day after 59 days will be
Options:
A)Monday
B)Tuesday
C)Saturday
D)Sunday
E)None of these
Rationale: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Friday, After 59 days, it will be = (Friday + 3 odd days)
= Monday. Answer : Option A
Answer: A
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
Options:
A) 5.5%
B) 3.6%
C) 4.4%
D) 5.2%
E) 6.0%
Rationale: Let amount spent by Jill = 100
Clothing=50, Food=20, others=30
Tax on clothing= 2.5
Tax on others=3
Percentage= 5.5/100=5.5%
Answer: A
Answer: A
Question: A city had 500 migrants in the year 1998. Since then, The number of migrants in a countrythe city has doubled every 4 years. If there were 500 migrants in the country in the year 1998, What was the increase in the population of migrants during the period from 2006 to 2010?
Options:
A)2000
B)3000
C)4000
D)8000
E)10000
Rationale: The population will increase in the following order:
1998: 500
2002: 1000
2006: 2000
2010: 4000
Difference between 2006 and 2010 = 2000
Option A
Answer: A
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Options:
A)Rs. 1900
B)Rs. 2660
C)Rs. 2800
D)Rs. 2840
E)Rs. 3000
Rationale: Explanation:
For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
B's share = Rs.(7030 X 14/37)=Rs. 2660.
ANSWER IS B
Answer: B
Question: Dana borrows 7500 pounds annually for her college education. If Dana gives her parents 5% of that amount back each month, how much will she still owe her parents after four years of college?
Options:
A)8000
B)9000
C)10000
D)11000
E)12000
Rationale: dana borrows 7500 and returns 5% per month.
so returns 375 per month. and 4500 per year.
so dana owes 7500-4500=3000 per year.
after 4 years she will owe 12000.
Ans (E)
Answer: E
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 4. The numbers are
Options:
A)12, 24, 30
B)12, 24, 38
C)12, 24, 362
D)4, 8, 12
E)12, 24, 321
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 4
\inline \fn_jvn \therefore The numbers are 4, 8, 12
Answer: D) 4, 8, 12
Answer: D
Question: In the line xy plane line m has the equation y = 4x - 8, then the line m passes through which of the following points?
Options:
A)(3, 1)
B)(3, 4)
C)(4, 2)
D)(4, 8)
E)(6, 15)
Rationale: Yes it is y=3x-8....extremely sorry for mistake....
IF that's the case then answer is D
y=3x-8
8=3X4-8
8=16-8
8=8 (satisfied)
Answer: D
Question: n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 25 ?
Options:
A)0.1
B)0.2
C)0.05
D)0.3
E)0.4
Rationale: Set N: there is 4 ways to chose a number
Set P: there is 5 ways to chose a number
so total outcome is 4*5 = 20 which is represent 20 pairs of number
now we have 1 pairs can give us 25 which are (11,14) .
1/20 = 0.05
Answer C
Answer: C
Question: Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent?
Options:
A)28%
B)23%
C)22%
D)26%
E)25%
Rationale: 800 --- 200
200 --- ? =>
200/800 *100
=25%
Answer: E
Answer: E
Question: three 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)360
E)3
Rationale: Arrangement of 3=3!. 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 3!/2=3.
Answer: E
Answer: E
Question: Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 12 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?
Options:
A)11.
B)12.
C)16.
D)14.
E)14.5
Rationale: Price of candy before price increase= 10/1.25= 8
Price of soda before price increase= 12/1.5= 8
Total price = 8+8= 16
C is the answer
Answer: C
Question: The length of the bridge, which a train 120 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)230
B)240
C)245
D)255
E)260
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (120 + x)/30 = 25/2 => 2(120 + x) = 750 => x = 255 m.
Answer: Option D
Answer: D
Question: In the quadrilateral PQRS d=8 cm, h1=6.2 cm and
h2=3.1 cm. Find the area
Options:
A)37.2
B)22
C)23
D)24
E)25
Rationale: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*8*(6.2+3.1)=37.2
ANSWER:A
Answer: A
Question: If small rectangular boxes, each measuring 4 inches by 7 inches by 8 inches are arranged in a rectangular box measuring 20 inches by 42 inches by 24 inches, how many smaller boxes fit into the larger box?
Options:
A)45
B)90
C)64
D)12
E)23
Rationale: The 4 inch side should be aligned to the 20 inch side ( 5 layer)
7 inch side should be aligned to the 42 inch side. (6 layer)
and 8 inch side should be aligned to the 24 inch side.(3 layer)
Maximum number of rectangles =5*6*3=90 Answer is B
Answer: B
Question: If a≠b and a·b≠0, which of the following may be true?
Options:
A)a/b=−b/a
B)a^2=−b^2
C)(a−b)^2<0
D)a−b=b−a
E)(a+b)(a−b)=0
Rationale: A and B are the same, but how are they wrong? Those equations still makes sense because we're not told whether a and b are integers only.
Consider a = \sqrt{-5} and b= \sqrt{5}
So, a^2 = -5
and b^2 = 5
Therefore, a^2 = - b^2 ;
ANSWER:B
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)22
B)77
C)36
D)71
E)81
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer:C
Answer: C
Question: 9log9(2) = ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
9log9(2) = 2
correct answer B
Answer: B
Question: Find the average marks of all the students in classes A and B, if :
classes A = 55 students (average marks of students is 85)
classes B = 48 students (average marks of students is 78)
Options:
A)88.5
B)46.3
C)81.7
D)78.3
E)23.4
Rationale: Sum of the marks for the class of 55 students = 55 * 85 = 4675
Sum of the marks for the class of 48 students = 48 * 78 = 3744
Sum of the marks for the class of 103 students =
4675 + 3744 = 8419
Average marks of all the students =8419/103
= 81.7
Answer:C
Answer: C
Question: The compound ratio of 7:6, 3:2 and 4:5?
