MU-NLPC/Calc-aqua_rat huggingface dataset:
A man buys an article for 13% less than its value and sells it for 13% more than its value. His gain or loss percent is: Choose one
A) no profit, no loss B) 20% profit C) less than 25% profit D) more than 25% profit E) None

Solution: Let the article be worth Rs. x.   C.P. 87% of Rs. x = Rs. 87x/100   S.P. = 113% of Rs. x = Rs. 113x/100   Gain = (113x/100 - 87x/100) = Rs. 13x/50   Gain % = 13x/50 * 100/87x * 100 = 29 77/87 % > 25%   ANSWER:more than 25% profit
Answer: D
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?	Choose the correct choice from the following
A) 25/5
B) 25/3
C) 25/2
D) 25/1
E) 25/9

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.Answer:25/2
Answer: C
From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly one person in the crew has previous experience in space flight. How many different crews of this type are possible?
Choose the correct choice from the following options.
A) 432
B) 94
C) 864
D) 1330
E) 7980

Solution: COMB(ENN) where E=experienced and N=no previous experience   12*9*8/(2!). We divide by 2! because there are 2! ways to choose the astronauts without previous experience.   =12*9*4 = 48*9   Because 48*9 ends with a 2, look for the answer that ends with a 2. Only 432 suffices.
Answer: A
A coin is tossed two times. What is the probability that there is at the least one tail?  Choose the correct choice from the following answers:
A) 3/4
B) 31/37
C) 31/18
D) 31/10
E) 31/19

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed two times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/4 ; P(T) = 1 - 1/4 = 3/4   3/4nswer: 3/4
Answer: A
Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If Q is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
Choose the correct choice from the following options:	A) 0<y<4	B) 4<y<10	C) 10<y<20	D) 20<y<30	E) y>30

Solution: Q Smallest prime factor is greater than 29. So answer is y>30
Answer: E
P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?  Choose the correct option:
A) 5  B) 10  C) 12  D) 15  E) 17

Solution: Work done by P in 1 day = 1/20   Work done by Q in 1 day = 1/12   Work done by P in 4 days = 4 × (1/20) = 1/5   Remaining work = 1 – 1/5 = 4/5   Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15   Number of days P and Q take to complete the remaining work = (4/5) / (2/15)= 
(4/5) / (2/15) = 6
6   Total days= 4 + 6= 
4 + 6 = 10
10   Answer is 10.
Answer: B
A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 78 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?	Choose the correct choice from the following answers:
A) 24
B) 12
C) 9
D) 6
E) 4

Solution: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say:   apples : peaches : grapes = 6x : 5x : 2x   We are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x:   6x + 5x + 2x = 78   13x = 78   x = 6   Now we can determine the number of pounds of apples and of grapes.   pounds of grapes = (2)(6) = 12   pounds of apples = (6)(6) = 36   Thus we know that there are  36 -12= 
 36 -12 = 24
24 more pounds of apples than grapes.   24nswer is 24.
Answer: A
An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is 1/4 empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?	Choose one
A) 21% B) 24% C) 22% D) 20% E) 18.75%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/2   3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4   4th step: brand Z is (1/4)*(3/4) = 3/16 = 18.75%   Answer (18.75%)
Answer: E
A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?  Answers:	A) 35	B) 37	C) 41	D) 43	E) 44

Solution: Let the original number be 'a'   Let the divisor be 'd'   Let the quotient of the division of aa by dd be 'x'   Therefore, we can write the relation as a/d = x and the remainder is 24.   i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.   We know that a=dx+24. Therefore, 2a = 2dx + 48   The problem states that (2dx+48)/d leaves a remainder of 11.   2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.   The remainder of 11 was obtained by dividing 48 by d.   When 48 is divided by 37, the remainder that one will obtain is 11.   Hence, the divisor is 37.   37
Answer: B
In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. How old is Janice's Daughter? Options:
A) 12 B) 36 C) 40 D) 42 E) 45

