MU-NLPC/Calc-aqua_rat huggingface dataset:
If it is true that z < 8 and 2z > -4, which of the following must be true?	Choose the correct choice:
A) -8 < z < 4  B) z > 2  C) z > -8  D) z < 4  E) None of the above

Solution: Two points:   1) z < 8   2) 2z > -4 or z > -2   From 1 and 2: -2 < z < 8   (A) is not true because z could be > 4.   (B) is not true because z could be < 2.   (C) is true because z's value is always > -8.   (D) is not true because z could be >4.   (E) is not true because z > -8 is true.
Answer: C
20% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 3000. Find the number of original inhabitants? Choose the most appropriate option
A) 2500  B) 3000  C) 1500  D) 2000  E) 5000

Solution: Let the total number of original inhabitants be x   Then, (100-25)% of (100-20)% of x = 3000   75/100 * 80/100 * x = 3000   x = 5000   Answer is 5000
Answer: E
Susan finds that she spends her free time during summer vacation between swimming, reading, and hanging out with friends in a ratio of 1:4:10. How many hours did she spend reading if she hung out with her friends for 20 hours? Choose one.
A) 2  B) 4  C) 5  D) 8  E) 10

Solution: The ratio is 1 hour swimming: 4 hours reading: 10 hours hanging out with friends.   Divide 20 by 10 to find 1 "part" of the ratio.   20/10= 
20/10 = 2
2   Multiply this by 4 to find the hours spent reading.   2*4= 
2*4 = 8
8   The answer is 8.
Answer: D
8 ÷ 4 (3 - 2) x 4 + 3 - 7 = ? Choose one
A) - 3  B) - 4  C) 4  D) 5  E) 6

Solution: Answer   Given expression = 8 ÷ 4 (3 - 2) x 4 + 3 - 7   = 8 x (1/4) x 1 x 4 + 3 - 7   = 8 + 3 - 7= 
8 + 3 - 7 = 4
4   Option: 4
Answer: C
Jug contains water and orange juice in the ratio 5:7 . another jug contains water and orange juice in ratio 7 : 2 . In what proportion should these 2 liquids be mixed to give a water and orange juice in ratio 3 : 4	Select
A) 4 : 5 B) 85 : 3 C) 88 : 3 D) 2 : 3 E) 87 : 7

Solution: Let x ml of Jug 1 be mixed with y ml of jug 2   5x/12 + 7y/9 = 3/7*(x+y)   7x/12 + 2y/9 = 4/7 *(x+y)   => (15x + 28y)/36 = 3/7 * (x+y)   => 105x + 196y = 108x + 108y   => 88y - 3x = 0   => x/y = 88/3   Answer - 88 : 3
Answer: C
If Jamie's income is Rs 20000, calculate his savings given that his income and expenditure are in the ratio 7:5.?  Options.
A) Rs 7500
B) Rs 4000
C) Rs 2000
D) Rs 8000
E) Rs 7000

Solution: Let the income and the expenditure of the person be Rs.7x and Rs.7x respectively.   Income, 7x = 28000 => x = 4000   Savings = Income - expenditure = 7x - 5x = 2x   So, savings 7  - 5= 
7  - 5 = 2
2x   So, savings= Rs.8000   Answer: Rs 8000
Answer: D
If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is: Select: A) 0.2 B) 0.4 C) 0.3 D) -0.4 E) 0.1

Solution: (0.2)x = 2.   Taking log on both sides   log (0.2)x = log 2.   x log (0.2) = 0.3010, [since log 2 = 0.3010].   x log (2/10) = 0.3010.   x [log 2 - log 10] = 0.3010.   x [log 2 - 1] = 0.3010,[since log 10=1].   x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].   x[-0.699] = 0.3010.   x = 0.3010/-0.699.   x = -0.4306….   x = -0.4 (nearest tenth)   Answer : -0.4
Answer: D
Find the odd man out
15, 35, 45, 24 ,55, 65, 95  Choose the correct choice from the following options:
A) 15 B) 24 C) 55 D) 95 E) 35

Solution: In the series, 24 is the number which is not divisible by 5.   ANSWER:24
Answer: B
If the sales tax be reduced from 4 (1/5) % to 3(1/4) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 5400? Choose the correct choice from the following answers
A) Rs. 100.2
B) Rs. 50.2
C) Rs. 20.5
D) Rs. 100
E) None of these

