divelab/Sys2Bench huggingface dataset:
Question: A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per second does the larger rim makes in terms of x ?
Options:
A)4x/5
B)75x
C)48x
D)24x
E)x/75
Rationale: Let's try the explanation. We have two wheels. One with 28pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 28pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 28pi*x=35pi*a.
(28pi*x)/(35pi). = 4x/5.
Ans :A
Answer: A
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options:
A)7.5
B)7.4
C)7.9
D)7.2
E)8.0
Rationale: Net part filled in 1 hour = (1/4 - 1/9) = 1/8
The cistern will be filled in 8/1 hrs i.e., 8 hrs.Answer: E
Answer: E
Question: A train 75 metres long overtook a man who was walking at the rate of 6 km/h and passed him in 18 seconds. Again, the train overtook a second person in 15 seconds. At what rate was the second person travelling ?
Options:
A)3 km/h
B)2.5 km/h
C)4 km/h
D)1.5 km/h
E)None of these
Rationale: Let actual speed of train ST km/h.
Then, ST - 6 = 75⁄18 × 18⁄5 = 15
⇒ ST = 21 km/h
Now, let speed of second man = Sm
21 - Sm = 75⁄15 × 18⁄5 = 18
⇒ Sm = 3 km/h
Answer A
Answer: A
Question: For a three-digit number xyz, where x, y, and z are the digits of the number, f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
Options:
A)1
B)2
C)3
D)9
E)27
Rationale: Since f(abc) = 3*f(def), I would assume that f = c - 1 from the function above.
The answer should be (A)
Answer: A
Question: If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3?
Options:
A)n
B)n^-1
C)n^2
D)n^1/2
E)n^3
Rationale: A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate:
n = 1/4
n^-1 = 4
n^2 = 1/16
n^(1/2) = 1/2
n^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is n. Answer A
Answer: A
Question: Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders.The average expense per boarder is Rs. 700 when there are 25 boarders and Rs 600 when there are 50 boarders.What is the average expense per boarders when there are boarder ?
Options:
A)550
B)580
C)540
D)570
E)None of these
Rationale: Explanation :
Let x be the fixed cost and y the variable cost
17500 = x + 25y … (i)
30000 = x + 50y … (ii)
Solving the equation (i) and (ii), we get
x = 5000, y = 500
Now if the average expense of 100 boarders be ‘A’.
Then,
=> 100 × A = 5000 + 500 × 100 .
∴ A = 550.
Answer : A
Answer: A
Question: A bookstore made 11000 dollars selling 3000 math books and 1000 physics books. A customer bought 1 math book and 1 physics book and paid 7 dollars. What is the price of each book?
Options:
A)4 and 3
B)1 and 6
C)2 and 5
D)None
E)Cannot be determined
Rationale: Solution:
Let x be the price of the math book and y be the price of the physics book
x + y = 7
3000 × x + 1000 × y = 11000
Use x + y = 7 to solve for y
x - x + y = 7 - x
y = 7 - x
Substitute 7 - x for y in 3000 × x + 1000 × y = 11000
3000 × x + 1000 × (7 - x) = 11000
3000x + 7000 - 1000x = 11000
2000x = 11000 - 7000
2000x = 4000
x = 2 since 2000 × 2 = 4000
Since 2 + 5 = 7, y = 5
The price of a math book is 2 dollars and the price of a physics book is 5 dollars.
Answer C
Answer: C
Question: Find the value of x: 2x² − 4.
Options:
A)0,2
B)-2,2
C)-2,1
D)0,4
E)-1,4
Rationale: That quadratic is factored as follows:2x² − 4 = (2x − 2)(x + 2).Now, it is easy to see that the second factor will be 0 when x = −2.As for the value of x that will make2x − 4	=	0,we must solve that equation We have:2x	=	4x = 2The solutions are:x	=	-2 and 2 B
Answer: B
Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 7 miles per day and it will take them two days, how many miles long is the route down the mountain?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: On the way down, the rate is 1.5*7 = 10.5 miles per day.
