divelab/Sys2Bench huggingface dataset:
Question: In a class of 210 students, 70 did not opt for math. 55 did not opt for science and 42 did not opt for either. How many students of the class opted for both math and science?
Options:
A)123
B)125
C)127
D)137
E)148
Rationale: 210 students total
70 did not opt for math
55 did not opt for science
42 did not opt for either
Total of 140 students in math and 13 did not opt for sci but did for math
140-13=127
127 students of the class opted for both math and science
Answer:C
Answer: C
Question: A boy is playing with a wheel of 16 inches diameter rotating at x inches/min. Another boy is playing with a wheel of 32 inches diameter moving at the rate of y inches/min. Fin the value of x in terms of y if both the wheels cover the distance at same time.
Options:
A)2y/4
B)3y/7
C)4y/8
D)2y/10
E)1y/2
Rationale: t=S1/V1=S2/V2
or 16/x=32/y
or x=16y/32=y/2
Answer is E
Answer: E
Question: A departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $26,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
Options:
A) $235,000
B) $365,000
C) $115,000
D) $240,000
E) $160,000
Rationale: 26,000 = 0.15 *(50000) + 0.10 (x - 50000)
26000 - 7500 = 0.10 (x-50000)
185000 = x - 50000
x = 2,35,000
Answer : A
Answer: A
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?
Options:
A)10
B)12
C)8
D)15
E)18
Rationale: Explanation:
Let the required hours needed be x
More pumps, less hours (Indirect proportion)
More Days, less hours (Indirect proportion)
Hence we can write as
(pumps)3:4
(days) 2:1}: : x : 8
⇒3×2×8=4×1 × x
⇒3×2×2= x
⇒x=12
Answer: Option B
Answer: B
Question: A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4
Options:
A)II,III only
B)I only
C)I,III only
D)II only
E)III only
Rationale: question is asking for must be there elements.
According to the question if t is there t+4 must be there.
if -3 is the starting element the sequence is as follows.
S ={-3,1,5,9....}
if -3 is not the starting element the sequence is as follows
S = {...-7,-3,1,5,9...}
By observing the above two sequences we can say that 9 must be there in set S.
Answer : B
Answer: B
Question: If k > 0, x + 2k = y, and y + 4k = z, what is the ratio between z - x and y - x ?
Options:
A)1 to 4
B)1 to 2
C)2 to 1
D)3 to 1
E)4 to 1
Rationale: y-x = 2k
z-y = 4k
Let's add the two equations together:
z-x = 6k
The ratio of z-x to y-x is 6:2 = 3:1.
The answer is D.
Answer: D
Question: When a=4+(3/4) and b=4-(3/4), (2^a^2)/(2^b^2)=?
Options:
A)496
B)486
C)4096
D)456
E)426
Rationale: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=6/4 and a+b=8, 2^(a-b)(a+b)=2^(6/4)(8)=2^12=4096
Therefore, the answer is C
Answer: C
Question: What is the remainder when you divide 2^200+2 by 7?
Options:
A)1
B)2
C)3
D)6
E)5
Rationale: answer is D. this is very similar to the 32^32^32+2 divided by 7 question.
Answer: D
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)4:5
B)4:2
C)4:3
D)4:9
E)4:1
Rationale: 12:9
= 4:3
Answer:C
Answer: C
Question: In a group of pigs and hens, the number of legs are 22 more than twice the number of heads. The number of pigs is
Options:
A)5
B)7
C)10
D)12
E)11
Rationale: Explanation:
Let the number of pigs be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 22
4x + 2y = 2x + 2y + 22
2x = 22
x = 11
Answer: E
Answer: E
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction Q of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
Options:
A)1/(3x)
B)3x/(x-3)
C)(x – 3)/(3x)
D)x/(x-3)
E)(x-3)/x
Rationale: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete Q=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Answer: C
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.2120?
Options:
A)Rs.1000.15
B)Rs.1100.95
C)Rs.1892.85
D)Rs.1050.85
E)Rs.1200.25
Rationale: 2120 = P [1 + (5*12/5)/100]
P= 1892.85
ANSWER:C
Answer: C
Question: The diagonal of a rhombus are 65 m and 60 m. Its area is:
Options:
A)1940
B)1950
C)1960
D)1990
E)1980
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 × 65 × 60 ) Cm(power)2
= 65 × 30 = 1950 Cm(power)2
Answer is B.
Answer: B
Question: If 7a = 8b and ab ≠0, what is the ratio of a/8 to b/7?
Options:
A)16/14
B)8/7
C)1
D)7/8
E)64/49
Rationale: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 7a = 8b
Here's one pair: a =8 and b =7
What is the ratio of a/8 to b/7?
