MU-NLPC/Calc-aqua_rat huggingface dataset:
The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Three pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ? Choose the correct choice from the following choices:
A) 5 B) 12 C) 24 D) 32 E) 120

Solution: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.   But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.   The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 24.   Answer: option 24
Answer: C
a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 3a = b = 3c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.  Pick:
A) 131
B) 292
C) 394
D) 424
E) 969

Solution: Ratio of a:b:c= 1:3:1   Two possible greatest single digit values for b are 9 and 6   if b is 9, then x= 393   if b is 6, then x= 262   difference= 393-262= 
393-262 = 131
131   131 is the answer
Answer: A
A man walking at a rate of 5km/hr crosses a bridge in 15 minutes. The length of the bridge is?	Choose one.
A) 1250m	B) 1310m	C) 1500m	D) 1000m	E) 1195m

Solution: Speed = 5*5/18 = 25/18 m/sec   Distance covered in 15minutes = 25/18 *15 *60= 
25/18 *15 *60 = 1_250
1250m   1250mnswer is 1250m
Answer: A
The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be	Choose the correct option:	A) 5 : 3	B) 8 : 11	C) 8 : 7	D) 6 : 5	E) 3 : 11

Solution: Let Mini’s age = 4x and Minakshi’s age = 3x   Then 4x + 3x = 14   x = 2   Mini’s age = 8 years   And Minakshi’s age = 6 years   Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7   ANSWER:8 : 7
Answer: C
If x is a sum of all even integers on the interval 13...45 and y is their number, what is the GCD (x, y)?  Choose the correct choice from the following answers:
A) 1 B) 16 C) 26 D) 52 E) 1014

Solution: x = 14 + 16 + ... + 44 = (largest + smallest)/2 *(# of terms) = (14 + 44)/2*16 = 29*16.   GCD of 16 and 29*16 is 16.   Answer: 16.
Answer: B
A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2445?
Answers:  A) s.800  B) s.810  C) s.815  D) s.900  E) s.920

Solution: 2445 * 1/3= 
2445 * 1/3 = 815
815   Option s.815
Answer: C
800 men have provisions for 20 days. If 200 more men join them, for how many days will the provisions last now?  Select the correct option:
A) 10  B) 8  C) 16  D) 11  E) 15

Solution: 800*20 = 1200*x   x = 16.Answer: 16
Answer: C
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 25%? Pick:
A) 20%
B) 25%
C) 13 %
D) 12.5%
E) 13%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 75   2/3 SP1 = 75   SP1 = 225/2   100 --- 12.5=> 12.50%   ANSWER:12.5%
Answer: D
The distance between two planets is 3.00 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)  Choose one.
A) 9.3 × 10^5  B) 9.2 × 10^5  C) 9.3 × 10^7  D) 9.9 × 10^7  E) 10.1 × 10^8

Solution: 3.00*10^6 light years = 3.00*10^6/3.26 parsecs.   3.00/3.26 is a little bit less than 1, something like 0.9, thus 3.00*10^6/3.26 = ~0.92*10^6 = 9.2*10^5.   Answer: 9.2 × 10^5.
Answer: B
The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
Choose the correct choice from the following answers:
A) 33  B) 77  C) 48  D) 99  E) 61

Solution: π * 12 * 4 = 48   Answer:48
Answer: C
The average weight of a group of boys is 35 kg. After a boy of weight 40 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? Choose the most appropriate option: A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 35x   After the boy weighing 40 kg joins the group, total weight of boys = 35x + 40   So 35x + 40 = 36(x + 1) = > x = 5.   Answer: 5
Answer: B
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?  Options:
A) 60 B) 88 C) 77 D) 65 E) 21

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   60nswer: 60
Answer: A
A man buys an item at Rs. 1200 and sells it at the loss of 20 percent. Then what is the selling price of that item
Choose the correct option:
A) Rs. 660	B) Rs. 760	C) Rs. 860	D) Rs. 960	E) None of these

Solution: Explanation:   Here always remember, when ever x% loss,   it means S.P. = (100 - x)% of C.P   when ever x% profit,   it means S.P. = (100 + x)% of C.P   So here will be (100 - x)% of C.P.   = 80% of 1200   = 80/100 * 1200= 
80/100 * 1200 = 960
960   Option Rs. 960
Answer: D
An alloy is to contain copper and zinc in the ratio 7 : 3. The zinc required (in kg) to be melted with 35 kg of copper, is?
Choose the correct choice
A) 10 and 2/3  B) 15  C) 9 and 2/3  D) 9  E) 10

