MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the average (arithmetic mean) of all multiples of 10 from 10 to 600 inclusive?	Choose the correct option:
A) 190
B) 195
C) 305
D) 205
E) 210

Solution: This question can be solved with the Average Formula and 'bunching.'   We're asked for the average of all of the multiples of 10 from 10 to 600, inclusive.   To start, we can figure out the total number of terms rather easily:   1(10) = 10   2(10) = 20   ...   60(10) = 600   So we know that there are 60 total numbers.   We can now figure out the SUM of those numbers with 'bunching':   10 + 600= 
10 + 600 = 610
610   20 + 590= 
20 + 590 = 610
610   30 + 580= 
30 + 580 = 610
610   Etc.   Since there are 60 total terms, this pattern will create 30 'pairs' of 610.   Thus, since the average= (Sum of terms)/(Number of terms), we have...   (30)(610)/(60) =305   Final Answer: 305
Answer: C
A man bought a computer at 30% discount on its original price. He sold it at a 520% increase on the price he bought it. What percent of profit did he make on the original price?
Pick one
A) 1% B) 2% C) 3% D) 4% E) 5%

Solution: Original price = 100   CP = 70   S = 70*(150/100)= 
70*(150/100) = 105
105   105 - 100= 
105 - 100 = 5
5%   Answer: 5%
Answer: E
Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?	Choose the correct choice from the following options: A) 2528 B) 2526 C) 2522 D) 2722 E) 2426

Solution: A = 1600(21/20)3 = 2522   Answer: 2522
Answer: C
The speed of a boat in still water in 26 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 20 minutes is:	Choose the correct answer:
A) 10.4 km
B) 10.66 km
C) 11.4 km
D) 11.22 km
E) 12 km

Solution: Explanation:   Speed downstream = (26 + 6)= 
(26 + 6) = 32
32 kmph   Time= 20 minutes = 20/60 hour = 1/3 hour   Distance travelled = Time × speed = (1/3)×32 = 10.66 km   Answer: Option 10.66 km
Answer: B
If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Choose the correct choice from the following answers
A) 4/5 B) 4/9 C) 4/6 D) 4/2 E) 4/1

Solution: x/3 – x/4 = 4/60   x = 4/5 km   4/5nswer: 4/5
Answer: A
How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?	Choose the most appropriate option
A) 360  B) 729  C) 365  D) 735  E) 345

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is ⁶P₄   = 6 * 5 * 4 * 3= 
6 * 5 * 4 * 3 = 360
360.   360nswer:360
Answer: A
The average age of A, B and C is 26 years. If the average age of A and C is 29 years, what is the age of B in years ? Choose the correct choice from the following options:
A) 19 B) 35 C) 20 D) 32 E) 21

Solution: 20   20   Age of B = Age of (A + B + 20) – Age of (A + 20) = 26 × 3 – 29 × 2 = 78 – 58 = 20 years
Answer: C
If -1<= x <= 2 and 3 <= y <= 8, which of the following represents the range of all possible values of y-x? Choose the correct choice:	A) 5 <= y-x <= 6	B) 1 <= y-x <= 5	C) 1 <= y-x <= 6	D) 1 <= y-x <= 9	E) 1 <= y-x <= 10

Solution: Maximum value of y-x= 8 - (-1)= 
8 - (-1) = 9
9   Minimum value of y-x= 3-2= 
3-2 = 1
1   1 <= y-x <= 9 mentions the correct range
Answer: D
How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together? Choices.
A) 9  B) 12  C) 5  D) 8  E) 4

Solution: 9nswer: Option 9   (700 â€“ 300)/42 = 9 22/42 => 9 Numbers
Answer: A
A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 100. How much did he have with him in the beginning? Choose the correct choice from the following: A) Rs 200 B) Rs 250 C) Rs 300 D) Rs 450 E) Rs 550

Solution: Suppose the amount in the beginning was Rs ’x’   Money spent on clothes = Rs 1x/3 Rs 250alance = Rs 2x/3   Money spent on food = 1/5 of 2x/3 = Rs 2x/15   Rs 250alance = 2x/3 - 2x/15 = Rs 8x/15   Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5   Therefore 2x/5 = 100 = 250   ANSWER:Rs 250
Answer: B
A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?
Select.
A) 25.7 years	B) 28 years	C) 29.3 years	D) 28.8 years	E) 29 years

