MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following must be true =>
A) The Average of N Consecutive integers is an integer for N being Even
B) The Average of N Consecutive integers is an integer for N being Odd
C) The product N(N+1)(N+2) for integer N must be divisible by both 3 and 6
D) 2N+1 is always Odd irrespective of N.	Answers: A) B,C,D B) A,C,D C) B,C D) Only D E) All of them

Solution: A) The Average of N Consecutive integers is an integer for N being Even. False. For consecutive integers when number of integers is even, average= middle two terms/2= O+E/2 (can not be an integer)   B) The Average of N Consecutive integers is an integer for N being Odd. The middle term will be the average, and this term is odd integer.   C) The product N(N+1)(N+2) for integer N must be divisible by both 3 and 6. Either the product will be 0 or will have multiple of both 2 and 3 and 6. True.   D) 2N+1 is always Odd irrespective of N. What if =1/2, then 2N+1= 2   only B and C are true.   ANSWER:B,C
Answer: C
area of square = sum of areas of rect1(41*27) and rect2(41*14). find square side
Options.
A) 93 B) 40 C) 41 D) 42 E) 58

Solution: area of square=1107+574= 
1107+574 = 1_681
1681   side of the square=sqrt(1681)=41   ANSWER:41
Answer: C
If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 5n years to that after 3n years?  Pick
A) (1+k/100)^2n	B) (1+k)^n	C) (1+kn/100)	D) (1+n/100)^k	E) (1+kn)

Solution: Amount after 3n years will be = x ( 1 + k/100)^5n   Amount after 3n years will be = x ( 1 + k/100)^3n   So, required ratio will be -   { x ( 1 + k/100)^5n } / {x ( 1 + k/100)^3n } = (1+k/100)^n   Hence answer will be a. (1+k/100)^2n   (1+k/100)^2n
Answer: A
Last year Elaine spent 10% of her annual earnings on rent. This year she earned 15% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?  Choose the correct choice from the following.
A) 252.5  B) 364.5  C) 367.5  D) 375  E) 345

Solution: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.   She would've spent $10 of this on rent.   This year she earned 15% more, or $115.   She would've spent 30% of this on rent, or $34.5   Do $34.5/$10   This will give you 345%   345 is the correct answer.
Answer: E
x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b?	Answers:
A) 24
B) 21
C) 20
D) 17
E) 15

Solution: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20.   Answer: 20.
Answer: C
Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 2000 widgets?	Choose the correct choice from the following
A) 3 hour and 20 minutes  B) 3 hour and 24 minutes  C) 3 hour and 30 minutes  D) 3 hour and 36 minutes  E) 3 hour and 40 minutes

Solution: (350+250)t=2000   600t=2000   t=10/3   t=3 hour and 20 minutes   3 hour and 20 minutesnswer: 3 hour and 20 minutes
Answer: A
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is : Options
A) 700 B) 690 C) 650 D) 698 E) 728

Solution: Explanation :   Simple Interest (SI) for 1 year = 854-815= 
854-815 = 39
39   Simple Interest (SI) for 3 years= 39 × 3 = 117   Principal = 815 - 117 = Rs.698   Answer : Option 698
Answer: D
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent? Choose the correct choice
A) 32  B) 20  C) 287  D) 277  E) 291

Solution: 900 ---- 180   100 ---- ? => 20   Answer: 20
Answer: B
If the average (arithmetic mean) of 5 positive temperatures is p degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:  Select:
A) 6p B) 4p C) 5p/3 D) 3p/2 E) 3p/5

Solution: The sum of three greatest should be more than sum of two lowest.   The total sum is; 5p   A. 6p; 6p is more than 5p. Not possible.   B. 4p; 5p-4p=p(Possible)   C. 5p/3; 10p/3; 10p/3 > 5p/3. Not possible   D. 3p/2; 7p/2; 7p/2 > 3p/2. Not possible   E. 3p/5; 22p/5; 22p/5 > 3p/5. Not possible.   Ans:4p
Answer: B
Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
Choose the correct option:
A) 20
B) 92
C) 300
D) 372
E) 476