Solution: Explanation:   Required difference = (4 (1/5) of Rs. 5400) - (3 (1/4) of Rs. 5400)   = (21/5 – 13/4) % of Rs. 5400   = (19/20) x (1/100) x 5400   = Rs. 51.30   ANSWNone of theseR None of these
Answer: E
If the a radio is sold for rs 490 and sold for rs 465.50.find loss%.
Choices:
A) 2% B) 4% C) 3% D) 5% E) 6%

Solution: sol. cp=rs490,sp= 465.50.   loss=rs(490-465.50)=rs 24.50.   loss%=[(24.50/490)*100= 
(24.50/490)*100 = 5
5%   ANSWER 5%
Answer: D
Paul’s salary is reduced by 50% and then reduced salary is increased by 50%. Find ,how many percentage his present salary is less as compared to his previous salary?  Answers:
A) 20% B) 25% C) 30% D) 15% E) 10%

Solution: 50*50   -------- = 25%   100   Answer: 25%
Answer: B
Peter invests a sum of money and gets back an amount of $ 810 in 3 years . David invests an equal amount of money and gets an amount of $854 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?	Choose the correct answer:	A) 670	B) 683	C) 698	D) 744	E) 700

Solution: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.   David invested for one year more than Peter and hence he got interest amount for one more year.   Interest earned per year = Amount received by David - Amount received by Peter = 854 - 810= 
854 - 810 = 44
44   Interest earned for 3 years= 44*3= 
44*3 = 132
132   Amount invested= 815 - 132= 
815 - 132 = 683
683   Answer: 683
Answer: B
Which of the following has a decimal equivalent that is a terminating decimal?  Choose the correct choice from the following choices:
A) 2/3^20
B) 3^5/20^3
C) 2^3/3^2
D) 8^2/7^5
E) 3^6/6^3

Solution: For a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values   Hence,   1. There is a 3 in the denominator, hence it is a non terminating decimal   2. Has both 2 and 5 in the denominator, hence terminating   3. There is a 3 in the denominator, hence it is a non terminating decimal   4. There is a 7 in the denominator, hence it is a non terminating decimal   5. Has both 2 & 3 in the denominator, hence non terminating   Option 3^5/20^3
Answer: B
What is theleast number should be added to 410, so the sum of the number is completely divisible by 20?	Choose the correct choice from the following choices:  A) 1  B) 2  C) 10  D) 6  E) 8

Solution: (410 / 20) gives remainder 10   10 + 10= 
10 + 10 = 20
20, So we need to add 10   Answer : 10
Answer: C
A dishonest DEALER professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? Choose the correct choice from the following answers.
A) 29%  B) 25%  C) 235%  D) 85%  E) 22%

Solution: 800 --- 200   100 --- ? => 25%   Answer: 25%
Answer: B
Let C be defined as the sum of all prime numbers between 0 and 38. What is C/3  Choose the correct choice from the following answers:
A) 155
B) 76.6
C) 61
D) 47
E) 43

Solution: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23 , 29, 31, 33, 37   Sum,C = 230   C/3 = 76.6   Answer 76.6
Answer: B
If 3g + 1 < 2g < 9 - g, which of the following must be true?
I. -1 < g < 3
II. g < -1
III. g < 3
Select the correct option.
A) II only	B) III only	C) I and II only	D) II and III only	E) I, II and III

Solution: Just try plugging g in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.   So you can immediately cross out any answers with I or III, leaving just (II only) II only.
Answer: A
For any positive integer n, n>1, thelengthof n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 60 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000. Choose the correct choice from the following choices:
A) 10
B) 9
C) 8
D) 7
E) 6

Solution: you are missing something in your post:   For any positive integer n , n > 1, thelengthof n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)   the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6   but we need n < 1000   using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 8 the length of 512.   the answer is (8)
Answer: C
If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place.	Choices.
A) 5 hours	B) 10 hours	C) 15 hours	D) 20 hours	E) 25 hours

Solution: 1/5+2/8 + 3/x = 1x =20 hours. ANSWER =20 hours
Answer: D
The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?  Choose the correct choice:
A) 7	B) 9	C) 11	D) 13	E) 14