Solution: Explanation:   Present age of the son be P, he was born P years ago.   The age of the man was: (48 - P).   His age when the son was born should be equal to 2/3 of P.   (48 - P) = 2/3 P   5P = 144 => P = 28.8   ANSWER IS 28.8 years
Answer: D
The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Steve and Danny have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies? Choose the correct choice from the following answers:
A) $0.32 B) $0.40 C) $0.45 D) $0.48 E) $0.54

Solution: If Steve and Danny submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combined no discount cost.   If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer  (80)*( 0.02)= 
 (80)*( 0.02) = 1.6
$1.60, or together, a cost of $3.20 --- that's the combined no discount cost.   If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer=($0.40).
Answer: B
6 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? Choose one
A) 19  B) 20  C) 30  D) 33  E) 34

Solution: Though 2*(6C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.   The first guy has to play 2 matches with the rest of 5, so he'll play 10 matches.   Similarly, second guy has to play with the rest of 4 as his 2 games with the first guy are already played. So he plays 8matches.   This continues like this and the total matches are 10+8+6...+2   10+8+...+2 = 2(5+4+...+1) = 2((5*6)/2) = 5*6= 
5*6 = 30
30.   ANSWER:30
Answer: C
Jim is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be Canola oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Jim accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be Canola oil?	Choose the correct choice from the following choices: A) 15/29 B) 5/8 C) 5/16 D) 1/2 E) 13/27

Solution: Canola oil = 5/8 = 15/24 --> 15 parts out of 24;   Vinegar = 1/4 = 6/24 --> 6 parts out of 24;   Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;   If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0= 
15+12+1+1+0 = 29
29 parts out of which 15 parts are Canola oil --> proportion= 15/29.   15/29nswer: 15/29.
Answer: A
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 57.76, the number of the member is the group is: Choose the correct answer.
A) 57 B) 76 C) 77 D) 87 E) 97

Solution: Money collected =(57.76 x 100) paise = 5776 paise   numbers of members = 5776 squareroot = 76   Answer 76
Answer: B
The sum of the squares of three numbers is 100, while the sum of their products taken two at a time is 48. Their sum is: Select:
A) 20 B) 30 C) 40 D) 50 E) None of these

Solution: x^+y^2+z^2=100   xy+yz+zx=48   as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)   so (x+y+z)^2=100+(2*48)   (x+y+z)^2=196   so x+y+z=14   ANSWNone of theseR:None of these
Answer: E
Find the value of 72519 x 9999 = m?
Pick one
A) 434539873	B) 355797990	C) 435453490	D) 725117481	E) 873430134

Solution: 72519 x 9999 = 72519 x (10000 - 1)   = 72519 x 10000 - 72519 x 1   = 725190000 - 72519= 
725190000 - 72519 = 725_117_481
725117481   725117481
Answer: D
Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. The children CEF have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?  Pick one
A) 600	B) 720	C) 1440	D) 4320	E) 4800

Solution: for such questions , we can treat both as one then total person=5..   these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 6 ways CEF .. so ans =5!*6=720   ans 720
Answer: B
A man gets a simple interest of Rs.200 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
Choose the correct choice from the following choices:  A) Rs.102.5  B) Rs.250  C) Rs.5012.50  D) Rs.5062.50  E) None of these.

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.200   (P)(8)(5)/100 = 200   P = 500   C.I on Rs.2P i.e., Rs.1000 at 5% p.a in two years   =1000{ [1 + 5/100]2 - 1} = 1000{ 212 - 202 /202}   = Rs.102.5   Rs.102.5NSWER:Rs.102.5
Answer: A
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 5, what is the probability that one of the two cards drawn is numbered 3 ? Pick: A) 1/3 B) 1/2 C) 1/4 D) 1/5 E) 1/6

Solution: (3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened.   From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2   Answer: 1/2.
Answer: B
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45kmph. For how many minutes does the bus stop per hour? Choose one
A) 12
B) 11
C) 10
D) 9
E) 8