Solution: # of letters = 8, # of ways to choose 3 letters out of 8 when order matters is P38=8!/(8−3)!=336 which means that there can be 336 different sequences. As 36 sequences were not assigned then  336-36= 
 336-36 = 300
300 sequences were assigned, so there are 300 participants.   ANSWER:300
Answer: C
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?  Answers
A) Rs2,00,000 B) Rs1,05,000 C) Rs4,05,000 D) Rs 6,50,000 E) None

Solution: Explanatory Answer   Let the cost of an equipment is Rs. 100.   Now the percentages of depreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which are in A.P., with a = 15 and d = - 1.5.   Hence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5   Also total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5   Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.   The total cost being Rs. 6,00,000/100 * 17.5 = Rs. 1,05,000.   Answer Rs1,05,000
Answer: B
A persons salary iis decreased by steps of 20%, 15% and 10%. What will be the percentage decrease, if the salary is decreased in a single shot?	Choose the correct choice from the following answers.
A) 34.8%
B) 36.8%
C) 38.8%
D) 39.8%
E) 32.8%

Solution: Let x is his initial salary.   After 1st decrease, x1 = x- (x*20/100) = x - x/5 = 4x/5   After 2nd decrease, x2 = 4x/5 - ((4x/5)*15/100) = 4x/5 - 3x/25 = 17x/25   After 3rd decrease, x3 = 17x/25 -((17x/25)*10/100) = 17x/25 - 17x/250 = 153x/250   So if its decreased in single shot, x - y(decreased) = 153x/250   => y = x - 153x/250 => y = 97x/250 => y = 0.388x => y = 38.8%   ANSWER:38.8%
Answer: C
Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?  Choose the correct choice from the following choices
A) 2:3:9  B) 24:25:36  C) 7:6:10  D) 12 : 15 : 16  E) None of these

Solution: Explanation:   Aman : Rakhi : Sagar =(70000Ã—36)=(70000Ã—36) :(105000Ã—30):(105000Ã—30) :(140000Ã—24):(140000Ã—24)   =12:15:16=12:15:16.   ANSWER IS 12 : 15 : 16
Answer: D
35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? Answers
A) 87  B) 18  C) 42  D) 16  E) 10

Solution: Binders Books Days   35 1400 21   x 1600 20   x/35 = (1600/1400) * (21/20) => x = 42   Answer:42
Answer: C
Which of the following numbers has the greatest number of distinct prime factors?
Choose the correct choice from the following answers:
A) 165  B) 192  C) 228  D) 330  E) 332

Solution: 165=3*5*11   192=2^6 *3   228=2^2 *3*19   330=2*3*5*11   332=2^2 * 83   330 has 4 distinct prime factors   Answer 330
Answer: D
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?	Select.
A) 766 sq.cm  B) 165 sq.cm  C) 186 sq.cm  D) 168 sq.cm  E) 600 sq.cm

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   Answer:600 sq.cm:
Answer: E
An bus covers a certain distance at a speed of 300 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
Choose the most appropriate option.
A) 1520 km/hr B) 1640 km/hr C) 1656 km/hr D) 1500 km/hr E) 1520 km/hr

Solution: Distance = (300 x 5) = 1500 km.   Required speed = 1500 km/hr.   1500 km/hr
Answer: D
Two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? Choose the correct answer:  A) 10  B) 11.3  C) 13  D) 14  E) 15

Solution: Speed of the first train = 120/9 = 13.3 m/sec.   Speed of the second train = 120/15= 
120/15 = 8
8 m/sec.   Relative speed= 13.3 + 8= 
13.3 + 8 = 21.3
21.3 m/sec.   Required time= (120 + 120)/21.3 = 11.3 sec.   Answer: Option 11.3
Answer: B
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Choose the correct choice:
A) 6	B) 4	C) 2	D) 5	E) 1

Solution: Let the two consecutive even integers be 2n and (2n + 2). Then,   (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n)   = 2(4n + 2)   = 4(2n + 1), which is divisible by 4.   ANSWER 4
Answer: B
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 45 sec. The length of each train is?  Pick one:
A) 50	B) 26	C) 27	D) 62.5	E) 21

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/45 = 25/9 => x = 65.5.   Answer: 62.5
Answer: D
A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 126 km downstream.
Select the correct option:
A) 4 hours B) 5 hours C) 6 hours D) 7 hours E) 8 hours

