mathewhe/aqua_rat huggingface dataset:
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability r that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: In order to determine the probability r that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Answer: (D)  68.75%
Question: If A : B=4 : 3 and B : C = 1 : 2, then A : B : C is:
(A) 2:5:9
(B) 4:6:3
(C) 7:5:3
(D) 4:3:6
(E) 8:6:1
Rationale: A:B=4:3, B:C=1:2, A:B:C=4Ã—1:1Ã—3:3Ã—2
â‡’ 4:3:6
Answer: D.
Answer: (D) 4:3:6
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings are divisible by 11?
(A) 9x + 4y
(B) x + y + 4
(C) 4x - 9y
(D) 4x + 6y
(E) None of these
Rationale: Explanation :
By hit and trial method, we get x=5 and y=1 such that 3x + 7y = 15 + 7 = 22 is a multiple of 11.
Then
(4x + 6y) = (4 × 5 + 6 × 1) = 26 which is not divisible by 11
(x + y + 4) = (5 + 1 + 4) = 10 which is not divisible by 11
(9x + 4y) = (9 × 5 + 4 × 1) = 49 which is not divisible by 11
(4x - 9y) = (4 × 5 - 9 × 1) = 20 - 9 = 11 which is divisible by 11. Answer : Option C
Answer: (C) 4x - 9y
Question: Set X consists of all the prime numbers between 10 and 25. What is the range of set X?
(A) 12
(B) 13
(C) 16.6
(D) 17
(E) 23
Rationale: Answer of set X is 12=X
Answer: (A) 12
Question: A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.99 days
(C) 2.67 days
(D) 2.98 days
(E) 2.44 days
Rationale: 1/4 + 1/8 = 3/8
8/3 = 2.67 days
Answer: C
Answer: (C) 2.67 days
Question: If four coins are tossed, the probability of getting two heads and two tails is -.
(A) 3/8
(B) 4/5
(C) 3/7
(D) 2/9
(E) 1/7
Rationale: n(E) = six ways
p(E) = 6/2^4 = 3/8
ANSWER A
Answer: (A) 3/8
Question: A jar has 500 marbles. 46% are dark colors, and the remainder light colors. Green, blue, and purple marbles are considered dark colors, and yellow, orange, and red are considered light colors. Green and blue make up 60% of the dark marbles, and there are half as many red marbles as there are purple marbles. What percent of the light marbles are not red?
(A) 54.5%
(B) 44.1%
(C) 44.8%
(D) 54.9%
(E) 46.2%
Rationale: 46% of 500 = 230 dark marbles
60% of 230 = 138 green and blue marbles
230-138 = 92 purple marbles
50% of 92 = 46 red marbles
500 total - 230 dark - 46 red = 224/500 = 44.8%
Answer is C
Answer: (C) 44.8%
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/12 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/15
(C) (c) 10/21
(D) (d) 7/25
(E) (e) 1/2
Rationale: This problem is very good example how easy and quick plug-in method might be.
Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 7/12*6=$7/2;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$7/2=$14;
Fraction of total revenue from large cups: 14/(36+14)=7/25.
Answer: D.
Answer: (D) (d) 7/25
Question: A sequence of odd integers begins at 61 and ends at 119. What is the sum of all numbers in this sequence?
(A) 2610
(B) 2700
(C) 2790
(D) 5400
(E) 6000
Rationale: Last Term = First Term + Common difference * (n-1)
119=61+2∗(n−1)
119=61+2n−2
58=2n−2
60=2n
n=30
Multiply 30 with the average from (61+119)/2 = 90 => 90*30 = 2700
ANSWER:B
Answer: (B) 2700
Question: The compound ratio of 1:3, 1:2 and 1:5?
(A) 1:30
(B) 1:5
(C) 1:7
(D) 1:1
(E) 1:6
Rationale: 1/3 * 1/2 * 1/5 = 1/301:30Answer: A
Answer: (A) 1:30
Question: Lilly has 10 fishes, rosy has 7 fishes. Totally how many fishes they have in all?
(A) 3
(B) 10
(C) 6
(D) 17
(E) 22
Rationale: 10+7=17. Answer is D.
Answer: (D) 17
Question: Three unbased coins are tossed. the probability of getting at most two head is ?