Solution: Explanation:   Speed of the bus excluding stoppages =54 kmph   Speed of the bus including stoppages =45 kmph   Loss in speed when including stoppages =54âˆ’45=9 kmph   â‡’ In 1 hour, bus covers 9 km less due to stoppages.   Hence, time in which the bus stops per hour   = Time taken to cover 9 km   =distance/speed =9/54hour=1/6hour=60/6= 
60/6 = 10
10min   ANSWER IS 10
Answer: C
In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?	Choose the correct choice from the following answers:
A) 978	B) 874	C) 1076	D) 1176	E) 1267

Solution: 80x + 400 = 12(x – 5)   x = 6.76   100 * 6.76 + 400= 
100 * 6.76 + 400 = 1_076
1076   ANSWER:1076
Answer: C
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?  Choose the correct option.
A) Rs.18390  B) Rs.10376  C) Rs.10456  D) Rs.10364  E) Rs.10500

Solution: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4   Simran's share = 24500 * 3/7 = Rs. 10500   Answer:Rs.10500
Answer: E
Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 420 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her five kids?	Options.
A) 8  B) 9  C) 3  D) 21  E) 10

Solution: cost of each apple = 4 dollars   Apples that Benny can buy with the amount she has=420/4 = 90.   Apples that each kid gets evenly = 105/5= 
105/5 = 21
21 Apples.   So the answer is 21=21
Answer: D
Akash leaves Chennai at 6am & reaches Bangalore at 10am. Prakash leaves Hyderabad at 8 am and reaches Chennai at 11:30 am. At what time do they cross each other?	Choose one:	A) 5 : 50am	B) 7 : 56am	C) 8 : 56am	D) 9 : 00am	E) 9 : 15am

Solution: Time taken by Akash = 4 h   Time taken by Prakash = 3.5 h   For your convenience take the product of times taken by both as a distance.   Then the distance = 14km   Since, Akash covers half of the distance in 2 hours(i.e at 8 am)   Now, the rest half (i.e 7 km) will be coverd by both prakash and akash   Time taken by them = 7/7.5 = 56 min   Thus , they will cross each other at 8 : 56am.   8 : 56am
Answer: C
If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 8? Choose the correct choice from the following
A) 1/4  B) 1/3  C) 1/2  D) 2/3  E) 3/4

Solution: because n(n+1) is always an even product of even*odd or odd*even factors,   there is a probability of 1 that that it will be divisible by 2,   and, thus, a probability of 1/2 that it will be divisible by 4   and, thus, a probability of 1/4 that it will be divisible by 8   1*1/4=1/4   1/4nswer : 1/4
Answer: A
If x and y are positive integers and 7 + x + y + xy = 21, what is the value of x + y?  Pick:
A) 3
B) 5
C) 6
D) 8
E) 9

Solution: Try each answer choices.   For A: 7 + 3 + xy = 21; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)   For B: 7 + 5 + xy = 21; xy = 9 (no combination of xy = 9 and x + y = 5)   For C: 7 + 6 + xy = 21; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)   For D: 7 + 8 + xy = 21; xy = 6 (no combination of xy = 6 and x + y = 8)   For E: 7 + 9 + xy = 21; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)   Therefore, answer 6.
Answer: C
What is greatest positive integer n such that 2^n is a factor of 12^12?  Choose one:
A) a)10
B) b)12
C) c)16
D) d)24
E) e)60

Solution: The given number is 12^12   =(2*2*3)^12   =(2^24)*(3^12)   So the greatest possible value for n such that 2^n can be factor of given number is 24.   Answer d)24
Answer: D
A river 7m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is?
Pick
A) 54996.5  B) 32296.5  C) 34996.5  D) 34996.5  E) 31255.5

Solution: Rate of water flow-4kmph--4000/60--66.66 m/min   depth of river--7m   width of river--75m   vol of water per min--66.66 *7*75---34996.5   Answer 34996.5
Answer: C
Express 20 mps in kmph? Pick.
A) 72  B) 88  C) 90  D) 21  E) 24

Solution: 20 * 18/5= 
20 * 18/5 = 72
72 kmph   72nswer: 72
Answer: A
Five different books (A, B, C, D and E) are to be arranged on a shelf. Books C and D are to be arranged first and second starting from the right of the shelf. The number of different orders in which books A, B and E may be arranged is  Pick one:  A) 5!  B) 3!  C) 2!  D) 3! * 2!  E) None