The distance of the route down the mountain is 2*10.5 = 21 miles.
The answer is D.
Answer: D
Question: A can do a work in 3 days. B can do the same work in 6 days. If both A & B are working together in how many days they will finish the work?
Options:
A)3
B)5
C)4
D)2
E)6
Rationale: A rate = 1/3
B rate = 1/6
(A+B) rate = (1/3)+(1/6) = 1/2
A & B finish the work in 2days
correct option is D
Answer: D
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)30 years
B)35 years
C)40 years
D)50 years
E)55 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.
C)
Answer: C
Question: A rectangular table seats 3 people on each of two sides, with every person directly facing another person across the table. If six people choose their seats at random, what is probability that any two of them directly face other?
Options:
A)1/5
B)1/8
C)1/7
D)15/56
E)4/7
Rationale: A B C
------------
| TABLE |
------------
D E F
A to F are 6 people.
Prob to select any 1 person = 1
Prob to select the person opposite to the chosen person = 1/5
For ex. If we select A as the person than prob of choosing D is 1/5.
Hence, answer will be A.
Answer: A
Question: If a store adds 20 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 50%, what will the new inventory of chairs be?
Options:
A)40
B)60
C)100
D)140
E)160
Rationale: Explanation:
Letâ€™s say t = total current inventory of chairs. The first sentence states that 20 + t = (3/2)t. First solve for the current inventory:
20 + t = (3/2)t
20 = (3/2)t âˆ’ t
20 = (1/2)t
40 = t
The manager wants to increase this by 50%.
50% of 40 is 20, so the new inventory will be 60.
Answer: B
Answer: B
Question: Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Q represents the product of all elements in set X and if 11Q is an even number, what is the range of set X?
Options:
A) 14
B) 16
C) 17
D) 20
E) 26
Rationale: Since 11Q = Even therefore Q has to beEVENsince 11 is a odd integer (Even * Odd = Even)
Similarly, Q is the product of all integers in set X But all integers in Set X are odd except the unknown K and since X contains only prime numbers, K has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)
Since you know value of K you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =17
Answer is C
Answer: C
Question: What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.?
Options:
A)Rs. 8908.42
B)Rs. 9720
C)Rs. 10123.20
D)Rs. 10483.20
E)None
Rationale: Amount = [22000 * (1 + 12/100)3]
= 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42
C.I. = (30908.42 - 22000) = Rs. 8908.42
ANSWER:A
Answer: A
Question: If the least common multiple of 9, 10, 12,
and v is 540, which of the following
could be v?
Options:
A)18
B)24
C)27
D)36
E)45
Rationale: To begin, notice that 540 isn’t a multiple of 24, so you can rule out Choice (B). Now find
the least common multiple (LCM) of 9, 10, and 12. The LCM of 9 and 10 is 90, so the LCM of
9, 10, and 12 must be a multiple of 90. Here are the first six multiples of 90:
90, 180, 270, 360, 450, 540
The number 180 is a multiple of 12 as well, so the LCM of 9, 10, and 12 is 180. However, 180
also is a multiple of 18, 36, and 45. So if any of these numbers were v, the LCM of 9, 10, 12,
and v would be 180. As a result, you can rule out Choices (A), (D), and (E), leaving Choice(C) as your only answer.
Answer: C
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)6500
B)2500
C)5000
D)10000
E)7500
Rationale: A : B : C
=20000×24:15000×24:20000×18
=20×4:15×4:20×3
=4×4:3×4:4×3
=4:3:3
B's share = 25000×(3/10)=7500
Answer is E.
Answer: E
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.20 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)399
B)272
C)799.2
D)277
E)311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1.2 = 799.2 Answer: C
Answer: C
Question: Bill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 17 songs, what are the chances that the third song he hears will be his favorite?
Options:
A)1/17
B)1/12
C)1/11
D)3/14
E)1/3
Rationale: The player plays the songs on the album at random, so there are 17 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.