Solution: Explanation:   3x + 5x + 7x = 45   x =3   3x = 9   9)
Answer: B
Two trains 200 m and 180 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
Choose the correct choice from the following
A) 72 sec B) 132 sec C) 192 sec D) 273.6 sec E) None

Solution: Solution   Relative Speed	= (45 - 40 )= 
(45 - 40 ) = 5
5 kmph=(5 x 5 / 18)m/sec   = (25 / 18 ) m/sec   Time taken	= (380 x 18 / 25) sec   = 273.6 sec.   Answer 273.6 sec
Answer: D
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 3 years and that for 15 years?  Choose the correct choice from the following choices.
A) 3 : 2  B) 1 : 5  C) 2 : 3  D) 3 : 1  E) 2 : 1

Solution: Explanation :   Simple Interest = PRT/100   Here Principal(P) and Rate of Interest (R) are constants   Hence, Simple Interest ∝ T   Required Ratio = Simple Interest for 3 years/Simple Interest for 15 years   =T1/T2   =3/15   =1/5   =1:5   Answer : Option 1 : 5
Answer: B
A 90-liter solution of cool-drink is made from 5% jasmine water. If 8 liters of jasmine and 2 liters of water were added to the solution, what percent of the solution is jasmine?
Choose the correct choice from the following answers: A) 6.5% B) 8.5% C) 10.5% D) 12.5% E) 14.5%

Solution: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)   (0.05(90) + 8) / 100 = 12.5/100 = 12.5%   The answer is 12.5%.
Answer: D
ABCD is a square where AB =âˆš6000. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD.	Choices:  A) 3008  B) 2002  C) 1008  D) 2016  E) 3000

Solution: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is   always   6000/2= 
6000/2 = 3_000
3000 .   correct answer 3000
Answer: E
The sale price sarees listed for Rs.400 after successive discount is 12% and 5% is? Choose the correct option.
A) 338	B) 277	C) 342	D) 334.4	E) 212

Solution: 400*(88/100)*(95/100)= 
400*(88/100)*(95/100) = 1_672/5 = around 334.4
334.4   Answer: 334.4
Answer: D
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:  Choose the correct choice from the following choices: A) 5:4 B) 4:5 C) 2:5 D) 5:2 E) None of them

Solution: Let the third number be x.   Then, first number = 120% of x = 120x/100 = 6x/5   Second number = 150% of x = 150x/100 = 3x/2   Therefore, Ratio of first two numbers = (6x/5 : 3x/2)   = 12x : 15x = 4 : 5.   Answer is 4:5.
Answer: B
There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?	Choices:
A) 2/23  B) 3/23  C) 4/25  D) 5/26  E) 8/21

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(8/21) = 8/21.
Answer: E
A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability E that all 3 jellybeans removed from the bag are blue?	Choose one.
A) 9/100  B) 2/19  C) 1/8  D) 3/20  E) 3/10

Solution: Method-1   10 red jellybeans and 10 blue jellybeans   Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140   Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all 2/19lue out of 10 2/19lue = 10C3 = 120   Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3   Probability E= 120 / 1140 = 2/19   Answer: option 2/19   Method-2   Probability of First jelly bean to be 2/19lue = 10/20 [Total 10 2/19lue out of total 20 jellybeans]   Probability of Second jelly bean to be 2/19lue = 9/19 [Total 9 2/19lue remaining out of total 19 jellybeans remaining]   Probability of Third jelly bean to be 2/19lue = 8/18 [Total 8 2/19lue remaining out of total 18 jellybeans remaining]   Required Probability = (10/20)*(9/19)*(8/18) = 2/19   Answer: option 2/19
Answer: B
The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? Choose the most appropriate option:
A) 28	B) 26	C) 18	D) 109	E) 12

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 324/3= 
324/3 = 108
108 sq m   l b= 108 i.e., l * l/3 = 108   l2 = 324 => l = 18.   Answer:18
Answer: C
Machine C takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine C to make 40 widgets? Choose the correct choice from the following:
A) 5 B) 6 C) 8 D) 10 E) 12