Solution: Solution   Since books C and D are arranged first and second, only books A, B and E will change order. Therefore it an arrangement problem involving 3 items and the number of different order is given by   3!   Answer 3!
Answer: B
Mike buys 3 cartons of eggs at the store. Each carton has 12 eggs. How many eggs does mike have?  Choose the correct choice from the following options:
A) 12	B) 18	C) 36	D) 35	E) 16

Solution: 12 eggs x 3 cartons =36 eggs   12 X 3 = 36   36.36
Answer: C
24 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Choose the correct choice from the following choices
A) 625	B) 600	C) 552	D) 676	E) 700

Solution: we can go in any bus out of the 24 buses.   Hence He can go in 24 ways.   Since we can not come back in the same bus that he used for travelling,   we can return in 23 ways.   Total number of ways = 24 x 23 = 552   ANSWER:552
Answer: C
3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Select.
A) 45% B) 48% C) 57% D) 59% E) 61%

Solution: Total number of votes polled = (5136 + 7636 + 11628)= 
(5136 + 7636 + 11628) = 24_400
24400   So, Required percentage= 11628/24400 * 100 = 48%   48%
Answer: B
Which of the following number is divisible by 24 ? Select the correct option.
A) 3125712	B) 3125717	C) 3125725	D) 3125736	E) 3125745

Solution: 24 = 3 x8, where 3 and 8 co-prime.   Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.   Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.   Consider option (D),   Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6)= 
(3 + 1 + 2 + 5 + 7 + 3 + 6) = 27
27, which is divisible by 3.   Also, 736 is divisible by 8.   3125736 is divisible by (3 x 8), i.e., 24   3125736)
Answer: D
In a group of 120 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20? Options:  A) 0.1  B) 0.13  C) 0.2  D) 0.25  E) 0.3

Solution: Number of people whose age is less than 20 is given by   120 - 90= 
120 - 90 = 30
30   Probability P that a person selected at random from the group is less than 20 is gieven by    30 / 120= 
 30 / 120 = 1/4 = around 0.25
0.25   correct answer 0.25
Answer: D
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?	Choose the correct choice from the following answers.
A) 4:5 B) 4:7 C) 5:3 D) 3:5 E) 3:5

Solution: Let 40% of A = 2/3 B. Then,   40A/100 = 2B/3 => 2A/5 = 2B/3   A/B = (2/3 * 5/2) = 5/3   A:B = 5:3.   Answer: 5:3
Answer: C
A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 70, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Choose one.
A) 71
B) 75
C) 76
D) 77
E) 78

Solution: ratio is 4:6:5 , numbers are 4x, 6x, 5x   total scores of each class is (65*4x + 6x * 70 + 77*5x) = 260x+420x+385x = 1065x   total number of students 260 +420 +385= 
260 +420 +385 = 1_065
1065x   total number of students= 15x   average = 1065x/15x = 71   71 is the answer1065 /15= 
1065 /15 = 71
71   71 is the answer
Answer: A
If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers	Select: A) 0 B) 25 C) 50 D) 75 E) 100

Solution: First even minus first odd = 2-1= 
2-1 = 1
1;   The sum of first 2 even integers minus the sum of first 2 odd integers= (2+4)-(1+3)= 
(2+4)-(1+3) = 2
2;   The sum of first 3 even integers minus the sum of first 3 odd integers= (2+4+6)-(1+3+5)= 
(2+4+6)-(1+3+5) = 3
3;   We can see the patterns here, so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100.   Answer: 100.
Answer: E
A car covers a distance of 640 km in 5 hours. Find its speed? Select.
A) 104
B) 288
C) 271
D) 276
E) 128

Solution: 640/5= 
640/5 = 128
128 kmph   Answer: 128
Answer: E
Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years.  Choose the most appropriate option.
A) Rs 1052
B) Rs 1152
C) Rs 1252
D) Rs 1352
E) None of these