In other words, what is the value of (a/8)/(b/7)?
Plug in values to get: (a/8)/(b/7) = (8/8)/(7/7)
= 1/1
= 1
C
Answer: C
Question: There are 35 students in a hostel. If the no. of students increases by 4, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
Options:
A)s. 99.75
B)s. 89.75
C)s. 72.75
D)s. 58.75
E)s. 49.75
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 4) = x – 1
or, 35x + 42 = 39x – 39
or, x = 20.25
Thus the original expenditure of the mess = 35 x 20.25=708.75
Therefore x-1 = 19.25
hence 42 x 19.25 = 808.50
808.50 - 708.75 = Rs. 99.75
A
Answer: A
Question: A total of 520 players participated in a single tennis knock out tournament. What is the total number of matches played in the tournament? (Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
Options:
A)511
B)519
C)256
D)255
E)1023
Rationale: There are 520 players, only 1 person wins, 519 players lose. in order to lose, you must have lost a game.
519 games.
Ans- B
Answer: B
Question: A number when divided by 342 gives a remainder 38, what remainder will be obtained by dividing the same number 21?
Options:
A)7
B)6
C)9
D)2
E)3
Rationale: Explanation:
342 + 38 = 380/21 = 2 (Remainder)
Answer: D
Answer: D
Question: A policeman spotted a criminal from a distance of 200 metres. When the policeman starts the chase, the criminal also starts running. If the criminal was running at 10 km/hr and the policeman was chasing at the speed of 12 km/hr, find the distance the criminal will run before he is catched by the policeman ?
Options:
A)1.5 km
B)700 m
C)900 m
D)1 km
E)None of these
Rationale: Explanation :
Solution: Relative speed = (12 - 10) = 2 km/hr.
Time taken by policeman to cover 200 m = (200/1000 * 1/2) hr
= 1/10 hr.
In 1/10 hrs, the criminal covers a distance of (10*1/10) km = 1 km.
Answer : D
Answer: D
Question: Gokul had 100 currency notes in all, some of which are of Rs 60 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did he have in the denomination of Rs 50?
Options:
A)109
B)95
C)106
D)100
E)105
Rationale: Let the number of 50-rupee notes = x
Then, the number of 60-rupee notes = (100 – x)
50x + 60(100 – x) = 5000 : x = 71
ANSWER:D
Answer: D
Question: A departmental store has 9 managers and 18 associates. The 9 managers have an average salary of $1300. The 18 associates have an average salary of $12,000. What is the average salary for the departmental store?
Options:
A)$3556.25
B)$3988.89
C)$3836.56
D)$3745.56
E)$3428.56
Rationale: Number of managers is 9
Their average salary is $1300
Number of associates is 18
Their average salary is $12,000
Total salary of managers is 9*1300=$11700
Total salary of associates is 18*12,000=$96,000
Total salary for the departmental store is 96,000+11700=107700
Average salary for the departmental store is 107700/9+18=3988.89
Answer is B
Answer: B
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)21
B)56
C)18
D)25
E)23
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56
Answer:B
Answer: B
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Options:
A)10
B)6
C)5
D)4
E)3
Rationale: Explanation :
Speed of the motor boat = 15 km/hr
Let speed of the stream = v
Speed downstream = (15+v) km/hr
Speed upstream = (15-v) km/hr
Time taken downstream = 30/(15+v)
Time taken upstream = 30/(15−v)
total time = (30/(15+v)) + (30/(15−v))
It is given that total time is 4 hours 30 minutes = 4(1/2) hour = 9/2 hour
i.e.,(30/(15 + v)) + (30/(15 − v)) = 9/2
⇒ (1/(15+v)) + (1/(15−v)) = 9/(2×30) = 3/20
⇒ (15 − v + 15 + v)/(15+v)(15−v) = 3/20
⇒ (30/152)− (v2) = 3/20
⇒ (30/225−v2) = 3/20
⇒ 10/(225−v2) = 1/20
⇒225 − v2= 200
⇒ v2 = 225 − 200 = 25
⇒ v = 5 km/hr. Answer : Option C
Answer: C
Question: Working together, 7 identical pumps can empty a pool in 4 hours. How many hours will it take 5 pumps to empty the same pool?
Options:
A)4 2/3
B)9 1/4
C)9 1/3
D)9 3/4
E)5 3/5
Rationale: The answer is E
7 pumps take 4 hours. 1 Pump will take 4*7 hours . Hence 5 pumps will take (4*7)/5 = 5 6/10 = 5 3/5 hours
Answer: E
Question: How many words can be formed by using all letters of the word ‘JUPITER’ ?