Solution: Explanation :   7 : 3 : 35 : x   => 7x = 3 * 35   => x = (3*35)/7= 
(3*35)/7 = 15
15 Kg.   Hence 15.   Answer : 15
Answer: B
In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?  Select
A) 40%	B) 80%	C) 58%	D) 50%	E) 60%

Solution: Number of students passed = 60% of 140 = 60/100 * 140= 
60/100 * 140 = 84
84   Number of students failed= 140 - 84= 
140 - 84 = 56
56.   Required percentage= 28/56 * 100= 
28/56 * 100 = 50
50%.   Answer:50%
Answer: D
3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?  Pick one:
A) 45%
B) 50%
C) 57%
D) 60%
E) 65%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   57%
Answer: C
If the President and Vice President must sit next to each other in a row with 8 other members of the Board, how many different seating arrangements are possible? Choose the correct choice from the following answers.
A) 120510	B) 632010	C) 725760	D) 705262	E) 851032

Solution: We need to take President and VP as one unit. Therefore we have 9 people to arrange=5! ways   Also, we both President and VP can be arranged in 2 ! ways.   Reqd no of ways=9!*2!= 725760 ways   Answer 725760
Answer: C
A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.204 less than the sum lent. What was the sum lent?  Select:
A) 228  B) 278  C) 300  D) 500  E) 821

Solution: P - 204 = (P*4*8)/100   P = 300   Answer: 300
Answer: C
On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 18. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?	Choose one:
A) (2, -16) B) (-5, -8) C) (12, 4) D) (3, 5) E) (9, -4)

Solution: The area of the triangle formed will be:   1/2 * base * height =   1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 18   Thus |product of coordinates of point C| = 36   The answer is (9, -4).
Answer: E
Product of two natural numbers is 19. Then, the sum of reciprocals of their squares is  Choose the correct choice from the following
A) 290/289	B) 1/289	C) 290/90	D) 362/361	E) None of these

Solution: Explanation:   If the numbers are a, b, then ab = 19,   as 17 is a prime number, so a = 1, b = 19.   1/a2+1/b2=1/1(2)+1/19(2)   1/ 2+1/ 2= 
1/ 2+1/ 2 = 1
1/1(2)+1/19(2)=362/361   Option 362/361
Answer: D
5/8 of 3/10 of a number is greater than 4/9 of 1/4 of the same number by 55. What is half of that number?  Options:
A) 310	B) 312	C) 320	D) 314	E) 360

Solution: Let no. be x   5/8*3/10*x - 4/9*1/4*x =55   by further solving   15x/80- 4x/36=55   11x/144=55   x=720   we have to find x/2   =720/2= 
720/2 = 360
360   ANSW360R:360
Answer: E
The average of 30 numbers is 48. If three numbers namely 45, 55 and 43 are discarded, the average of remaining numbers is?
Choose the correct option:
A) 47	B) 47.03	C) 48.03	D) 48	E) 49

Solution: Explanation:   Total of 30 numbers = 30 * 48= 
30 * 48 = 1_440
1440   Average o 27 numbers= 1440 - (45 + 55 + 43) / 27   = 48.03   Answer: Option 48.03
Answer: C
If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions R represents the final price of the item?	Choose one
A) R=(10,000z + 100z(x – y) – xyz)/10,000 B) R=(10,000z + 100z(y – x) – xyz)/10,000 C) R=(100z(x – y) – xyz)/10000 D) (100z(y – x) – xyz)/10000 E) 10000 /(x – y)

Solution: -R=(10,000z + 100z(x – y) – xyz)/10,000-   z=Original Price   x=MU   y=MD   New price with MU:   z(x/100+1)   New price with MD:   z[(x/100+1)(-y/100+1)]   Solvingâ€¦   =z[((x+100)/100)((-y+100)/100)]   =z(x100-xy+10000-100y)/10000   =(zx100-xyz+10000z-100yz)/10000 --> similar to R=(10,000z + 100z(x – y) – xyz)/10,000
Answer: A
If 10 litres of an oil of Rs.50 per litres be mixed with 5 litres of another oil of Rs.67 per litre then what is the rate of mixed oil per litre?
Options: A) Rs.49.17 B) Rs.51.03 C) Rs.54.17 D) Rs.55.66 E) None of the above

