MU-NLPC/Calc-aqua_rat huggingface dataset:
If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?  Choose the correct choice from the following choices:
A) a/2
B) b/2
C) b/2
D) (a+b)/2
E) (b+2)/2

Solution: A and B both have to be even to fulfill the condition.   a could be = 4, 6, 8 ...., b = 2,4, ....   so a - b = 2 (Even)   a/b= 2k (Even)   a/2=2k   a = 4k   so a must be multiple of 4   now try the options   Ans. (a+b)/2
Answer: D
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?  Select the correct option
A) 288	B) 299	C) 266	D) 450	E) 291

Solution: 10 * 150= 
10 * 150 = 1_500
1500   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1500 – 1050= 450   Answer: 450
Answer: D
If x is an integer, and 196 < x^2 <= 361, which of the following is the sum of all possible values of x?  Options.
A) 135 B) 124 C) 116 D) 105 E) None of the above

Solution: The range of x is from 15 .. to 19 and -15 to -19 so the sum is 0 hence ans None of the above, I guess, unless I am missing something!
Answer: E
A = {2, 3, 5, 7, 17}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?	Select:  A) 15  B) 16  C) 19  D) 20  E) 36

Solution: Step 1: Find out the number of products you get.   5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4= 
5*4 = 20
20   Step 2: Remove the products that appear more than once.   Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.   2, 3   2, 4, 6   The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.   Answer= 20 - 1 = 36   Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.   36
Answer: E
The numbers 272738 and 232342, when divided by n, a two digit number, leave a remainder of 13 and 17 respectively. Find the sum of the digits of n? Choose the most appropriate option:
A) 7	B) 8	C) 9	D) 4	E) 5

Solution: From the given information, (272738 - 13, 232342 - 17) are exactly divisible by that two digit number.   We have to find the HCF of the given numbers 272725, 232325.   HCF = 25.   So sum of the digits = 7.   7nswer:7
Answer: A
Two letters from the word KYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?	Select the correct option
A) 14/27 B) 15/28 C) 27/28 D) 16/28 E) 30/28

Solution: There are 6 consonants and 2 vowels in KYANTKAR .   probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)   Probability of both vowels = 227/282/827/282 = 1/28   So,Answer is 1 - 1/28 = 27/28   Answer : 27/28
Answer: C
In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 III are not defective. What is the percentage of defective in the stockpile? Select:
A) 3%  B) 5%  C) 2.5%  D) 4%  E) 6%

Solution: Explanation :   Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.   Products from M1 = 40, from M2 = 30 and from M3 = 30.   Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.05 x 30 = 1.5   Therefore, total number of defective products = 3.   3%nswer : 3%
Answer: A
If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:	Options
A) Rs. 50  B) Rs. 160  C) Rs. 200  D) Rs. 225  E) Rs. 325

Solution: Let C.P. be Rs. x.   Then, 5% of x = 350 - 340= 
350 - 340 = 10
10   x/20= 10 => x = 200   ANSWER:Rs. 200
Answer: C
A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time, how many books of the special collection were loaned out during that month? Choose the correct choice from the following choices
A) 20	B) 30	C) 35	D) 40	E) 55

Solution: Total = 75 books.   65% of books that were loaned out are returned --> 100%-65%=35% of books that were loaned out are NOT returned.   Now, there are 68 books, thus 76-68--  100 -65= 
--  100 -65 = 35
35% of books that were loaned out are NOT returned.   Now, there are 68 books, thus 76-68=7 books are NOT returned.   {loaned out}*0.35=7 --> {loaned out}=20.   20nswer: 20.
Answer: A
What is the 10th digit of (5!*4!*4! - 5!*4!*3!)/2880?	Choose one.
A) 4  B) 1  C) 6  D) 7  E) 8

Solution: (5!*4!*4! - 5!*4!*3!)/2880?   =5!*4!(4! -3!)/4!*5!   =4!-3!   =18   Sum of digits =1   Answer 1
Answer: B
How many trailing zeroes would be found in 4617!, upon expansion?
Choose one:
A) 1150 B) 1151 C) 1152 D) 1153 E) 1154

Solution: for no of trailing zeros we have to find the no of 5 in 4617!,because 4617!=1*2*3*4*5*.........4616*4617.   no of 5 in 4617!= (4617/5^1)+(4617/5^2)+(4617/5^3)+(4617/5^4)+(4617/5^5)+... up to 5^n 4617.   now no of 5 =4617/5 + 4617/25 + 4617/125 + 4617/625 +4617/3125   =923 + 184 + 36 + 7 + 1 ( only take the integer value )   =1151   so the no of zeros at the end of 4617! is 1151.   ANSWER:1151
Answer: B
A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 2 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. Choose the correct choice from the following choices
A) 1/7	B) 1/12	C) 1/14	D) 1/18	E) 1/21