Options:
A)3220
B)3640
C)4420
D)5040
E)5680
Rationale: The word contains 7 different letters.
The number of permutations is 7! = 5040
The answer is D.
Answer: D
Question: A cistern which could be filled in 5 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
Options:
A)76 hrs
B)99 hrs
C)55 hrs
D)90 hrs
E)10 hrs
Rationale: 1/5 - 1/x = 1/10
=> 10 hrs
Answer: E
Answer: E
Question: The difference between 3/5 of 2/3 of a number and 2/5 of 1/4 of the same number is 288. What is the number?
Options:
A)960
B)850
C)895
D)955
E)975
Rationale: according to the given condition
x*(2/3)*(3/5) - x*(2/5)*(1/4) = 288
so 2x/5 - x/10 = 288
or 3x/10 = 288
or x = 2880/3 = 960
ANSWER:A
Answer: A
Question: A school having three classes only have student strength of 40, 20 and 40 respectively. The pass percentages of these classes are 20%, 30% and 100% respectively. What is the pass percentage for the entire school?
Options:
A)54%
B)76%
C)34%
D)66%
E)46%
Rationale: 20% of 40+30% of 20+100% of 40
=8+6+40 =
now 54 of 100
= 54%
ANSWER:A
Answer: A
Question: There is a total of 90 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/6 and the probability that it will be green is 1/5. What is the probability that the marble will be either red or blue?
Options:
A)3/5
B)7/15
C)11/15
D)19/30
E)23/30
Rationale: P(red or blue) = 1 - P(white) - P(green) = 30/30 - 5/30 - 6/30 = 19/30
The answer is D.
Answer: D
Question: Aarti can do a piece of work in 5 days. In how many days will she complete three time of work of same type?
Options:
A)6 days
B)18 days
C)21 days
D)3 days
E)15 days
Rationale: We have the important relation, More work, More time (days)
A piece of work can be done in 5 days.
Three times of work of same type can be done in 5 x 3
= 15 days
Answer E
Answer: E
Question: Tough and Tricky questions: Word Problems.
ABZ Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
Options:
A)$4,035
B)$4,036
C)$9,035
D)$16,140
E)$36,140
Rationale: The ABZ company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Answer: C
Question: The sum of the present ages of a father and his son is 47 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:
Options:
A)13
B)15
C)17
D)19
E)21
Rationale: Let the present ages of son and father be x and (47 - x) years respectively.
Then, (47 - x) - 6 = 4(x - 6)
41 - x = 4x - 24
x = 13
The son's age after 6 years will be 19.
The answer is D.
Answer: D
Question: A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 20.00?
Options:
A)$ 10.00
B)$ 11.20
C)$ 14.40
D)$ 16.00
E)$ 18.00
Rationale: For retail price = $20
First maximum discounted price = 20 - 30% of 20 = 20-6 = 14
Price after additional discount of 20% = 14 - 20% of 14 = 14 - 2.8 = 11.2
Answer: Option B
Answer: B
Question: Population of a city decreases by 10% at the end of first year and increases by 10% at the end of second year and again decreases by 10% at the end of third year. If the population of the city at the end of third year is 4455, then what was the population of the city at the beginning of the first year?
Options:
A)5,000
B)4,500
C)4,950
D)1,000
E)2,000
Rationale: M. F = 90/100*110*100*90/100 = 81*11/1000
Population before 3Yrs = I.Q /M. F = 4455*1000/81*11
= 5000
ANSWER:A
Answer: A
Question: If N = 2^0.15 and N^b = 8, b must equal
Options:
A)3/80
B)3/5
C)20
D)5/3
E)80/3
Rationale: 15/100 = 3/20
N = 2 ^ 3/20
N^b = 2^3
(2^3/20)^b = 2^3
b = 20
Answer: C
Answer: C
Question: A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally p% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?
Options:
A)100p/(1-p)
B)80p/(1-p)
C)75p/(1-p)
D)100p/(80-0.2p)
E)100p/(80+0.2p)
Rationale: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that p = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is E: 100p/(80+0.2p) >>> 100x10 / 82
Answer: E
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?
Options:
A)8:4
B)8:7
C)8:2
D)8:3
E)8:1
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer: B
Answer: B
Question: There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 64%
Options:
A)18.75
B)19.75
C)20.75
D)21.75
E)22.75
Rationale: 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*64/100=50.40
so x=18.75
ANSWER:A
Answer: A
Question: 270 candidates appeared for an examination, of which 252 passed. The pass percentage is :
Options:
A)(93 + 1/9 )%
B)(93 + 1/3 )%
C)(93 + 9/3 )%
D)(94 + 9/3 )%
E)(43 + 1/3 )%
Rationale: Answer: B) (93 + 1/3 )%
Answer: B
Question: In an examination 80% pass in english, 70%pass in maths , 10%fail in both ,
144 pass in both . How many all appeared to the test?