Solution: Explanation:   It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.   Lets see the question now.   Speed downstream = (16 + 5)= 
(16 + 5) = 21
21 kmph   Time= distance/speed = 126/21= 
126/21 = 6
6 hours   Option 6 hours
Answer: C
Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?
Select the correct option:
A) Rs. 520  B) Rs. 480  C) Rs. 420  D) Rs. 200  E) Rs. 600

Solution: Explanation:   SI in 2 years = Rs. 20, SI in 1 year = Rs. 10   CI in 2 years = Rs. 21   % rate per annum = [(CI – SI) / (SI in 1 year)] *100   = [(21 – 20) / 20] * 100   = 5 % p.a.   Let the principal be Rs. X   Time = T = 2 years   % rate = 5% p.a.   SI = (PRT/100)   20 = (X*5*2) / 100   X = Rs. 200   ANSWER: Rs. 200
Answer: D
The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?	Choose the most appropriate option.
A) 3:9  B) 3:0  C) ratio 3:5  D) 3:2  E) 3:1

Solution: Let the present ages of the two brothers be x and 2x years respectively.   Then, (x - 5)/(2x - 5) = 1/3   3(x - 5) = (2x - 5) => x = 10   Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5   Answer: ratio 3:5
Answer: C
If the sum of a number and its square is 210, what is the number? Choose the correct choice from the following answers
A) 14
B) 26
C) 28
D) 91
E) none of these

Solution: Let the number be x. Then,   x + x2 = 210   (x + 15)(x - 14) = 0   x = 14   14NSWER:14
Answer: A
The edges of a cuboid are 4 cm, 4 cm and 6 cm. Find the volume of the cuboid?	Choose the correct answer.
A) 90	B) 60	C) 96	D) 80	E) 72

Solution: 4*4*6= 
4*4*6 = 96
96   Answer: 96
Answer: C
What is the average (arithmetic mean) of all the multiples of ten from 10 to 210 inclusive? Pick: A) 90 B) 95 C) 100 D) 120 E) 110

Solution: 10 and 190 inclusive would mean there are 21 terms.   No need to add up all the terms and further divide by 21 since the terms are evenly spaced in ascending order from 10, 20, 30........210   The middle term is the average which is the tenth term = 120   120 is the answer.
Answer: D
Working together, Jose and Jane can complete an assigned task in 5 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 15 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose Choose the correct answer: A) 26 days B) 15 days C) 60 days D) 65 days E) 36 days

Solution: Assume:   Jose does 1 job in x days, so Jose does 1/x job in a day   Jane does 1 job in y days, so Jane does 1/y job in a day   Together, they does (x+y)/xy job in a day. This is equals to 1/20. So   (x+y)/xy = 1/5   5(x+y) = xy   Next, we're told 1 job takes 15 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.   x/2 + y/2 = 15   x+y = 30   So   xy = 150   The answer choices are:   26 days   15 days   60 days   65 days   36 days   From the answer choices, So I'll go for 15 days for Jose and 10 days for Jane.   Answer : 15 days
Answer: B
Which four figure number contains four different digits and meets the following criteria? The first digit is twice the value of the fourth digit and two more than the second digit. The third digit is one more than the first digit and four more than the fourth digit. Choose the correct choice:
A) 5367  B) 6473  C) 3573  D) 3262  E) 7364

Solution: 6473   6473
Answer: B
k = 2^n + 9, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
Choose the correct option:
A) 2^n - 8  B) 2^n - 2  C) 2^n+5  D) 2^n + 4  E) 2^n

Solution: Given: k, M and N are integers   If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)   We're told that 9 is a divisor of 2^n + 9   We also know that 9 is a divisor of9.   So, applying the aboverule, 9 is a divisor of 2^n + 9 +9, and 9 is a divisor of 2^n +9 -9 =2^n   2^n
Answer: E
Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?	Select
A) 12, 9	B) 10, 5	C) 12, 7	D) 11, 6	E) 13, 8

Solution: Explanation:   x – y = 5   4x – 6y = 6   x = 12 y = 7   ANSWER IS 12, 7
Answer: C
Lakshmi took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If she paid Rs. 960 as interest at the end of the loan period, what was the rate of interest?	Choose the correct choice from the following
A) 8 B) 7 C) 6 D) 5 E) 4