Solution: Let Jane's age be J and daughters' age be D...   Given J   + 3= 
  + 3 = 3
3(D + 3 )=> J - 6 = 3D -> Eq1.   Given J-6 = (D-6)^2 --> Eq 2..   sub J-6 value in eq 2... 3D = D^2 - 12D + 36.   0 = D^2 - 15D + 36 => D = 12 or D = 3.   When D = 12 we get from eq 1... J+3 = 45 => J =42..   When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15..   IMO option 12 is correct answer..
Answer: A
The cost of 3 kg of sugar is $12. What will the cost of 8 kg of sugar be? Choose the correct choice
A) 32 B) 48 C) 64 D) 120 E) 180

Solution: 3 kg costs $12   1 kg costs $4   8 kg costs $32   The answer is 32.
Answer: A
A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is: Choose the correct choice
A) 25 km/hr  B) 26 km/hr  C) 22 km/hr  D) 24 km/hr  E) 28 km/hr

Solution: rate upstream =8/24*60= 
8/24*60 = 20
20kmph   speed of stream=4kmph   let speed of boat in still water=xkmph   speed upstream=x-4kmph   x-4=20   x=24kmph   ANSWER:24 km/hr
Answer: D
A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 5% p.a for 2 years. Find his gain in the transaction per year.  Select the correct option.
A) 50
B) 150
C) 225
D) 112.5
E) 212.5

Solution: Explanation :   The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest   Simple interest that he needs to pay = PRT/100=5000×4×2/100=400   He also lends it at 5% p.a for 2 years   Simple interest that he gets = PRT/100=5000×5×2/100=500   His overall gain in 2 years = Rs.500 - Rs.400 = Rs.100   His overall gain in 1 year = 100/2 = Rs.50   50nswer : Option 50
Answer: A
If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of even integers from 30 to 50, inclusive, what is the value of x + y ?	Choose the correct choice from the following answers:
A) 810
B) 811
C) 830
D) 850
E) x + y=851

Solution: 21 integers from 30 to 50 inclusive   so 11th integer is mean, it is 40   21*40= 
21*40 = 840
840   from 21 integers 11 ones is even    840+11= 
 840+11 = 851
851   ANSWx + y=851R:x + y=851
Answer: E
A chair is bought for Rs.500/- and sold at a loss of 20% find its selling price Choose the correct choice from the following options.
A) Rs.500/-
B) Rs.600/-
C) Rs.400/-
D) Rs.700/-
E) Rs.800/-

Solution: Loss = 500*20/100= 
500*20/100 = 100
100   S.P= Rs.400/-.P - Loss   = 500- 100   =Rs.400/-   Answer :Rs.400/-
Answer: C
In a group of 400 players some are outdoor players, some are indoor players and some plays both. 350 plays outdoors and 110 plays indoor. How many plays indoor as well as outdoor games.  Choose the correct choice:
A) 70
B) 60
C) 90
D) 100
E) 110

Solution: Consider total number of players n(O U I) = 400   Players who plays outdoors n(O) = 350   Players who plays indoors n(I) = 110   Players who plays both n(O âˆ© I) = ?   n(O U I) = n(O)+ n(I) - n(O âˆ© I)   400 = 350 + 110 - n(O âˆ© I)   n(O âˆ© I) = 460 - 400   n(O âˆ© I) = 60   SO People read both science fiction and literacy works are 60   ANSWER:60
Answer: B
A man can row a boat at 26 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?	Choose one: A) 30/83 hours B) 80/13 hours C) 15/13 hours D) 16/19 hours E) 15/8 hours

Solution: Speed downstream = 26 + 6= 
26 + 6 = 32
32 kmph.   Time required to cover 60 km downstream= d/s = 60/32   = 15/8 hours.   Answer:15/8 hours
Answer: E
Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 30~ ?  Choose the correct choice from the following options.
A) 1
B) 0
C) 2
D) 8
E) 31

Solution: n~ = (n-1)!   so 30~ = (30-1)= 
(30-1) = 29
29!   when 29!/30 we have 16*2 inside 29!   hence 30 gets cancelled and we get remainder as 0   0
Answer: B
If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of (r − s)^2?	Choose the correct choice from the following options.
A) 8  B) 2  C) 64  D) − 3  E) − 5

Solution: We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.   The roots here are -r and -s.   -r - s = -(-2)/1 = r + s = -2   (-r)*(-s) = -15/1 = rs   So one of r and s is -5 and the other is 3. So   (r - s)^2 could be 64.   Answer (64)
Answer: C
in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 1*72+3*7+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7? Options:
A) 11101 B) 11110 C) 10111 D) 11011 E) 11010

