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aqua_rat__PGueNBnGaPqxjHq0

Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 Choose the correct option: A) 1034355 B) 1035677 C) 1045778 D) 1067675 E) 1083875

Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 1083875 <result>E</result>

E

Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007

aqua_rat__RM3KJBF40CBXdfFZ

A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work? Options: A) 6 days B) 2 days C) 8 days D) 4 1/5 days E) 9 days

Work done by A in 3 days = 3/10 Remaining work = 7/10 Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6 Remaining work = 7/10 * 6/1 = 21/5 = 4 1/5 days. Answer: 4 1/5 days <result>D</result>

D

A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?

aqua_rat__7w5tYpBfMaHfuCm6

A block of wood has dimensions 10cm x 10cm x 80cm. The block is painted red and then cut evenly at the 40 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red? Pick one: A) 5.6% B) 8.4% C) 11.2% D) 14.8% E) 17.5%

The area of each half is 100+4(400)+100 = 1800 The area that is not painted is 100. The fraction that is not painted is 100/1800 = 1/18 = 5.6% The answer is 5.6%. <result>A</result>

A

A block of wood has dimensions 10cm x 10cm x 80cm. The block is painted red and then cut evenly at the 40 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?

aqua_rat__ymUdXR3bvQiPOFSm

Which of the following equations represents a line that is perpendicular to y=1/4*x+2? Choose the correct choice from the following choices. A) y−2x=8 B) 2x+4y=10 C) 3y+6x=12 D) 4y−8x=16 E) 5x−10y=20

For two lines to be perpendicular, the product of slopes should be equal to -1. Slope of line 1 = 1/2 Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --&gt; Slope = -2 Answer: 4y−8x=16 <result>D</result>

D

Which of the following equations represents a line that is perpendicular to y=1/4*x+2?

aqua_rat__RyCnYqJWziyEfqHd

If a man can cover 15 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Choose the most appropriate option: A) 196km B) 190km C) 200km D) 202.5km E) 210km

15 m/s = 15 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 15 * 18/5 * 15/4= <gadget id="calculator">15 * 18/5 * 15/4</gadget> <output>405/2 = around 202.5</output> 202.5 km. Answer:202.5km <result>D</result>

D

If a man can cover 15 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?

aqua_rat__JOPaFI6FJgFPe3uy

Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 6000 Km? Choose the correct choice from the following answers. A) 10. B) 25. C) 300. D) 38. E) 50.

Total distance= Distance travelled by A +Distance travelled by car B Distance= speed*time Distance of A= 3x * 6 Distance of B= x*2 (3x * 6) + (x*2) = 6000 x= 300 KM/hr 300. is the answer <result>C</result>

C

Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 6000 Km?

aqua_rat__wEln7yXpXMX1mOkX

If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to : Choose the most appropriate option: A) 22 B) 37 C) 38 D) 398 E) 72

Explanation: 3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3) = (6 + 10 - 9 + 15)= <gadget id="calculator">(6 + 10 - 9 + 15)</gadget> <output>22</output> 22. 22nswer: 22) 22 <result>A</result>

A

If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :

aqua_rat__tndRLCiDX0aJ2MTr

A water tank is one-fourth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 8 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely? Pick one. A) 4 min. to empty B) 6 min. to full C) 10 min. to empty D) 9 min. to full E) 8 min. to full

Clearly, pipe B is faster than pipe A and so, the tank will be emptied. Part to be emptied = 1/4 Part emptied by (A + B) in 1 minute = (1/8 - 1/10) = 1/40 1/40 : 1/4 :: 1 : x x = (1/4 * 1 * 40)= <gadget id="calculator">(1/4 * 1 * 40)</gadget> <output>10</output> 10 min. So, the tank will be emptied in 10 min. ANSWER:10 min. to empty <result>C</result>

C

A water tank is one-fourth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 8 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

aqua_rat__s8eDKrSA9sTLFWvl

The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#30? Choose the correct choice A) 10 B) 11 C) 12 D) 13 E) 14

First, let's translate the expression 21#30, using the definition given: 21#30 = 21×24×27×30 We need the prime factorization of this product. Let's factor out 3 from each multiple. 21#30 = 3^4(7×8×9×10) Now let's replace each consecutive integer with its prime factorization: 21#30 = 3^4(7×2^3×3^2×(2×5)) Let's group the prime bases: 21#30 = 2^4×3^6×5×7 The sum of the exponents is 4 + 6 + 1 + 1= <gadget id="calculator"> 4 + 6 + 1 + 1</gadget> <output>12</output> 12 The answer is 12. <result>C</result>

C

The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#30?

aqua_rat__ilpzms3h15lcKMGd

The average of five consecutive odd numbers is 51. What is the difference between the highest and lowest number? Pick one. A) .8 B) 9 C) 6 D) 5 E) 2

Explanation: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5 = 51 5x + 20 = 255 x = 47 So, required difference = (47 + 8) – 47 = 8 .8NSWER: .8 <result>A</result>

A

The average of five consecutive odd numbers is 51. What is the difference between the highest and lowest number?

aqua_rat__W5UZLA1oS1SI7eU9

A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $810 was the net sum to be paid for the entire work, what was the average daily wage of B? Pick: A) $144 B) $90 C) $60 D) $54 E) $48

The correct answer is $54. <result>D</result>

D

A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $810 was the net sum to be paid for the entire work, what was the average daily wage of B?

aqua_rat__NsI4J1dJzCoJjYQn

Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. The two companies merge, every employee stays with the resulting company, and no new employees are added. If the resulting companyís workforce consists of 25 percent managers, what percent of the workforce originated from Company A? Choose the correct option: A) 10% B) 20% C) 25% D) 50% E) 75%