Solution: 50*10= 
50*10 = 500
500   67*5= 
67*5 = 335
335   835/15= 55.66   ANSWER:Rs.55.66
Answer: D
List K consists of 10 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K?  Choose the correct answer:  A) 5  B) 6  C) 7  D) 11  E) 12

Solution: 5nswer = 5 = 5   If least = -3, then largest = 6   Range = 6- 1= 
6- 1 = 5
5
Answer: A
At a dinner party, 8 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?  Choose the correct option:
A) 5	B) 10	C) 5040	D) 3200	E) 12000

Solution: Has to be C.   Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle   hence (8-1)= 
(8-1) = 7
7!= 5040
Answer: C
On a certain Monday, Carlos drove to work at an average speed of 20 miles per hour and home from work along exactly the same route at an average speed of 40 miles per hour. Which of the following is closest to his average speed for both trips combined?  Choose one:
A) 24	B) 26	C) 27	D) 26.66	E) 28

Solution: To solve the average speed questions, we need to know the total distance and the total time.   Let us assume that the distance from work = 26.66   This will also be the distance from work to home   Hence total distance travelled = 226.66   Time in going to work = 26.66/20,   Time in coming back from work = 26.66/40   Hence average speed of both the trips = 226.66/ (26.66/20 + 26.66/40)   = 2*40/3 = 26.66   26.66
Answer: D
If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?	Pick one.
A) 47.6 kg	B) 52.6 kg	C) 59.6 kg	D) 56.6 kg	E) 57.6 kilogram

Solution: (3 * 5)/48 = (9 * 2)/ x   x = 57.6 kg   ANSW57.6 kilogramR:57.6 kilogram
Answer: E
Three numbers are in the ratio 3 : 5 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 50. Find the third number? Select.
A) A)54
B) B)50
C) C)48
D) D)46
E) E)63

Solution: Let the numbers be 3x, 5x, 7x.   Largest number = 7x.   Smallest number = 3x.   Third number = 5x.   7x + 3x = 5x + 50   5x = 50 => third number is 50.   Answer:50
Answer: B
The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.	Pick one:
A) 19828.89	B) 19828.8	C) 19828.85	D) 19828.83	E) 19828.81

Solution: Let the sum be Rs.P   P{ [ 1 + 8/100]2 - 1 } = 2828.80   P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08= 
1360/0.08 = 17_000
17000 Principal + Interest= Rs. 19828.80.Answer: 19828.8
Answer: B
Find the least number must be subtracted from 105829 so that remaining no.is divisible by 21?
Pick.
A) 7  B) 10  C) 20  D) 32  E) 35

Solution: On dividing 105829 by 21 we get the remainder 10, so 10 should be subtracted   Answer is 10
Answer: B
A wholesaler makes a 10% commission on the selling price for each bag of cat food it sells. If it sells 100 bags of cat food and makes $160 in commission, what was the selling price of each bag?  Choose the correct choice from the following.
A) $4.00	B) $4.80	C) $9.60	D) $16.00	E) $32.00

Solution: Commission per one bag: 160/100= 
160/100 = 8/5 = around 1.6
1.6   1.6= 10% of the selling price   1.6=0.1x   x=16   Answer is $16.00.
Answer: D
If x+y=5z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z? Choose the correct choice from the following
A) 2z+1	B) 3z	C) 2z	D) z/3	E) 3z/2

Solution: Pick any number like X=12, Y=8 and Z= 4 so that X+Y=5Z, now then the arithmetic mean will be   (12+8+4)/3= 
  (12+8+4)/3 = 8
8. Now, just look at the answers and put the value of Z there.   (A) 2.4+1=9, but it should be 8.   (B) 3.4=12,no   (2z) 2.4=8, it can be the answer, lets check us the other options   (D) 4/3, no   (E) (3.4)/2=6, no   so the answer will be 2z..
Answer: C
In what time will a train 110 m long cross an electric pole, it its speed be 144 km/hr?
Choose the correct choice from the following choices.
A) 2.75 B) 3.75 C) 4.75 D) 5.75 E) 6.75