Solution: 4+3= 
4+3 = 7
7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0)   3+4 + 1 carry from above step= 1 and 1 carry to next digit   2+5 + 1 carry to next digit= 1 and 1 carry   1+6= 11   so ans=11110   ANSWER:11110
Answer: B
Notebooks are sold in packages of four or seven only. If Wilson bought 69 notebooks exactly, what could be the number of large packs Wilson bought?  Choose the correct choice from the following choices:
A) 3  B) 4  C) 7  D) 8  E) 9

Solution: Let number of packs of four = f   let number of packs of seven = s   4f + 7s = 69   Now , we need to test for values of s .   Since sum 69 is odd and 4f will always be even , e can't be even .   Now , we can test for values e = 3 , 7 and 9   4*5 + 7*7 = 20 + 49= 
20 + 49 = 69
69   Answer 7
Answer: C
A and B start walking towards each other at 6pm at speed of 4kmph and 6kmph. They were initially 18km apart. At what time do they meet?  Choose the most appropriate option
A) 8pm  B) 6pm  C) 7pm  D) 10pm  E) 5pm

Solution: Time of meeting = distance / relative speed = 18/6+3 = 18/9= 
18/9 = 2
2 hrs after 6pm= 8pm   8pmnswer is 8pm
Answer: A
Which of the following number is divisible by 4 and 9?	Choose the correct answer.
A) 2377	B) 2736	C) 2876	D) 1988	E) 1192

Solution: Explanation:   For a number to be divisible by 4, the number formed by the last two digits of that number must be divisible by 4.   For a number to be divisible by 9, the sum of its digits must be divisible by 9.   Among the choices, choices (a) and (b) are divisible by 4 but of the first two choices, only choice (b) is divisible by 9.   Hence choice (b) is divisible by both 4 and 9.   Answer: 2736
Answer: B
Find the perimeter and area of a square of side 13 cm.  Choose the correct choice from the following answers:
A) 121	B) 144	C) 169	D) 196	E) 225

Solution: We know that the perimeter of square = 4 Ã— side   Side= 13 cm   Therefore, perimeter = 4 Ã— 13 cm = 52 cm   Now, area of the square = (side Ã— side) sq. units   = 13 Ã— 13 cmÂ²   = 169 cmÂ²   ANSWER : 169
Answer: C
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 7 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Select the correct option:
A) 56% B) 80% C) 100% D) 120% E) 125%

Solution: For A, r=8/2pi. Its capacity = (4pi)^2 * 7= 112pi   For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi   56%/B = 112pi/200pi = 0.56   56%112  /200= 
112  /200 = 14/25 = around 0.56
0.56   56%
Answer: A
The sum of first nine prime numbers is?	Choose the correct choice from the following options
A) 12  B) 100  C) 24  D) 28  E) 30

Solution: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23)= 
(2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100
100.   Note: 1 is not a prime number.   Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.   100
Answer: B
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?	Pick one:
A) 30%  B) 70%  C) 100%  D) 250%  E) 150%

Solution: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.   New C.P. = 125% of Rs. 100 = Rs. 125   New S.P. = Rs. 420.   Profit = Rs. (420 - 125) = Rs. 295.   Required percentage=295/420x100%=1475/21%= 70%   Answer is 70%.
Answer: B
If 15 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?	Options:
A) 95	B) 90	C) 85	D) 80	E) 60

Solution: Let x be the number of students in the school. 0.15x students went to the trip and took more than 100$. They compose   (100-75)= 
  (100-75) = 25
25% of all students who went to the trip. Therefore the toal of 0.15x/0.25=0.6x students went to the camping which is 60%.   The answer is 60  0.15 /0.25= 
  0.15 /0.25 = 0.6
0.6x students went to the camping which is 60%.   The answer is 60
Answer: E
How many words can be formed by using all letters of the word â€œBIHARâ€  Choose the correct option:  A) 320  B) 200  C) 420  D) 120  E) 300