Solution: i approached this one by plugging in numbers...started with C.   if 40 are made in 8 hours, then 20 are made in 4 hours. so time of C is 4, and time of B is 2.   rate together: 20/4 + 20/2 = 5+10= 
5+10 = 15
15. so in 1 hour, together make 15 widgets. in 3 hours= 45. way too much. we can eliminate right away C, B, and A - because B and C reduces the time - the total # of widgets made will be even higher.   now between D and E -> try only one ..if it doesn't work, then the other one is the answer.   i picked E:   12h to make 40 widgets, and 6 hours to make 20. this is the time of C. time of B=4 hours.   20/6 + 20/4 = 10/3 + 20/4   find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:   40+60/12 = 100/12   divide by 4:   25/3   so this is the rate given.   12 is the correct answer
Answer: E
50 boys and 100 girls are examined in a test; 50% of the boys and 40% of the girls pass. The percentage of the total who failed is ?
Choices.
A) 42.5%	B) 62.1%	C) 56.7%	D) 39.9%	E) 51.4%

Solution: Total number of students = 50+100= 
50+100 = 150
150   Number of students passed= (50% of 50+40% of 100) = 25+40= 
25+40 = 65
65   number of failures= 85*100/150 = 56.7%   Answer is 56.7%
Answer: C
What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively?
Choices.
A) Rs. 6000
B) Rs. 6300
C) Rs. 6400
D) Rs. 6480
E) Rs. 7000

Solution: Area of the parallelogram = Length of the base * Perpendicular height   = 54 * 24= 
54 * 24 = 1_296
1296 m.   Total cost of levelling= Rs. 6480   Rs. 6480
Answer: D
The radius of a cone is 4 m, height 5 m. Find the curved surface area?  Choose the correct choice from the following options:
A) 1 B) 3 C) 5 D) 7 E) 9

Solution: 5one curved surface area = πrl = 22/7 × 4 × 5 = 440/7 = 62 6/7   Slant height (l) = √r(power2)+h(power2) = √16+9= 
16+9 = 25
√25= 5
Answer: C
Product of two co-prime numbers is 117. Their L.C.M should be Choose the correct choice from the following
A) 1	B) 117	C) equal to their H.C.F	D) cannot be calculated	E) None

Solution: Solution   H.C.F of co-prime numbers is 1.   So, L.C.M	= 117/1= 
117/1 = 117
› 117.   Answer 117
Answer: B
Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?  Choose the correct answer: A) 2888 B) 2689 C) 2522 D) 277 E) 2911

Solution: A = 1600(21/20)3 = 2522.Answer: 2522
Answer: C
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 4x boxes?	Choose the most appropriate option.
A) 3 minutes	B) 4 minutes	C) 5 minutes	D) 6 minutes	E) 8 minutes

Solution: Rate = Work / Time   Given Rate of Machine A = X / 10 min   Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .   Rate of Machine B = 4x / 10   we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates   let's first find the combined Rate of Machine A and B   Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10   Now combine Time = combine work needs to be done / Combine Rate = 4x/5x * 10 = 8 Min   Ans: 8 minutes4 /5  * 10= 
4 /5  * 10 = 8
8 Min   Ans: 8 minutes
Answer: E
A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 5.4 kilometer long bridge, at the same speed?  Pick.
A) 4 min  B) 2 min  C) 8 min  D) 6 min  E) 3 min

Solution: S = 600/40= 
600/40 = 15
15 mps   S=5400/15= 
5400/15 = 360
360 sec= 6 min.Answer:6 min
Answer: D
The average of 6 observations is 15. A new observation is included and the new average is decreased by 1. The seventh observation is?  Choose one: A) 1 B) 8 C) 5 D) 6 E) 7

Solution: Let seventh observation = X.   Then, according to the question we have   => (90 + X) / 7 = 14   => X = 8   Hence, the seventh observation is 8   ANSWER:8
Answer: B
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary? Choose one:
A) 6000	B) 5000	C) 5500	D) 4000	E) 3500

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 â€“ 96 =Rs. 4   100 ------ 4   ? --------- 200 => 5000   ANSWER 5000
Answer: B
A bag contains 12 white and 18 black balls.Two balls are drawn in succession without replacement. What is the probability that first is white and second is black? Options
A) 36/145 B) 29/145 C) 18/145 D) 20/145 E) 15/145