Solution: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.   The number of ways to sell 2 bottles of apple juice is 61/142*41/144 = 15*1= 
15*1 = 15
15   P(selling 2 bottles of apple juice)= 15/210 = 5/70 = 1/14   The answer is 1/14.
Answer: C
fill in ht blank:(a) the point with coordinates (0,0) is called ____ of a rectangular ____ system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___	Choose the correct choice from the following answers
A) (a) the point with coordinates (0,0) is called origin of a rectangular xyz system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y B) (a) the point with coordinates (0,0) is called end of a rectangular line system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y C) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let y equal 0 and solve for z ; to find x- intercept , we let x equal 0 and solve for y D) (a) the point with coordinates (0,0) is called end of a rectangular end system, (b) to find the y-intercept of a line, we let z equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x E) none of the above

Solution: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer (none of the above)
Answer: E
At what time between 2 and 3 o'clock will the hands of a clock be together?  Answers:
A) 10x10/11	B) 10x11/10	C) 11x10/11	D) 12x10/11	E) None

Solution: At 2 o'clock, the hour is at 2 and the minute hand is at 12,i.e. they are 10 min. Spaces apart. To be together, the minute hand must gain 10 minutes over the hour hand. Now,55 minutes will be gained in 60 min. 10 minutes spaces will be gained in (60/55 x10) min. = 10x10/11 min. The hands will coincide at 10x10/11 min.past 2.   10x10/11nswer 10x10/11
Answer: A
Goldenrod and No Hope are in a horse race with 6 contestants. How many different W arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?  Select:  A) 720  B) 360  C) 120  D) 24  E) 21

Solution: no hope finishing before goldenrod= 1/2 of the times   therefore the different arrangements W are 1/2* 6! = 360 = 360
Answer: B
Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days? Choose the correct choice from the following answers.
A) 33	B) 40	C) 99	D) 277	E) 28

Solution: We have M1 D1 = M2 D2   So, 24 * 35 = M2 * 21 => M2 = 40.   Answer:40
Answer: B
In a stack of boards at a lumber yard, the 25th board counting from the top of the stack is immediately below the 15th board counting from the bottom of the stack. how many boards are in the stack?  Options:
A) 38  B) 36  C) 35  D) 34  E) 32

Solution: 1 2 3 ... 14 15 16 ...................   ..............25 24 ................. 1   So the number of boards = 25+13= 
25+13 = 38
38   Option: 38
Answer: A
The wages earned by Robin is 20% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?  Choose the correct answer.
A) 18.75% B) 33% C) 30% D) 50% E) 100%

Solution: Let wage of Erica = 10   Wage of Robin = 1.2*10= 
1.2*10 = 12
12   Wage of Charles= 1.6 *10= 
1.6 *10 = 16
16   Percentage by which wage earned by Charles is more than that earned by Robin= (16-12)/12 * 100%   = 4/12 * 100%   =33%   Answer 33%
Answer: B
Johnny travels a total of one hour to and from school. On the way there he jogs at 6 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?  Choose the correct choice from the following answers: A) 2 miles B) 4 miles C) 4.8 miles D) 9.2 miles E) 10 miles

Solution: Answer: D) 9.2 miles.   Average speed for round trip = 2*a*b/(a+b), where a,b are speeds   so, average speed was = 2*6*20/(6+20) = 9.2m/hr   the distance between schoolhome should be half of that. ie. 9.2 miles   Answer 9.2 miles
Answer: D
An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?	Options.
A) 16
B) 36
C) 49
D) 144
E) 196

Solution: 49 = 7^2 so it can not be the square of an even number multiplied by an odd number.   The answer is 49.
Answer: C
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
Choose the correct choice from the following choices
A) 19	B) 88	C) 77	D) 14	E) 17

Solution: Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs.Answer:14
Answer: D
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?	Options.
A) 277  B) 268  C) 287  D) 480  E) 281

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer:480
Answer: D
A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 4 specified cars. In how many ways cars can be arranged? Choose the most appropriate option:
A) 1210	B) 650	C) 576	D) 1640	E) 1440