Total outcomes ==> 17
Total positive outcomes ==> 1
Correct answer is A) 1/17
Answer: A
Question: If x, y, and z are positive integers such that x^2 + y^2 + z^2 = 64,470, which of the following could be the values of x, y, and z?
I)x=541 y=401 z=100
II)x=530 y=400 z=100
III)X=501 y=300 z=200
Options:
A)I only
B)II only
C)III only
D)I​ and II
E)I and III
Rationale: 10 sec answer if you know how to find the units digit of a number
The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0
x = 530, so x^2 will have units digit 0
y = 400, so y^2 will have units digit 0
z = 100, so z^2 will have units digit 0
Calculate the units digit , the units digit will be 0
Only option II will satisfy the condition , hence this will be our answer is option B.
Answer: B
Question: The division of a whole number N by 13 gives a quotient of 22 and a remainder of 2. Find N.
Options:
A)797
B)197
C)288
D)997
E)297
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 22* 13 + 2 = 288 correc answer C
Answer: C
Question: The income of P and Q are in the ratio of 2 : 3 and their expenses are in the ratio of 3 : 5. If each of them saves Rs. 500, then the income of P is:
Options:
A)Rs. 3000
B)Rs. 2000
C)Rs. 1500
D)None of these
E)Cannot be determined
Rationale: Let incomes for P and Q be = 2x, 3x
And their expenses be 2x-500, 3x-500
2x − 500/3x − =3/5
�solving X= Rs. 1000. So Income of P is Rs. 2000.
Answer:	B
Answer: B
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables e are there in the warehouse?
Options:
A)6
B)8
C)10
D)15
E)30
Rationale: Total number of ways to choose 2 chairs from 5 e= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A
Answer: A
Question: An unbiased cubic die is thrown.What is the probability of getting a multiple of 2?
Options:
A)1/6
B)3/4
C)2/6
D)1/2
E)1
Rationale: S={1,2,3,4,5,6}
P(E)=n(E)/n(S)
n(s)=Total numbers in a die=6
Let E be the event of getting the multiple of 2
then ,E={2,4,6}
P(multiple of 2) = 3/6=1/2
ans D
Answer: D
Question: 125 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Options:
A)3:9
B)3:1
C)3:7
D)3:4
E)3:6
Rationale: Milk = 3/5 * 125 = 75 liters
Water = 50 liters
75 : (50+P) = 3:4
150 + 3P = 400 => P = 50
50 liters of water are to be added for the ratio become 3:4.
Answer: D
Answer: D
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
Options:
A)77
B)15
C)66
D)44
E)21
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.
Answer:B
Answer: B
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 5, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
Options:
A)1/625
B)2/625
C)4/625
D)25/625
E)50/625
Rationale: Probability of choosing right numbers in two places = 1/5 * 1/5 = 1/25
Probability of not choosing right numbers in two places = 1-1/25 = 24/25
--
At most two attempts: 1) Wrong-1st Attempt, Right - 2nd, 2) Right - 1st Attempt
1) = 24/25 * 1/25 = 24/625
2) = 1/25
Add 1 and 2, 24/625 + 1/25 = 49/625 ~ 50/625
Answer E
Answer: E
Question: What is the greatest prime factor of 8^12 - 2^30?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: 8^12 - 2^30?
8 = 2^3
8^12 = 2^36
2^36 - 2^30 = 2^30 (2^6 - 1) = 2^30 (64 - 1) = 2^30 (63) = 2^30 (7*3*3)
hence 2,3,7 are the prime factors of 8^12 - 2^30. here, 7 is the greatest prime factor.
Option D is correct.
Answer: D
Question: In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 36000*10^(-3) Petri dishes. How many germs live happily in a single dish?