Options:
A)260
B)240
C)370
D)120
E)150
Rationale: E : 80%, Fail in both: 10%, therefore only M pass is 10%
M: 70%, fail in both: 10%, therefore only E pass is 20%
100% = all fail + only E pass + only M pass + both E and M
pass
100%=10%+20%+10% + both E and M pass
Therefore, both E and M pass = 60%
60%=> 144
100% => 240
Answer: B
Answer: B
Question: A taxi charges p dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.
Options:
A)pn – c/8(100)
B)cp + 4n-8/200
C)p + (4cn-8c)/100
D)p + 100cn/4
E)4cp(n-2) – 100
Rationale: This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost p is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost p, or subtract the additional cost from p. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).
Answer: C
Question: How many words can be formed from the letters of the word ‘DIRECTOR’
So that the vowels are always together?
Options:
A)1240
B)2630
C)4702
D)2160
E)1205
Rationale: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
ANSWER D 2160
Answer: D
Question: Five persons having ages in ascending order with exact difference of 5 years, decided to donate for a charity ,an amount equal to fifty times of their ages. The total donation was Rs 8750.Find the ages of five persons ?
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: 25,30,35,40,45 are the ages.
let ages be x-10,x-5,x,x+5,x+10
given 50(5x)=8750
x=35
ANSWER:E
Answer: E
Question: If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?
Options:
A)3:1
B)8:1
C)9:1
D)12:1
E)9:1
Rationale: a1 : a2 = 3 : 1
6 a12 : 6 a22 = 9: 1
ANSWER:C
Answer: C
Question: A bag is filled with pennies and nickels in the ratio of 2 to 1. There are 10 nickles in the bag, how many coins are there in that bag?
Options:
A)30
B)50
C)65
D)70
E)80
Rationale: A ratio of pennies to nickels of 2 to 1 means that we can write the number of pennies and nickels in the form
number of pennies = 2x and number of nickels = x
But we know the number of nickels, 10. Hence
x = 10
The total number of coins is given by
2x + x = 3x = 3 × 10 = 30
Answer : A
Answer: A
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 3 cups of tea. Last week Mo drank a total of 26 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week?
Options:
A)0
B)1
C)4
D)5
E)6
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 26 T-C=10 -> T= 18. C=8.
Mo drinks 3 cups of tea a day then number of days that are not rainy = 18/3 = 6
So number of rainy days = 7-6 = 1
B is the answer.
Answer: B
Question: There are 5 orators A, B, C, D, E. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
Options:
A)5! / 3!
B)8! / 6!
C)5! x 3!
D)8! / (5! x 3!)
E)8! / (5! x 4!)
Rationale: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 2 people have to be arranged in 2 places.
Thus, 5C3 x 2! = 5! / 3!
ANSWER:A
Answer: A
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12015 after 8 years at the same rate of simple interest. The rate of interest per annum is?
Options:
A)12.05%
B)5%
C)13.05%
D)22.05%
E)18.05%
Rationale: S.I. for 3 years = (12015 - 9800) = Rs. 2215
S.I. for 5 years = Rs. 2215/3 * 5 = Rs. 3691.
Principal = (9800 - 3675) = Rs. 6108
Hence, rate = (100 * 3691) / (6125 * 5) = 12.05%
ANSWER:A
Answer: A
Question: If the two hands in a clock are 11 minutes divisions apart,then the angle between them is
Options:
A)66Â°
B)18Â°
C)24Â°
D)60Â°
E)None of these
Rationale: In a clock, each minute makes 6Â°
âˆ´ 11 minutes will make 6 Ã— 11 = 66Â°
Answer A
Answer: A
Question: Let's say in a lottery Samuel have a 4% chance of winning the jackpot.
All lined up and 1st four people on the line lose. Samuel is 5th in the row.
What's the chance of Samuel winning now?
Options:
A)2%
B)3%
C)4%
D)5%
E)6%
Rationale: Solution:
4%
Explanation:
The winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.
Answer C
Answer: C
Question: One out of every 3000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?
Options:
A)450
B)900
C)90,000
D)1350,000
E)900,000
Rationale: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 3000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/3000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1350,000.
The answer is (D).
Answer: D
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)9
B)12
C)10
D)13
E)15
Rationale: Explanation:
Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
Hence we can write as
(persons)39:30
(hours) 5:6}:: x:12
⇒39×5×12=30 × 6 × x
⇒39×5×2=30 × x
⇒39=3×x
⇒x=13
Answer: Option D
Answer: D