Solution: Sol. The word BIHAR contains 5 different letters.   Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120   ANSWER 120
Answer: D
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:  Choose the correct choice from the following:
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: EXPLANATION   Let the numbers 13a and 13b.   Then, 13a x 13b = 2028   ab = 12.   Now, the co-primes with product 12 are (1, 12) and (3, 4).   [Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]   So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).   Clearly, there are 2 such pairs.   Answer 2
Answer: B
K is 50% faster than L. If L starts at 9 A.M. and K starts at 10 A.M. L travels at a speed of 50 km/hr. If L and K are 300 kms apart, The time when they meet when they travel in opposite direction is ?  Options:
A) 12 pm B) 22 pm C) 72 pm D) 92 pm E) 23 pm

Solution: Explanation:   let 't' be the time after which they met since L starts.   Given K is 50% faster than L   50 t + 1.5*50(t-1) = 300   50 t +75 t = 300 + 75= 
300 + 75 = 375
375 / 125= 
375 / 125 = 3
3 hrs past the time that L starts   So they meet at (9 + 3)= 
(9 + 3) = 12
12:00 noon.   12 pmnswer: 12 pm
Answer: A
A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether ?  Choose the correct choice from the following options.
A) 100
B) 104
C) 108
D) 106
E) None of these

Solution: Explanation:   Since each pole at the corner of the plot is common to its two sides, so we have :   Total number of poles needed = 27 x 4 - 4 = 108 - 4= 
108 - 4 = 104
104.   Answer: 104
Answer: B
The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
Choose the correct choice:	A) 4/7	B) 3 by 2	C) 3/5	D) 9/4	E) 3/1

Solution: Let the earnings of P and Q be 9x and 10x respectively.   New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]   => 9*(1 + 1/4)/10*(1 - 1/4)   => 9/10 * (5/4)/(3/4) = 3/2   Answer: 3 by 2
Answer: B
A man decided to cover a distance of 80km in 8 hrs. He can walk at a speed of 6 km/hr and cycle at 8 km/hr successively. How long will he walk and how long will he cycle ?	Select the correct option
A) 26.6km,53.3km  B) 27.6km,53.3km  C) 26.6km,54.3km  D) 26.6km,55.3km  E) 28.6km,53.3km

Solution: as speed in 80km/8hrs=10 km/hr   as ques solve through mixture and alligation method   6 km/hr and 8km/hr   10km/hr   10-8 10-6   2km/hr 4km/hr   so the ratio is 1:2   ahd we have to find the distance through walk and through cycle   1/3*8080  /8= 
80  /8 = 10
10 km/hr   as ques solve through mixture and alligation method   6 km/hr and 8km/hr   10km/hr   10-8 10-6   2km/hr 4km/hr   so the ratio is 1:2   ahd we have to find the distance through walk and through cycle   1/3*80=26.6km   2/3*80=53.3km   26.6km,53.3kmNSWER:26.6km,53.3km
Answer: A
A corporation that had $115.19 billion in profits for the year paid out $230.10 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9) Answers:
A) 50%
B) 20%
C) 5%
D) 2%
E) 0.2%

Solution: required answer = [employee benefit/profit] *100   =[(230.10 million)/(115.19 billion)]*100   =[(230.10*10^6)/(115.19*10^9)]*100   =(2/1000)*100= 
(2/1000)*100 = 1/5 = around 0.2
0.2%   So answer is (0.2%)
Answer: E
By selling 20 pens for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%? Choose the correct choice from the following choices:	A) 8.76	B) 10.76	C) 8.76	D) 9.76	E) 5.76

Solution: 70% --- 20130% --- ?70/130 * 20 = 10.76Answer: 10.76
Answer: B
A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture	Choose the correct choice from the following:
A) 15 litres
B) 10 litres
C) 30 litres
D) 22 litres
E) 8 litres

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively   4x/(3x+5)=4/5   20x=4(3x+5)   8x=20   x=2.5   Quantity of alcohol = (4 x 2.5) litres = 10 litres.   Answer is 10 litres.
Answer: B
3,6,9,12,15....
Options.
A) 58	B) 60	C) 18	D) 62	E) 63