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 110/40= 
110/40 = 11/4 = around 2.75
2.75 sec.   2.75nswer: Option 2.75
Answer: A
For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 25 people, 8 of whom are females, by how much does the index for the females exceed the index for the males in the group? Choose the correct choice:
A) 0.05
B) 0.36
C) 0.2
D) 0.25
E) 0.6

Solution: Index for females = (25-8)/25 = 17/25= 
17/25 = 17/25 = around 0.68
0.68   Index for males= (25-17/25 = 8/25= 
8/25 = 8/25 = around 0.32
0.32   Index for females exceeds males by   0.68 - 0.32= 
  0.68 - 0.32 = 0.36
0.36   Answer: 0.36
Answer: B
A retail item is offered at a discount of c percent (where c > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of c, would result in the same final price?  Choose the most appropriate option
A) p+5/1.05
B) c/1.05 +5
C) 1.05c-5
D) c-5/1.05
E) 1.05(p – 5)

Solution: Let x be the price of the item.   Final price after discount and sales tax = x * (1 - c/100) * 1.05   Let d be the percent discount which would result in the same final price.   Then,   x * (1 - c/100) * 1.05 = x * (1 - d/100)   => 1.05 - 1.05c/100 = 1 - d/100   => d/100 = 1.05c/100 - .05   => d = 1.05c - 5   Hence ,option 1.05c-5 is correct.
Answer: C
Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Select the correct option: A) 228 B) 288 C) 27 D) 200 E) 881

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 15000(1 - 4/100) = 15000 - 600   m = 8000(1 + 10/100) = 8000 + 800   Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200   As this is positive, an overall profit of Rs. 200 was made.Answer:200
Answer: D
How many 3 digit numbers are divisible by 6 in all ? Select the correct option:
A) 149	B) 150	C) 151	D) 166	E) 172

Solution: Explanation:   Required numbers are 102, 108, 114, ... , 996   This is an A.P. in which a = 102, d = 6 and l = 996   Let the number of terms be n. Then,   a + (n - 1)d = 996   102 + (n - 1) x 6 = 996   6 x (n - 1) = 894   (n - 1) = 149   n = 150.   ANSWER IS 150
Answer: B
By how much is 30% of 80 greater than 4/5th of 25 ?  Choose the correct choice from the following.
A) 2  B) 4  C) 10  D) 15  E) 17

Solution: Answer   It is (30 x 80)/100 - (4 x 25)/ 5 = 24 - 20= 
24 - 20 = 4
4   Correct Option: 4
Answer: B
An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?	Choose the most appropriate option
A) 175 seconds
B) 195 seconds
C) 155 seconds
D) 115 seconds
E) 115 seconds

Solution: Explanation:   Let the time required by x seconds.   Then, More cloth means More time (Direct Proportion)   So,   0.128 : 1 :: 25 : x => x = {\color{195 secondslue} \frac{25\times 1}{0.128}}   => x = 195.31   So time will be approx 195 seconds   Answer: 195 seconds
Answer: B
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions ?	Choose the correct answer:
A) 32 B) 42 C) 36 D) 65 E) 28

Solution: Number of ways of arranging the vowels =3P3=3!=6.   Also, the 3 consonants can be arranged at the remaining 3 positions.   Number of ways of these arrangements =3P3=3!=6.   Total number of ways =(6*6)= 
(6*6) = 36
36.   Answer is 36
Answer: C
A woman has $133,982 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her Three children?	Choose the correct choice:
A) $1
B) $11
C) $3
D) $2
E) none

Solution: To find the least amount the woman should add to her saving account to split the money evenly among her 3 children,   she needs to make the total divisible by 3   Simply add the individual digits of the total = 1+3+3+9+8+2= 
1+3+3+9+8+2 = 26
26   If you add 1 , the number is divisible by 3 (26+ 1)   Correct Option : $1
Answer: A
A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 70, how many questions did Student A answer correctly?  Choices.
A) 55
B) 90
C) 73
D) 82
E) 91

Solution: let the number of correct responses be x   then the number of incorrect responses =100-x   according to question   x-2(100-x)=70 (subtracting twice of incorrect from correct)   3x=270   x=90   ANSWER:90
Answer: B
If Tom paid $250 toward buying a brand new oven, which represents 20% of the total cost of the oven, how much remains to be paid? Pick one:  A) $1000  B) $1100  C) $1050  D) $1300  E) $2000