Solution: Let rate = R% and time = R years.   Then, (1500 * R * R) / 100 = 960   15R2 = 960   R2 = 64 => R = 8   8nswer:8
Answer: A
If Danny scored 86, 75, 52, 87, 85 and 82 marks (out of 100) in English, Social Studies, Art, Music, Biology and French. What are his average marks ?
Choose the correct answer:
A) 77.8 B) 75.8 C) 67.8 D) 87.8 E) 97.8

Solution: Explanation:, 75, 52, 87 and 82   Average = (86+ 75 + 52 + 87 + 85 + 82 )/ 6 = 77.8.   77.8nswer: 77.8)77.8
Answer: A
Let the polynomials be:
P1(x)=3x2−7x+3,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=	Select the correct option
A) 2x2 + 11x - 7 B) -2x2 - 11x + 5 C) -2x2 - 11x + 6 D) 2x2 - 9x + 7 E) None of these

Solution: Solution:   P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=   3x2−7x+3−5x2−4x+2=3x2−7x+3−5x2−4x+2=   −2x2−11x+5   Answer -2x2 - 11x + 5
Answer: B
Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?  Pick one:
A) 12 : 15 28
B) 12 : 15 :29
C) 12 : 15 :99
D) 12 : 15 :16
E) 12 : 15 :11

Solution: Explanation:   Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24) = 12 : 15 : 16.   Answer: 12 : 15 :16) 12 : 15 :16
Answer: D
A factory has 15 machines of equal efficiency in its factory. The annual manufacturing costs are Rs.42,000 & establishment charges are Rs.12,000. The annual output of the company is Rs.70,000. The annual output and manufacturing costs are directly proportional to the number of machines. The shareholders get 12.512.5 profit, which is directly proportional to the annual output of the company. If 7.147.14 machines remain closed throughout the year, then the % decrease in the amountof profit of the shareholders would be? Choose the correct choice from the following choices.
A) 12.5%	B) 13.5%	C) 14%	D) 15%	E) 16%

Solution: Option(B) is correct   Original profit   = 70,000−42,000−12,000=16,00070,000−42,000−12,000=16,000   If 7.14%7.14% of 14 i.e. one of the machines closed throughout the year, then change in profit will be:   =1314×[70,000−42,000]=1314×[70,000−42,000]   =14,000=14,000   Thus, decrease in the profit %%   =200016000×100=200016000×100   =12.5%   12.5%
Answer: A
Sue planted 4 times as many apple seeds as she planted orange seeds. 15 percent of the apple seeds grew into trees, and 10 percent of the orange seeds grew into trees. If a total of 420 apple trees and orange trees grew from the seeds, how many orange seeds did Sue plant?  Pick one:	A) 540	B) 600	C) 660	D) 720	E) 760

Solution: Sue planted 4 times as many apple seeds as she planted orange seeds.   Yes, apple:orange be 4:1 but this translates to Apple = 4*Orange and not 4*Apple = Orange   Let Orange be x   Apple = 4*Orange = 4x   0.15Apple + 0.10Orange = 420   => 0.15*4x + 0.10*x = 420   => 0.7x = 420   => x = 600   So, answer will be 600
Answer: B
The proportion of water to alcohol in Solution A is 5:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? Choose one:	A) 36.7%	B) 37.6%	C) 38.3%	D) 39.8%	E) 40.5%

Solution: Let V be the total volume of the new solution.   Then a volume of V/2 was added from each solution A and B.   The amount of alcohol added to the new solution was:   (1/6)(V/2)+(3/5)(V/2)=V/12+3V/10=23V/60.   The concentration of alcohol is 23/60=38.3%   The answer is 38.3%.
Answer: C
Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.  Choose the correct option.
A) 40  B) 60  C) 120  D) 90  E) 100

Solution: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:   Sa/Sb = √(b/a)   i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.   Sa/Sb = √(4/9) = 2/3   This gives us that the ratio of the speed of A : speed of B as 2:3.   Since speed of A is 60 kmph, speed of B must be 80*(3/2) = 90 kmph   90
Answer: D
A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates C apply to what fraction of a week?	Choose one
A) 1/2 B) 5/8 C) 9/14 D) 16/21 E) 9/10