Options:
A)100
B)200
C)300
D)400
E)500
Rationale: 0.037*10^5 can be written as 3600
74000*10^(-3) can be written as 36
Required= 3600/36= 100
ANSWER:A
Answer: A
Question: A man purchases a cow for Rs.3000 and sold it on the same day allowing the buyer a credit of 2 years. If the buyer will pay Rs.3600 after 2 year at a rate of simple interest 50/7 % per annum, then the man has a gain of
Options:
A)Rs 171.43
B)Rs 172.43
C)Rs 173.43
D)Rs 174.43
E)Rs 175.43
Rationale: value of Rs3000 after 2 years at 50/7 % S.I will be = 3000 + (3000*2*50/7)/100 = 3000 + 428.57
= 3428.57
therefore C.P of article after 2 years will be Rs 3428.57
but the buyer pays Rs 3600
therefore gain = 3600-3428.57 = Rs 171.43
ANSWER:A
Answer: A
Question: Number of ways in which the letters of word GARDEN can be arranged with vowels in alphabetical order, is
Options:
A)360
B)240
C)120
D)480
E)None of these
Rationale: Solution
Order of vowels of fixed
∴ required number of ways are 6!/2!. Answer A
Answer: A
Question: Find out the wrong number in the following series:
5, 15, 30, 80, 180, 540, 1080
Options:
A)5
B)15
C)80
D)180
E)540
Rationale: 5*3=15 15*2=30
lykwise 30*3=90 90*2=180
180*3=540 540*2=1080
so 80 is wrong no because we r continously multipying by 3 and 2
ANSWER:C
Answer: C
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
Options:
A)2
B)6
C)4
D)9
E)8
Rationale: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0 => x = 6.
Answer: B
Answer: B
Question: What is the area of a square field whose diagonal of length 20 m?
Options:
A)338
B)377
C)200
D)887
E)1771
Rationale: d2/2 = (20 * 20)/2 = 200
Answer:C
Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Options:
A)1/455
B)1/451
C)1/457
D)1/459
E)1/452
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C3/15C3
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: A
Question: Nine people are on an elevator that stops at exactly 9 floors. What is the probability that exactly one person will push the button for each floor?
Options:
A)9!/9^9
B)9^9/9!
C)9/9!
D)9/9^9
E)1/9^9
Rationale: Each person out of 9 has 9 options, hence total # of outcomes is 9^9;
Favorable outcomes will be 9!, which is # of ways to assign 9 different buttons to 9 people
So basically # of arrangements of 9 distinct objects: 9!.
P=favorable/total=9!/9^9
Answer: A.
Answer: A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)288 m
B)667 m
C)240 m
D)176 m
E)197 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: C
Question: A sum was put a simple interest at a certain rate for 4 years. Had it been put at 3% higher rate, it would have fetched Rs. 120 more. The sum is:
Options:
A)s.750
B)s.1000
C)s.1250
D)s.1500
E)s.1750
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+3) Ã— 4/100âˆ’xÃ—RÃ—4/100=120
â‡’x Ã— 3Ã—4/100=120
â‡’x Ã— 4 /100=40
â‡’4x=4000
â‡’x=1000
Answer : Option B
Answer: B
Question: Vijay bought 160 shirts at the rate of Rs. 265 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)Rs. 258
B)Rs. 333
C)Rs. 277.5
D)Rs. 285
E)None of these
Rationale: Total CP per shirt = 265 + 1400/160 + 1.75 + 320/160 = Rs. 277.5
SP = CP[(100 + profit%)/100]
= 277.5 * [(100 + 20)/100] = Rs. 333.
ANSWER:B
Answer: B
Question: If x, 5, 6, 7 are there and the range and median of them are the same, what is the value of x?
Options:
A)0
B)1
C)6
D)3
E)4
Rationale: Try taking the values of x as you suggested and then see if the median and the range are equal.
Once you do that, you will get the answer yourself.
Tried substituting values starting with 5, 6, 7 ...
only x = 6 satisfies the condition.
C
Answer: C
Question: The triplicate ratio of 1:4 is?