Solution: The probability that first ball is white=12C1/30C1=12/30=2/5   Since.the balls is not replaced; hence the number of balls left in bag=29.   Hence the probability of second ball is black is 18C1/29C1=18/29   Required probability =(2/5)*(18/29)=36/145   The answer is option 36/145
Answer: A
With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?  Pick:
A) 400 km
B) 480 km
C) 490 km
D) 380 km
E) 330 km

Solution: B   480 km   Let the distance be x km. Then,   x/(7 1/2) - x/8 = 4   2x/15 - x/8 = 4 => x = 480 km.
Answer: B
The average monthly salary of 20 employees in an organisation is Rs. 1700. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?  Choose the correct choice from the following
A) 3800 B) 3890 C) 88798 D) 2789 E) 2891

Solution: Explanation:   Manager's monthly salary Rs. (1800 * 21 - 1700 * 20) = Rs. 3800.   3800nswer: 3800) 3800
Answer: A
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 20%?
Choose the correct choice from the following:
A) 20%
B) 70%
C) 29%
D) 50%
E) 24%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 80   2/3 SP1 = 80   SP1 = 120   100 --- 20 => 20%   20%nswer:20%
Answer: A
Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 1250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. Choose the correct choice from the following answers
A) 513  B) 512  C) 517  D) 519  E) 521

Solution: Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, C, D,E The answer to be B   Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.   If x = initial number of trees = 512   Year 1 = 5/4x   Year 2 = (5/4)(5/4)x   Year 3 = (5/4)(5/4)(5/4)x   Year 4 = (5/4)(5/4)(5/4)(5/4)x   Only for Answer D: (5/4)(5/4)(5/4)(5/4) 512 = 1250   Hence, correct answer = 512
Answer: B
In a forest 170 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Choose the most appropriate option:
A) 150
B) 750
C) 1,250
D) 1,700
E) 2,500

Solution: The percentage of tagged deer in the second sample = 5/50*100= 
5/50*100 = 10
10%.   So, 170 tagged deers comprise 10% of total # of deers --> total # of deers= 170*10 = 1,700.   Answer: 1,700.
Answer: D
Fresh grapes contain 60% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 20kgs of raisins? Choose the correct choice from the following answers
A) 75 kgs  B) 64kgs  C) 37.5 kgs  D) 65 kgs  E) 70 kgs

Solution: The weight of non-water in 20 kg of dried grapes (which is 100-25= 
100-25 = 75
75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-60= 
100-60 = 40
40% of whole weight),   so 20*0.75= x*0.4   --> x = 37.5.   Answer: 37.5 kgs
Answer: C
In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old? Choose the correct choice.
A) 20
B) 40
C) 10
D) 39
E) 48

Solution: Let us write the fraction for each group of students   Group A: younger than 10: 50% = 50/100 = 1/2   Group B: 10 years old: 1/20   Group 10: older that 10 but younger than 12: 1/10   Group D: 12 years or older: 70 students   The fraction for group A, B and 10 together is given by   1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator   = 13 / 20 , add numerators   The fraction for group D is given by   20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students   If X is the total number of students, then   7 / 20 of X = 70   or (7 / 20) * X = 70   Solve for X   X = 70 * (20 / 7)= 
70 * (20 / 7) = 200
200   Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to   (1 / 20) of 200= 10 students   correct answer 10
Answer: C
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  Pick.
A) 250 B) 100 C) 150 D) 300 E) 200

Solution: Let amount paid to X per week = x   and the amount paid Y per week = y   x=120% of y = 120y/100 = 12y/10   22y/10=550   y=250   250NSWER 250
Answer: A
X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a negative number.
Select the correct option:
A) 2 only.	B) 3 only.	C) 1 and 3 only.	D) 2 and 3 only.	E) 1, 2 and 3.

Solution: Statement I is TRUE   Statement II is not TRUE   Statement III is TRUE   Answer : 1 and 3 only.
Answer: C
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?  Pick one:
A) 17 kmph
B) 40 kmph
C) 18 kmph
D) 13kmph
E) 19 kmph

Solution: Speed downstream = 60 + 20= 
60 + 20 = 80
80 kmph   Speed upstream= 60 - 20= 
60 - 20 = 40
40 kmph   Answer:40 kmph
Answer: B