Options:
A)7:5
B)1:87
C)1:6
D)1:9
E)1:2
Rationale: 7/6 * 3/2 * 4/5 = 7/5
7:5
Answer: A
Answer: A
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
Options:
A)Rs. 2160
B)Rs. 3120
C)Rs. 3972
D)Rs. 6240
E)Rs. 6000
Rationale: Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
ANSWER IS C
Answer: C
Question: A baker charges P dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: We're told that by selling cakes at P dollars/cake, a baker will make $320.
Reducing the price by 20% and selling 2 MORE cakes will also make her $320.
We're asked for the original number of cakes that the baker intends to sell.
$320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....
Let's TEST ANSWER D: 8 cakes
IF....
Original cakes = 8
8(P) = $320, so P = $40/cake
20% off = $8 off = 40-8 = $32/cake
+2 more cakes = 8+2 = 10 cakes
10(32) = $320
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
D
Answer: D
Question: present ages of A and B are in the ratio of 7:5 respectively. 5 years hence, the ratio of their ages will become 15:12 respectively . what A's present age in years?
Options:
A)20
B)7/3
C)15/4
D)21/5
E)20/3
Rationale: A and B be 7x years and 5x years respectively
(7x+5)/(5x+5)=15/12
4(7x+5)= 5(5x+5)
x = 3/5
therefore A's present age : 7x=21/5 years
correct answer(D)
Answer: D
Question: the reciprocal of the hcf and lcm of two are 1/12 and 1/312 .if one of the number is 24 then other no. is
Options:
A)126
B)136
C)146
D)156
E)166
Rationale: reciprocal of the hcf and lcm of two are 1/12 and 1/312
so, HCF = 12 , LCM = 312
LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a
so, other = 12*312 / 24 = 156
ANSWER:D
Answer: D
Question: A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?
Options:
A)24
B)30
C)36
D)90
E)96
Rationale: 120 spend $100 on gas & electricity
60 spend $100 on gas but not on electricity
For every one that spent <$100 on both there are 4 that spent $100 on electricity not gas
Let the ones that spent on neither be x
The ones that spent on just electricity will be 4x
Total households = Those who spend >$100 on both + Those who spend >$100 on just one + Those who spend <$100 on both = 120 + 60 + 4x + x
300 = 180 + 5x implies x=24
Answer is (A)
Answer: A
Question: How many tow-digit integers exist such that all their digits are even?
Options:
A)20
B)100
C)120
D)125
E)135
Rationale: 0 is also an even integer
so last digit can be filled in 5 ways- 0,2,4,6,8
for both second and third digit there are 5 possibilities-
5 X 5 = 25
_______________
The first digit can be any of the four: 2, 4, 6, or 8. For both seconddigits, there are 5 possibilities. The answer is 4∗5=20.
The correct answer is A
Answer: A
Question: In Orange County, one ninth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
Options:
A)212
B)235
C)240
D)252
E)275
Rationale: The number must be a multiple of both 9 and 7 so the answer is 252.
The answer is D.
Answer: D
Question: Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit?
Options:
A)1%
B)2%
C)3%
D)4%
E)5%
Rationale: A dozen toys cost $360, so each toy cost $30.
selling price / cost price = 30.60 / 30 = 1.02
The percentage profit is 2%.
The answer is B.
Answer: B
Question: The greatest possible length which can be used to measure exactly the length 5m, 4m 45m, 10 m 45 cm is
Options:
A)15 cm
B)25 cm
C)5 cm
D)42 cm
E)43 cm
Rationale: Explanation:
Required Length = H.C.F of 500 cm, 445 cm and 1045 c
= 5 cm. Answer: C
Answer: C
Question: Smithtown High School is holding a lottery to raise money. The tickets are assigned numbers from 1 to 200. Tickets with numbers divisible by 2 win t-shirts, tickets with numbers divisible by 3 win gift certificates, and tickets with numbers divisible by 7 win movie passes. How many tickets win none of the prizes?
Options:
A)6
B)52
C)58
D)142
E)194
Rationale: Total numbers divisible by:
3->200/3=66.66; Ignore the decimal part=66
2->200/2=100;
7->200/7=28.Something; Ignore decimal part=28
3*2->200/6=33
3*7->200/21=9
2*7->200/14=14
3*2*7->200/42=4
Thus, total numbers that can win prize= 66+100+28-33-9-14+4=142 [:Note Used the same formula as we do for overlapping sets A∪B∪C=n(A)+n(B)+n(C)−n(A∩B)−n(A∩C)−n(B∩C)+n(A∩B∩C)
Non-winnable numbers=200-142=58
Ans: "C"
Answer: C
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/7 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
Options:
A)1/2
B)7/13
C)4/13
D)8/29
E)6/33
Rationale: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 2/7 of O = 2/7*12 = 24/7 hrs to make x units
and Mach M = 3/4 of N = 3/4*24/7 = 1/6hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = 7/24 units
Mach M = x/6 units
In 1 hr, together they make - x/12+7/24+x/6 = 13/24
So what ratio of this has Mach N made?
(7/24) / (13/24) = 7/13
Ans:B=7/13
Answer: B
Question: Three rugs have a combined area of 204 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?
Options:
A)18 square meters
B)20 square meters
C)24 square meters
D)28 square meters
E)30 square meters
Rationale: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}
140 = 204 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 20.
Answer: B.
Answer: B