Options:
A)1:7
B)1:8
C)1:3
D)1:64
E)1:2
Rationale: 1^3: 4^3 = 1:64
Answer: D
Answer: D
Question: If y exceeds x by 25%, then x is less than y by?
Options:
A)29%
B)80%
C)87%
D)20%
E)28%
Rationale: X=100	y=125
125--------25
100--------? => 20%
Answer: C
Answer: C
Question: One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
Options:
A)18
B)16
C)12
D)8
E)4
Rationale: A) 18 trucks rented means 2 were left and 9 were returned - 11 trucks - no good
B) 16 trucks rented means 4 were left and 8 were returned - 12 trucks - good
Answer is (B)
Answer: B
Question: From the given equation find the value of B: BÂ² + 1B - 56
Options:
A)3
B)5
C)8
D)12
E)4
Rationale: (B âˆ’ 7)(B + 8)
B = 7 or 8
Answer is C
Answer: C
Question: What is 12.5 % of 4/12 of 600?
Options:
A)25
B)24
C)30
D)27
E)28
Rationale: 12.5 % = 12.5 / 100 = 1/8 of 4/12 = 1/8 * 4/12 = 1 / 24 of 600 = 1/24 * 600 = 25
Ans -A
Answer: A
Question: If Raj was one-third as old as Rahim 5 years back and Raj is 17 years old now, How old is Rahim now?
Options:
A)40
B)41
C)36
D)48
E)54
Rationale: Explanation:
Raj’s age today = 17 decades,
Hence, 5 decades back, he must be 12 years old.
Rahim must be 36 years old, Because (3×12).
5 years back Rahim must be 41 years old today. Because (36+5). Answer: B
Answer: B
Question: If x/|y| = -1 which of the following must be true?
Options:
A)x^1 = y^1
B)x^3 = y^3
C)x^4 = y^4
D)x^5 = y^5
E)x^2 = y^2
Rationale: x/|y| = -1
|y| = -x, this implies that x is 0 or negative.
Square: y^2 = x^2.
Answer: D.
Alternatively you can try number plugging: try x = -2 and y = 2 or -2. You'll see that only E is always true.
Answer E
Answer: E
Question: The cost of 2 benchs and 3 tables is Rs.1300. The cost of 3 benchs and 2 tables is Rs.1200. The cost of each table is more than that of each bench by?
Options:
A)900
B)200
C)100
D)400
E)600
Rationale: C
100
2C + 3T = 1300 --- (1)
3C + 3T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T - C = 100
Answer: C
Question: For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.45 – 6.45*?
Options:
A)0.45
B)0.5
C)6.45
D)0.25
E)6.0
Rationale: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.45* =6 (the greatest positive even integer less than or equal to 6.45 is 6).
Hence, 6.45 – 6.45* = 6.45 - 6 = 0.45
Answer: A.
Answer: A
Question: If the cost price is 75% of selling price then what is the profit percentage.
Options:
A)30.33
B)31.33
C)32.33
D)33.33
E)34.33
Rationale: selling price=Rs100 : then cost price=Rs 75:profit =Rs 25.
Profit={(25/75)*100}%=33.33%
Answer is D.
Answer: D
Question: In the graph below, no axes or origin is shown. If point B's coordinates are (12,3), which of the following coordinates would most likely be A's?
Options:
A)(17, -2)
B)(10, 6)
C)(6, 8)
D)(-10, 3)
E)(-2, -17)
Rationale: wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10.
A rules..
Answer: A
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 61 = x?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: B) 2
Answer: B
Question: There are 30 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
Options:
A)10
B)30
C)435
D)60
E)90
Rationale: 30 players are there.
two players play one game with one another.
so 30C2=30*29/2
=435
SO OPTION C is correct
Answer: C
Question: In a certain random experiment, exactly one of the outcomes A, B, and V will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and V will occur twice?
Options:
A)5/243
B)1/12
C)10/81
D)1/6
E)16/81
Rationale: Number of ways in which a group of 2A,2B,2V can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/V; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: C