Solution: we arranged 2 specified cars in 4 slots = 4!   remaining 4 cars in 4 slots = 4!   number of ways = 4!*4! = 576   correct option is 576
Answer: C
A train 150 m long crosses a platform 100 m long in 10 sec; find the speed of the train?	Choose the correct choice from the following choices
A) 100 B) 70 C) 95 D) 90 E) 85

Solution: D = 150 + 100= 
150 + 100 = 250
250   T= 10   S = 250/10 * 18/5= 
250/10 * 18/5 = 90
90 kmph.   Answer: 90
Answer: D
Tom drives from town T to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between T and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?	Choose the most appropriate option:
A) 12  B) 20  C) 24  D) 30  E) 36

Solution: Let's assume that it takes 4 hours to go from point T to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to   120/6= 
  120/6 = 20
20   Hence the answer is 20.
Answer: B
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? Pick
A) 337
B) 267
C) 176
D) 100
E) 981

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   Answer:100
Answer: D
In a hostel there were 100 students. To accommodate 30 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 most appropriate option:	A) A)Rs.5800	B) B)Rs.5480	C) C)Rs.5400	D) D)Rs.5900	E) E)Rs.3900

Solution: 100x + 400   = 130(x – 5)   x = 35   100 *35 + 400= 
100 *35 + 400 = 3_900
3900   Answer:Rs.3900
Answer: E
If two men starting from same point, walking in the opposite directions with 9km/hr and 11km/hr as average speeds respectively. Then the distance between them after 8 hours is?	Options:
A) 106  B) 160  C) 610  D) 155  E) 165

Solution: Explanation:   Total distance = Distance traveled by person A+ Distance traveled by person 160   = (9Ã— 8) + (11Ã— 8)   = 72+ 88= 
72+ 88 = 160
160 Km   Answer:160
Answer: B
The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is?
Choose the correct choice: A) 22 B) 27 C) 18 D) 19 E) 11

Solution: Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :   Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice   (20-x)/(x-15) = 2/3 60 - 3x = 2x - 30   5x = 90 x = 18.   Answer: 18
Answer: C
5,6,8,11,?,20,26,33  Choose the correct option
A) 10
B) 13
C) 15
D) 8
E) 19

Solution: The Pattern is + 1, + 2, +3, ...   11+4= 
11+4 = 15
15   Answer :15
Answer: C
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?  Pick one:
A) Rs.6850 B) Rs.7268 C) Rs.6871 D) Rs.6150 E) Rs.6381

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1125   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1125   45k= 1125 => k = 25   246k = 246(25) = Rs. 6150   Thus the total rent paid by all the four agencies is Rs. 6150.   Answer:Rs.6150
Answer: D
20 machines can do a work in 10days. How many machines are needed to complete the work in 40days?	Choices.
A) 10 B) 6 C) 4 D) 7 E) 5

Solution: Required number of machines = 20*10/40= 
20*10/40 = 5
5   Answer is 5
Answer: E
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:  Choose the correct choice from the following answers:
A) 31 B) 35 C) 32 D) 38 E) 40

Solution: A + B + C = (45 * 3)= 
(45 * 3) = 135
135 --- (i)   A + B= (40 * 2)= 
(40 * 2) = 80
80 --- (ii)   B + C= (43 * 2)= 
(43 * 2) = 86
86 --- (iii)   Adding (ii) and (iii), we get: A + 2B + C= 166 --- (iv)   Subtracting (i) from (iv), we get: B = 31   B's weight = 31 kg.   31NSWER 31
Answer: A
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 140? Choose the correct choice from the following choices:
A) 3  B) 6  C) 28  D) 42  E) 70

Solution: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)   140 = 4*5*7   The G28F could be 4 or 28   The answer is 28.
Answer: C
Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Select the correct option: A) 11 min B) 56 min C) 13 min D) 20 min E) 19 min

Solution: Speed Ratio = 1:4/5 = 5:4Time Ratio   = 4:51 -------- 5 4 --------- ? è 20   Answer:20 min
Answer: D
A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But
whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11
mornings and 12 afternoons. How many days did they stay there totally?
Choices
A) 16 B) 18 C) 20 D) 13 E) 14

Solution: Explanation :   Clearly 11 mornings and 12 afternoons = 23 half days   => Since 13 days raining means 13 half days.   => So 23-13= 
23-13 = 10
10 halfdays ( not effecetd by rain )=> So 10 halfdays =5 fulldays   Hence ,   Total no. of days = 13+5= 
13+5 = 18
18 days   Answer : 18
Answer: B
Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
Choose the correct choice from the following answers
A) 1.5 B) 1.7 C) 2.3 D) 2.5 E) 3.0