Solution: 1*3= 
1*3 = 3
3   2*3= 
2*3 = 6
6   3*3= 
3*3 = 9
9   4*3= 
4*3 = 12
12   5*3= 
5*3 = 15
15   6*3= 
6*3 = 18
18   ANSWER:18
Answer: C
A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $18000 left with him. find salary..
Choose the most appropriate option
A) $10800	B) $18000	C) $180000	D) $1800	E) None

Solution: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount   [1-(1/5 + 1/10 + 3/5)} * total salary= $18000, = [1-9/10] * Total salary = $18000, Total salary = $18000*10= 
18000*10 = 180_000
$180000, correct answer ($180000)
Answer: C
For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?  Choose the correct answer:
A) 12%
B) 26%
C) 29%
D) 30%
E) 60%

Solution: In the first plot 25% of 300 seeds germinated, so 0.25 x 300 = 75 seeds germinated.   In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.   Since 75 + 70= 
75 + 70 = 145
145 seeds germinated out of a total of 300 + 200= 
300 + 200 = 500
500 seeds, the percent of seeds that germinated is (145/500) x 100%, or 29%.   Answer: 29%.
Answer: C
The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 50 percent of the pollutant?	Choose the correct choice from the following:
A) $400,000 B) $100,000 C) $50,000 D) $10,000 E) $5,000

Solution: To remove 90% of pollutant   C= 100,000(90)/(100-90) = 900,000   To remove 50% of pollutant   C' = 100,000(80)/(100-80) = 500,000   Difference = C - C' = 400,000   $400,000nswer - $400,000
Answer: A
Which of the following is not a leap year?  Choose the correct choice from the following options.
A) 700	B) 800	C) 1000	D) 1100	E) 1200

Solution: The century divisible by 400 is a leap year.   The year 700 is not a leap year. 700NSWER : 700
Answer: A
The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is Choose the correct choice
A) 38 B) 30 C) 39 D) 12 E) 11

Solution: Explanation:   Total age increased = (8 * 2)= 
(8 * 2) = 16
16 years.   Sum of ages of two new men= (21 + 23 + 16)= 
(21 + 23 + 16) = 60
60 years   Average age of two new men= (60/2)= 
(60/2) = 30
30 years.   Answer: 30
Answer: B
Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work?
Answers:
A) 2hrs
B) 4hrs
C) 6hrs
D) 8hrs
E) 10hrs

Solution: machine X will do 9/10 in 9 hrs, so X does 9/10 of the work ..   Therefore, Y will do the remaining 1/10 th work alone..   As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job...   ans 10   10hrs
Answer: E
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Choose the correct answer
A) 18/35 B) 18/22 C) 18/29 D) 18/12 E) 18/33

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35   = 18/35   18/35nswer:18/35
Answer: A
The sum of two numbers is 20 and their product is 375. What will be the sum of their reciprocals? Choose the correct answer.
A) 1/40
B) 4/75
C) 75/4
D) 75/8
E) 75/6

Solution: (1/a)+(1/b)=(a+b)/ab=20/375=4/75   ANSWER:4/75
Answer: B
A straight fence is to be constructed from posts 5 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)	Choose the correct choice from the following answers
A) 17
B) 28
C) 34
D) 39
E) 50

Solution: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}   The minimum length is with 2 posts = 0.5 + 5 + 0.5= 
0.5 + 5 + 0.5 = 6
6 feet. To increase the fence, each time we should add{post= 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:   6 feet;   5 + 5.5= 
5 + 5.5 = 10.5
10.5 feet;   11.5 + 5.5= 16 feet;   17 + 5.5 = 21.5 feet;   22.5 + 5.5 = 27 feet;   28 + 5.5 = 32.5 feet;   33.5 + 5.5 = 38 feet.   ...   We skipped 34 feet.   Answer: 34.
Answer: C
How many arrangements of the letters of the word DEFEATED are there in which the three E are separated?
Choose the correct choice from the following answers.
A) 840  B) 750  C) 770  D) 760  E) 820

Solution: Total arrangements-Three E's together-Exactly Two E's together   Total arrangement= 8!/3!2!   Three E's together= 6!/2!   Exactly Two E's together= Two E's together - Three E's together = 7!/2!−6/!2!=6∗6!/2!   8!/3!2!−6!/2!−6∗6!/2!   8!/3!2!−7!/2!=7!/2!∗13=840   840ns: "840"	840
Answer: A