(A) 1/2
(B) 7/8
(C) 3/4
(D) 1/5
(E) 2/3
Rationale: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {THH,HTH,HHT,TTT,TTH,THT,HTT}
P(E)=n(E)/n(S)=7/8
Answer(B)
Answer: (B) 7/8
Question: Pipe A can fill a tank in 3 hours, pipe B in 4 hours, and pipe C in 6 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 1
(B) 1.3
(C) 1.6
(D) 1.9
(E) 2.2
Rationale: The part filled by A + B + C in 1 hour is 1/3 + 1/4 + 1/6 = 3/4
All the three pipes together will fill the tank in about 1.3 hours.
The answer is B.
Answer: (B) 1.3
Question: Dhoni spent 25 percent of his earning last month on rent and 10 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Dhoni have left over?
(A) 50%
(B) 55%
(C) 60%
(D) 62%
(E) 52.5%
Rationale: Say Dhoni's earning last month was $100.
Dhoni spent 30 percent of his earning last month on rent --> $25 on rent;
10 percent less than what he spent on rent to purchase a new dishwasher --> $25*0.9=$22.5 on the dishwasher.
Left over amount 100 - (25 + 22.5) = $52.5
Answer: E
Answer: (E) 52.5%
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 80%
(C) 29%
(D) 90%
(E) 70%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Answer: (A) 20%
Question: The average score of a cricketer for ten matches is 38.9 runs. if the average for the first six matches is 42, then find the average for the last four matches.
(A) 33.5
(B) 33.5
(C) 34.25
(D) 35
(E) None of these
Rationale: Solution
Required average =(38.9x10)-(42x6)/4 =137/4= 34.25 Answer C
Answer: (C) 34.25
Question: The greatest number that divides 2928 and 3240 leaving remainders 5 and 1 respectively is:
(A) 74
(B) 78
(C) 79
(D) 81
(E) 85
Rationale: explanation:
2928-5= 2923 ,3240-1= 3239
Highest number that can divide 2923 and 3239 is HCF of numbers.
HCF of 2923 and 3239 = 79
Answer:C
Answer: (C) 79
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) 337
(B) 500
(C) 266
(D) 288
(E) 211
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer: B
Answer: (B) 500
Question: One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 4 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
(A) $ 5,000
(B) $ 6,000
(C) $ 8,000
(D) $ 10,000
(E) $ 12,000
Rationale: This question can be solved by TESTing THE ANSWERS.
We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.
We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?
Let's TEST Answer B: $6,000
1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360
These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...
Let's TEST Answer C: $8,000
1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480
These totals are the SAME, so this must be the answer.
Final Answer:
A
Answer: (A) $ 5,000
Question: A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
(A) 70
(B) 210
(C) 336
(D) 840
(E) 1680
Rationale: This is a combinations problem so you need to use the correct formula:
10-2 cards =8 total cards. all possible permutations of 4 chosen from 8 cards are 8!/4!(8!-4!) = 8!/4!*4! =8*7*6*5*/4*3*2*1* =70
ANS:A
Answer: (A) 70
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 70.
(A) 3
(B) 4
(C) 12
(D) 32
(E) 35
Rationale: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by 70, remainder will be -4 i.e. n will be 4 less than a multiple of 70. So you must add 4 to n to make it a multiple of 70
D
Answer: (D) 32
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 30% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
(A) $32,500
(B) $47,500
(C) $82,500
(D) $92,000
(E) $100,000
Rationale: Team K's contract = $100,000 + $100,000*1.3 + $100,000*1.3*1.3 + $50,000 = $449,000
Team L's contract = $150,000 + $150,000*1.1 + $150,000*1.1*1.1 = $496,500
The difference = $47,500.
Answer: B.
Answer: (B) $47,500
Question: 40% of a 70% vinegar solution is replaced with water. From the resulting solution, again 10% is replaced with water. This step is repeated once more. What is the concentration of vinegar in the final solution obtained?
(A) 34%
(B) 23%
(C) 42%
(D) 28%
(E) 37%
Rationale: A quick answer: (70)(0.6)(0.9)(0.9)
Imagine you have 100 ml of 70% vinegar solution.
In step 1, 40% of the vinegar solution is replaced with water. This means 60% of the original vinegar quantity remains. Hence the resultant concentration is (70)(0.6) = 42%
Next, 10% of this solution is replaced with water and the process is repeated. Both the times, 90% of the previous vinegar quantity remains. Thus, 42x0.9x0.9 = 34%
This gives the final concentration as 70x0.6x0.9x0.9 = 34%
Answer: A
Answer: (A) 34%
Question: How many integers between 362,855 and 852,755have tens digit 1 and units digit 3?