Solution: Ratio of A to B in the final mixture = 50-30 : 30-15 = 4:3   Gallons of A used = 4/7*4 = 2.28   ANSWER:2.3
Answer: C
By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?	Choose the correct choice from the following.
A) 32 6/7%	B) 22 6/7%	C) 72 6/7%	D) 42 6/7%	E) 12 6/7%

Solution: Explanation:   SP = CP + g   50 SP = 50 CP + 15 SP   35 SP = 50 CP   35 --- 15 CP gain   100 --- ? => 42 6/7%   Answer: 42 6/7%
Answer: D
If the remainder is 8 when positive integer n is divided by 12, what is the remainder when n is divided by 6?	Choose the correct choice from the following options.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Assume x is quotient here,   n=12x+8 ----------(1)   and n=6x+ ?   We can also write equation (1) as:   n=(12x+6)+2.   ie 6(2x+1)+2 ie the first term is perfectly divisible by 6.   So,the remainder left is 2.   So,answer (2) is right choice.
Answer: C
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? Answers:  A) 175 m  B) 180 m  C) 185 m  D) 170 m  E) 190 m

Solution: Explanation:   Length of the train be â€˜Xâ€™   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   ANSWER IS 180 m
Answer: B
A and B start a business with Rs.5000 and Rs.7000 respectively. How should they share their profits at the end of one year?	Choose the correct option
A) 3:5	B) 3:4	C) 5:7	D) 3:2	E) 3:9

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and B =   5000 : 7000 => 5:7   Answer:5:7
Answer: C
In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots? Choose the correct answer
A) -12
B) -6
C) 12
D) 6
E) 24

Solution: Explanation:   The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a).   Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12.   we get, sum of the roots = 1 / a = 1   a = 1   Product of the roots = -12 / 1 =-12   -12NSWER: -12
Answer: A
A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 5. What are the coordinates of P?
Choose the correct choice from the following choices:
A) (5/2, 5/2)
B) (7/2, 7/2)
C) (9/2, 9/2)
D) (11/2, 11/2)
E) (15/2, 15/2)

Solution: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.   The x, y coordinates are 5/6 of the distance from 3 to 6.   x = 3 + (6-3)*(5/6) = 3 + 5/2 = 11/2 = y   The answer is (11/2, 11/2).
Answer: D
Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company M last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?	Choose the correct option:
A) 5/22
B) 4/22
C) 3/22
D) 9/22
E) 7/22

Solution: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.   Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be  12*1= 
 12*1 = 12
12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22   7/22
Answer: E
A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? Answers:
A) 1243 toys B) 1375 toys C) 1543 toys D) 1212 toys E) 1598 toys

Solution: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.   5500 * 4 = 1375 toys   correct answer 1375 toys
Answer: B
A 6 litre sol is 40% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?  Choose one:
A) A.0.6	B) B.1.2	C) C.2.1	D) D.3	E) E.5.4

Solution: 40% of 6 = 2.4   50% of 6 = 3   shortage is 0.6   so we need to have 0.6/50% to get 50% alcohol content.   = 1.2 B.1.2
Answer: B
The average age of 44 students in a group is 12 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
Choose the correct choice from the following answers:
A) cannot be determined	B) None of these	C) 55	D) 56	E) 57

Solution: Age of the teacher = (45 × 13 – 44 × 12) years   = 57 years.   Answer 57
Answer: E
The greatest common factor of positive integers m and n is 15. What is the greatest common factor of (2m^2, 2n^2)? Choose the correct choice from the following choices.
A) 15
B) 30
C) 150
D) 450
E) 900

Solution: m = 15j and n = 15k, where the greatest common factor of j and k is 1.   2m^2 = 2*15*15*j^2 and 2n^2 =  2*15*15= 
 2*15*15 = 450
450   The answer is 450.
Answer: D
What number has a 5:1 ratio to the number 10? Choose one.
A) 11
B) 50
C) 17
D) 12
E) 18

Solution: 5:1 = x: 10   x = 50   Answer: 50
Answer: B
In a dairy farm, 34 cows eat 34 bags of husk in 34 days. In how many days one cow will eat one bag of husk ?
Pick one.
A) 34 days	B) 40 days	C) 46 days	D) 50 days	E) None of these

Solution: Explanation:   Less Cows, More days (Indirect Proportion)   Less bags, Less days (Direct Proportion)   [Cows1 34   Bags 34 1]::34:x   =>x∗34∗1=34∗1∗34   =>x=34   Option 34 days
Answer: A