Solution: Number of hours between 8 PM to 8 AM = 12   Number of hours with reduced rates = (12*5)+(24*2)   Hours with reduced rates 9/14/Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14   Answer: 9/14
Answer: C
Karan started a business investing Rs 29000. After five months, Satish joined with a capital of Rs 18000. If at the end of the year, they earn a profit of Rs. 16970, then what will be the share of Satish in the profit ?
Pick one:
A) 4512  B) 4552  C) 4511  D) 4529  E) 4771

Solution: Now as per question, Karan invested for 12 months and Satish invested for 7 months.   So   Karan:Satish = (29000*12):(18000*7)   = 348:126   = 58:21   Satish Ratio in profit will be   =(16970 )=Rs. 4511   Answer: 4511
Answer: C
The average age of husband, wife and their child 3 years ago was 21 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is  Choose one
A) 22 years	B) 40 years	C) 50 years	D) 55 years	E) None

Solution: Solution   Sum of the present ages of husband, wife and child	= (21x3+3x3) years   = 72 years.   Sum of the present ages of wife and child	= (20x2+5x2) years   = 50 years.   âˆ´ Husband's present age	= (72 - 50)= 
(72 - 50) = 22
22 years.   22 yearsnswer 22 years
Answer: A
What is the least possible product of 4 different integers, each of which has a value between –4 and 10, inclusive?	Choose the correct choice
A) –5040
B) –2880
C) –720
D) –600
E) –120

Solution: Maximize the total product with a -ve sign   so -4 * 10 * 9 * 8 = 720 * -4 = -2880   Answer is –2880.
Answer: B
Jones has 6 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 12 shoes, what is the probability that she will select 2 shoes of the same color?  Choose the correct choice.
A) 2/5 B) 1/13 C) 1/9 D) 1/10 E) 1/25

Solution: Can be tackled in this way as well: Probability of selecting any 1 out of 12 shoes = 12/12= 
12/12 = 1
1   Probability of selecting the next shoe (out of 13 available) having the same color= 1/13 (as after selecting the 1st one, there is only 1 another shoe left with the same color).   Thus the total probability = 1*1/13=1/13.   1/13 is the correct answer.
Answer: B
43 : 34 :: 52 :? Pick: A) 49 B) 25 C) 36 D) 64 E) 56

Solution: Ans 25   Reverse of 52   ANSWER:25
Answer: B
One fourth of a solution that was 15% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight? Select:
A) 24%
B) 34%
C) 22%
D) 19%
E) 8.5%

Solution: consider total solution to be 100 liters and in this case you'll have: 75*0.15+25*x=100*0.16 --> x=0.19.   Answer: 19%.
Answer: D
There are 38 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
Pick: A) 6 B) 12 C) 19 D) 24 E) 27

Solution: 38*2/3 *3/4= 
38*2/3 *3/4 = 19
19   Answer: 19
Answer: C
The sector of a circle has radius of 21 cm and central angle 110o. Find its perimeter?
Choose the correct choice from the following options:
A) 91.5
B) 91.4
C) 91.7
D) 82.3
E) 91.1

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (110/360 * 2 * 22/7 * 21) + 2(21)   = 40.3 + 42= 
40.3 + 42 = 82.3
82.3 cm   Answer:82.3
Answer: D
In a test containing 16 questions , contestants get a base core of 20 points for taking the test. 5 points for each correctly answered question and 2 points for each unanswered question.An incorrectly answeredquestion is worth 0 points.Of the following scores which one is not attainable
Choose the correct choice from the following:
A) 96
B) 97
C) 94
D) 95
E) 93

Solution: 1. 15 corrected and 1 uncorrected   20+5*15+0= 
20+5*15+0 = 95
95   2.15 corrected and 1attempted   20+5*15+2= 
20+5*15+2 = 97
97   3. 14corrected+2attempted   20+14*5+2*2= 
20+14*5+2*2 = 94
94   so 96 is not possible   96NSWER:96
Answer: A
Out of 10 persons working on a project, 7 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?	Choose the correct choice from the following: A) 5/7 B) 119/3 C) 5/120 D) 119/120 E) 5/6

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - 3C₃/¹⁰C₃ = 1 - (1)/(10 * 9 * 8)   = 119/120   Answer: 119/120
Answer: D