Solution: Explanation:   Let's start with what the total price of the oven would be. If 20% is equal to $250 then 100% equals $x. We just have to multiply $250 by 5 to get total amount=$1250. Out of this amount we then need to deduct the amount already paid which was $250 so we have $1250-$250=$1000   $1000nswer: Option $1000 1250- 250= 
 1250- 250 = 1_000
$1000   $1000nswer: Option $1000
Answer: A
Fred purchased an item for $15.00. Fred sees the same item a week later on sale for $12.00. What percentage has the item been marked down from what Fred paid? Choose the correct answer:
A) 3 B) 5 C) 15 D) 20 E) 30

Solution: F.P.=15   S.P.=12   markdown is (1-(S.P./R.P.))*100=(1-(12/15))*100= 
(1-(12/15))*100 = 20
20%   ANSWER:20
Answer: D
P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 145 days, in how many days can R alone complete the remaining work?  Choose one.
A) 50 days
B) 110.6 days
C) 100 days
D) 150 days
E) 80 days

Solution: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days   Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days   P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 395 days   P works for 60 days--> 60/200 work done => 30%   Q works for 145 days--> 145/250 work done => 58%   28% work left ... R alone will take 28% * 395 = 110.6 days   Answer is (110.6 days)
Answer: B
210 college students were asked in a survey if they preferred Windows or Mac brand computers. 90 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 60 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
Options
A) 25	B) 40	C) 50	D) 60	E) 75

Solution: 210 = 90(Mac) + x(Window) + 60(both) => x=60   ANSWER:60
Answer: D
A boy was asked to find the arithmetic mean of the numbers 23, 17, 19, 25, 23, 18, 29, 27, 31 and P. He found the mean to be 24. What should be the number in place of P?	Select:
A) 3  B) 7  C) 33  D) 28  E) 38

Solution: Explanation :   Clearly, we have (23+17+19+25+23+18+29+27+31+P/10) =24   Number in place of P is   => 212+P = 240   => P= 240 -212   => P = 28.   Answer : 28
Answer: D
The workforce of Company X is 60% female. The company hired 30 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers? Answers.
A) 160 B) 220 C) 240 D) 360 E) 420

Solution: Let's xx be total quantity of employees   0.6x=females before adding men   0.55(x+30)=females after adding men   as quantity of women doesn't change we can make an equation:   0.6x=0.55(x+30)   0.05x=16.5   x=330 - this is quantity of employees before adding 30 men   So after adding it will be 360   Answer is 360
Answer: D
Sanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? Options
A) 1/24  B) 1/8  C) 1/4  D) 1/3  E) 3/8

Solution: Total Sanya# of ways - 4! = 24.   1/3esired:   A-Mapped to the only correct address----------x 1 way only   B-Mapped to other two incorrect addresses - x 2 ways   C-Mapped to other two incorrect addresses - x 2 ways   1/3-Mapped to other two incorrect addresses - x 2 ways   Therefore, 1*2*2*2/24 = 1/3.?
Answer: D
Four person are chosen at random form a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is: Choose the correct choice from the following answers.
A) 10/21 B) 20/21 C) 17/21 D) 19/21 E) 14/21

Solution: Number of ways of choosing 4 persons out of 9   =9c4   =126   No.of ways of choosing 2 children out of 4 and 2 persons out of (3+2)= (4c2+5c2)   =60   P(E)=60/126   =10/21   10/21NSWE 10/21 10/21
Answer: A
25% of 30% of 45% is equal to? Answers:
A) 0.03329	B) 0.03375	C) 0.0331	D) 0.03299	E) 0.03312

Solution: (25/100) * (30/100) * (45/100)   1/4 * 3/10 * 9/20   27/800= 
27/800 = 27/800 = around 0.03375
0.03375   Answer: 0.03375
Answer: B
A boy goes to his school from his house at a speed of 3km/hr and return at a speed of 2km/hr. If he takes 5 hours in going and coming, the distance between his house and school is?	Choose the correct option:
A) 5km
B) 6km
C) 10km
D) 12km
E) 8km

Solution: Average speed = 2*3*2/3+2 = 12/5 km/hr   Distance traveled = 12/5 * 5= 
12/5 * 5 = 12
12km   Distance between house and school= 12/2= 
12/2 = 6
6km   Answer is 6km
Answer: B