Solution: Explanation:   S.I. = 956 - 800= 
956 - 800 = 156
Rs 156   R=156∗100 /800∗3   R=6 1/2%   New Rate = 6 1/2+4   =21/2%   New S.I. = 800×21/2×3100=252   Now amount will be  800 + 252= 
 800 + 252 = 1_052
1052   Option Rs 1052
Answer: A
A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area Y covered by the two roads? Select the correct option.
A) 400 B) 1550 C) 1575 D) 1600 E) 1625

Solution: Area 1575overed by Road Along the Length = 5*200= 
5*200 = 1_000
1000 Square Meter   Area 1575overed by Road Along the Width= 5*120= 
5*120 = 600
600 Square Meter   1575ommon Area in both Roads (where the roads intersect)= Square with Side 5 meter = 5*5= 
5*5 = 25
25   Total Area of the Roads Y= 1000+600-25= 
1000+600-25 = 1_575
1575   Answer: option 1575
Answer: C
Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 5 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
Answers:
A) 4 minutes
B) 2/7 minutes
C) 32/7 minutes
D) 224/7 minutes
E) 28 minutes

Solution: Pipe A can fill a tank in 32 minutes --> the rate of A = 1/32 tank/minute;   Pipe B can fill the same tank5 times fasterthan pipe A --> the rate of B = 1/32 + 5/32 = 6/32 tank/minute.   Their combined rate = 1/32 + 6/32 = 7/32 tank/minute;   Therefore, A and B can fill the tank in 32/7 minutes.   Answer: 32/7 minutes
Answer: C
Find the unit's digit in 264^102+264^103	Answers:  A) zero 0  B) 1  C) 2  D) 4  E) 5

Solution: Required unit's digit = unit's digit in 4102+4103.4102+4103.   Now, 4242 gives unit digit 6.   ⇒ 41024102 gives unit digit 6.   ⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.   Hence, unit's digit in 264102+264103264102+264103   = unit's digit in (6+4)=0   zero 0
Answer: A
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/4.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?  Choose the correct choice from the following options:
A) 5.  B) 7.  C) 9.  D) 10.  E) 17.

Solution: We need to get some number which is less than 50 and exactly divisible by 4,5 and 10   Lets take LCM of three balls 4,5 and 10 =20.   The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls.   The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls.   The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS.   Then out of 20 - ( 5 + 4 + 2 )= 
20 - ( 5 + 4 + 2 ) = 9
9 YELLOW balls.   IMO option 9. is correct.
Answer: C
The average age of three boys is 20 years and their ages are in proportion 3:5:7. What is the age in years of the eldest boy?	Choose the correct choice from the following.
A) 6
B) 9
C) 28
D) 24
E) 21

Solution: 3x + 5x + 7x = 60   x =4   7x = 28   Answer:28
Answer: C
If x is less than y by 25% then y exceed x by:  Choose the correct choice from the following choices
A) 33.33%	B) 25%	C) 75%	D) 66.66%	E) None of these

Solution: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)   => 25(100-25)*100   =33.33%   33.33%NSWER:33.33%
Answer: A
The ratio 2 : 3 expressed as a percent equals  Pick one
A) 12.5%	B) 40%	C) 67%	D) 125%	E) None

Solution: Solution   2 : 3	= 2/ 3   = (2 / 3 x 100)%.   = 66.6 %.   Answer 67%
Answer: C
Twenty percent of the women in a college class are science majors, and the non-science majors make up 60% of the class. What percentage of the men are science majors if 40% of the class are men?  Answers:
A) 40%	B) 50%	C) 60%	D) 70%	E) 80%

Solution: Science majors make up 0.4 of the class.   60% of the class are women and   0.2*0.6= 
  0.2*0.6 = 0.12
0.12 of the class are female science majors.   Then 0.28 of the class are male science majors.   0.4x= 0.28   x = 0.7 = 70%   The answer is 70%.
Answer: D
The average student age of a certain class which has 30 students is 10. If one student aged 11 go to another class and the age of the class teacher is included the average changes to 11. What is the age of class teacher?
Pick:
A) 32
B) 41
C) 45
D) 48
E) 50

Solution: Sum of ages of class before replacement= 30x10=300   Sum of ages of class without teacher= 300-11= 
300-11 = 289
289   Sum of ages of class after replacement=30x11=330   Age of teacher=330-289= 
330-289 = 41
41   Answer: 41
Answer: B