(A) 4,888
(B) 4,898
(C) 4,889
(D) 4,869
(E) 4,896
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 362,855 and 852,755 is 852,755-362,855=489,900 - one number per each hundred gives 133,900/100=4,889 numbers.
Answer: C.
Answer: (C) 4,889
Question: What is the unit digit in (4137)^754?
(A) 12
(B) 48
(C) 57
(D) 96
(E) 9
Rationale: Explanation:
Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
Answer E
Answer: (E) 9
Question: What is the decimal equivalent of (1/5)^2?
(A) 0.0016
(B) 0.04
(C) 0.16
(D) 0.25
(E) 0.5
Rationale: (1/5)² = (1/5)(1/5)= 1/25
APPROACH #1: use long division to divide 25 into 1 to get 1/25 = 0.04
B
Answer: (B) 0.04
Question: What is the prime factors’ number of 48?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^4*3^1
prime factors’ number will be 4+1 = 5.
Hence, answer is D.
Answer: (D) 5
Question: A truck carrying cans of soup contains A stacks. Each stack contains B cases, and each case contains C cans. How many cans of soup are contained in 3 trucks?
(A) 3AB/C
(B) 3AC/B
(C) 3ABC
(D) AB/3C
(E) AC/3B
Rationale: There are C cans in each case.
There are BC cans in each stack.
There are ABC cans in each truck.
There are 3ABC cans in 3 trucks.
The answer is C.
Answer: (C) 3ABC
Question: What is the present worth of Rs. 330 due in 2 years at 5% simple interest per annum?
(A) 128
(B) 277
(C) 120
(D) 300
(E) 371
Rationale: Let the present worth be Rs. x. Then,
S.I. = (330 - x)
(x * 5 * 2) / 100 = (330 - x)
10x = 33000 - 100x
110x = 33000 => x = 300.
Answer: D
Answer: (D) 300
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 1:3
(B) 3:1
(C) 1:2
(D) 3:2
(E) 2:1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
Therefore, 27x + 17y/(x+y)= 23
=27x + 17y = 23x + 23y
=4x = 6y
=x/y	= 3/2.
Answer is D.
Answer: (D) 3:2
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.87. How much was lent at 5%?
(A) 228
(B) 299
(C) 300
(D) 500
(E) 188
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 87
5x/100 + 90 â€“ 6x/100 = 87
x/100 = 3
=> x = 300
Answer:C
Answer: (C) 300
Question: The average speed of a train is 87kmph. The train was scheduled to start at 9am in Bangalore, and as per schedule it has to reach a destination of 348km away from Bangalore at 1:45pm same day and a halt was scheduled onthe way. For how long was the halt scheduled?
(A) 45 minutes
(B) 50 minutes
(C) 55 minutes
(D) 60 minutes
(E) None of these
Rationale: Speed of train = 87 kmph and distance it covers is 348 km.
Time taken to cover the distance= Distance/Speed
= 348/87= 4 hours.
But total time taken by train to reach destination is = 1:45 pm – 9 a.m =4 hours 45 minutes.
Time of halt = Total time – take taken without halt
= 4 hours 45 minutes – 4 hours = 45 minutes A)
Answer: (A) 45 minutes
Question: A code is to be made by arranging 7 letters. Four of the letters used will be the letter A, one of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
(A) 42
(B) 210
(C) 420
(D) 840
(E) 5,040
Rationale: we have 7 letters out of which 3 are of one kind, 2 are of another kind..
so total ways = 7!/3!1!=840
ans D
Answer: (D) 840
Question: The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
(A) 16
(B) 3/√2
(C) 8
(D) 2√2
(E) (√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 × 3) = 9/2; so z = 9/2.
The next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 9/2. Clearly s = √9/2 = 3/√2 , oranswer choice (B).
Answer: (B) 3/√2
Question: If the average of 55, 48, 507, 2, 684 and y is 223, then what is y?
(A) 701
(B) 120
(C) 42
(D) 868
(E) 1
Rationale: y=42, because:
(55+48+507+2+684+y)/6 = 223
(55+48+507+2+684+y)/6 *6 = 223*6
(55+48+507+2+684+y)-1296= 1338-1296
y=42
So the correct answer is C, 42.
Answer: (C) 42
Question: If p/q =4/5, then the value of 1/7 + {(2q - p) / (2q + p)} is ?
(A) 4 / 7
(B) 34
(C) 1
(D) 2
(E) 3
Rationale: Answer
Given Exp. = 4 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 1/7 + {2-p/q) / (2 + p/q)}
= 1/7 + {(2 - 4/5) / (2 + 4/5)}
= 1/7 + 6/14
= 1/7 + 3/7
=4/7
Correct Option: A
Answer: (A) 4 / 7
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) Rs.187
(B) Rs.199
(C) Rs.189
(D) Rs.176
(E) Rs.129
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer: C
Answer: (C) Rs.189
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 388
(B) 105
(C) 288
(D) 266
(E) 281
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer:B
Answer: (B) 105
Question: A fair coin with sides marked heads and tails is to be tossed seven times. What is the probability that the coin will land tails side up more than four times?
(A) 29/128
(B) 56/256
(C) 65/256
(D) 70/256
(E) 81/256
Rationale: More than 5 times tails = 6times +7times+5times = 7C6 + 7C7 + 7C5= 29
2 2 2 2 2 2 2
2^8 times total events and 29 events where tails side up .
So probability = 29/2^7 = 29/128 (Answer A)
Answer: (A) 29/128
Question: After decreasing 24% in the price of an article costs Rs.532. Find the actual cost of an article?
(A) 118
(B) 677
(C) 700
(D) 2688
(E) 1991
Rationale: CP* (76/100) = 532
CP= 7 * 100 => CP = 700
Answer: C
Answer: (C) 700
Question: What should come in place of the question mark(?) in the following equation?
4 1⁄2 × 4 1⁄3 - 8 1⁄3 ÷ 5 2⁄3 = ?
(A) 8
(B) 18 1⁄34
(C) 1 33⁄34
(D) 7⁄17
(E) None of these
Rationale: ? = 9⁄2 × 13⁄3 - 25⁄3 × 3⁄17
= 39⁄2 - 25⁄17 = 663−50/34=61334=18 1/34
Answer B
Answer: (B) 18 1⁄34
Question: The compound ratio of 5:6, 3:2 and 4:5 is?
(A) 3:5
(B) 2:7
(C) 1:1
(D) 1:4
(E) None
Rationale: Answer: Option C
5/6 : 3/2 : 4/5 = 1:1
Answer: (C) 1:1
Question: If Y < X and XM < YM, what must be true
(A) M < X.
(B) M < Y.
(C) M < 0.
(D) X < 0.
(E) Y < 0.
Rationale: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when -ve is multiplied on both sides. That means M is -ve
C is the answer
Answer: (C) M < 0.
Question: Seven friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 7-person seating arrangements are possible?
(A) 1800
(B) 3600
(C) 5400
(D) 7200
(E) 9000
Rationale: The number of ways to arrange 7 people in a row is 7!
From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 5 other friends is 6! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 7 friends with the 2-person unit together is 6!*2
The total number of permutations where these two friends are not seated next to each other is 7! - 6!*2 = 5*6! = 3600
The answer is B.
Answer: (B) 3600
Question: A dealer professing to sell his goods at cost price, uses 900gm weight for 1 kg. His gain percent is
(A) 13%
(B) 12 1/3%
(C) 11 1/9%
(D) 10%
(E) 12%
Rationale: Gain % = ( Error/ (( True value) - Error)) *100 %
= (1000gm -900gm) / (1000 -100)* 100 %
= 100/900*100%
= 100/9
= 11 1/9 %
ANSWER:C
Answer: (C) 11 1/9%
Question: Car ‘X’ covers a distance of 385 kms in 7 hours and car ‘Y’ covers a distance of 715 kms in 13 hrs. What is the difference in the speed of the two cars?
(A) 2kms/hr
(B) 1km/hr
(C) 3kms/hr
(D) 5kms/hr
(E) None of these
Rationale: the speed of Car â€˜Xâ€™=385kms/7hr=55kms/hr
the speed of car â€˜Yâ€™=715kms/13hr=55kms/hr
the difference is 0km/hr
ANSWER:E
Answer: (E) None of these
Question: In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 65% average total marks, it is necessary for him in third yearly examination to secure marks :
(A) 300
(B) 350
(C) 400
(D) 475
(E) 500
Rationale: total marks:1500 for three exams
65% of 1500=975
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =975
X=475
ANSWER:D
Answer: (D) 475