Let say Company A has x employes and B has y employees. Now they merge and total no of employees = x+y employees. Per the question Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. We translate it into equation as follows: .1x + .3y = .25 (x+y) =&gt; x + 3y =2.5 (x+y) =&gt; .5y = 1.5x =&gt; y=3x. Now we know total employee = x+y. we need to find %age of x in total (x+y) ie x/(x+y) X100% =&gt; x/(3x+x) [substitute y=3x] =&gt; x/4x X 100% =&gt; .25 X 100 % =&gt; 25%. ANSWER:25% <result>C</result>

C

Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. The two companies merge, every employee stays with the resulting company, and no new employees are added. If the resulting companyís workforce consists of 25 percent managers, what percent of the workforce originated from Company A?

aqua_rat__MH2STInrgZbzZQ5J

A train 125 m long passes a man, running at 2 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? Choose the most appropriate option A) 36 B) 50 C) 28 D) 47 E) 29

Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 2) km/hr. x - 2 = 45 ==&gt; x = 47 km/hr Answer: 47 <result>D</result>

D

A train 125 m long passes a man, running at 2 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?

aqua_rat__SXQPMnrDvyEbZClE

The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112 What is the 100th digit of d to the right of decimal point ? Choose the correct choice from the following. A) 0 B) 1 C) 5 D) 8 E) 9

Now, let's see first we have those single digit numbers that occupy 9 spaces Then the next integers from 10 to 19 will be 10 of them that will occupy 2 places each hence 20 The next ones will be from 20 to 29, 10 of them again, 2 places each hence 20 and so on ... Until we get to 50-59 which will be 10 integers again, 2 places each hence 20 digits. Now the 100th digit will be in the 50-59 range taking into consideration the first 9 single digit integers. We also know that the tenth digits is always in an even place while the units digit is in the odd place. Therefore, the 100th digit will be the tenth digit of the given range (50-59) thus 5 Answer is 5 <result>C</result>

C

The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112 What is the 100th digit of d to the right of decimal point ?

aqua_rat__YDbtl3UnP4gIRRoC

Angelina walked 100 meters from her home to the grocery at a constant speed. She then walked 180 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym? Choose the correct choice from the following answers: A) 2 B) 3 C) 0.5 D) 6 E) 12

let the speed be X... so time taken from home to grocery= 100/x.. the speed to gym = 2x.. so time taken = 180/2= <gadget id="calculator">180/2</gadget> <output>90</output> 90/x.. its given 100/x-90/x=40.. 10/x=40.. x=0.25m/secs.. so grocery to gym=2*0.25= <gadget id="calculator">2*0.25</gadget> <output>0.5</output> 0.5m/s... Answer : 0.5 <result>C</result>

C

Angelina walked 100 meters from her home to the grocery at a constant speed. She then walked 180 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?

aqua_rat__PY27FLCjoaXMPEz7

The sum of all the integers f such that -26 < f < 24 is Choose one: A) 0 B) -2 C) -25 D) -49 E) -51

Easy one - -25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23 Cancel everyhitng and we're left with - -25 and -24 f= -49. -49 is the answer. <result>D</result>

D

The sum of all the integers f such that -26 < f < 24 is

aqua_rat__4SlXVTMtG0NW1jxK

Tough and Tricky questions: Arithmetic. (54^2 + 54^2)/18^2 = Pick one A) 24 B) 8 C) 29 D) 58 E) 116

24ns is 24 my approach was: (54^2 + 54^2)/18^2 =54(54+54)/18*18 =54*108/18*18=3*6=24 24 <result>A</result>

A

Tough and Tricky questions: Arithmetic. (54^2 + 54^2)/18^2 =

aqua_rat__4mXDaVAqolokxSm4

In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, find the number of keepers. Choose the most appropriate option A) 25 B) 20 C) 15 D) 13 E) 14

Let the number of keepers be x then, Total number of heads =(50 + 45 + 8 + x)= (103 + x). Total number of feet = (45 + 8) x 4 + (50 + x) x 2 =(312 +2x). (312 + 2x)-(103 + x) =224 ==&gt; x =15. Hence, number of keepers =15. Answer 15. <result>C</result>

C

In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, find the number of keepers.

aqua_rat__KIh0gI1w3PsvELqU

Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability Q that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls? Choose the correct choice from the following answers A) 8/28 B) Q=9/28 C) Q=10/28 D) Q=10/18 E) 11/18

(3c2*2c1*3c2)/8c5 =(3*2*3)/(8*7*6/3*2) =18/56 =9/28 Q=9/28 <result>B</result>

B

Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability Q that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?

aqua_rat__U1FqYfvLUSpP21fd

Express a speed of 63 kmph in meters per second? Pick A) 10 mps B) 14 mps C) 17.5 mps D) 19.4 mps E) 10.8 mps

63* 5/18= <gadget id="calculator">63* 5/18</gadget> <output>35/2 = around 17.5</output> 17.5 mps Answer: 17.5 mps <result>C</result>

C

Express a speed of 63 kmph in meters per second?

aqua_rat__BSvqi7vlp8t6VRhc

UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? Select the correct option A) 76% B) 58% C) 68% D) 89% E) 49%

let total no of Vehicles bought be 100, Toyota 70 and Honda 30, so total number of SUV's bought for Toyota and Honda respectively 70* 70/100= <gadget id="calculator"> 70* 70/100</gadget> <output>49</output> 49 and 30* 30/100= <gadget id="calculator"> 30* 30/100</gadget> <output>9</output> 9 so total 58 SUV's were bought out of 100 Vehicles bought..so required % is 58% ANSWER:58% <result>B</result>

B

UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase?

aqua_rat__jdmKGh359JGJzGD2

A computer store offers employees a 10% discount off the retail price. If the store purchased a computer from the manufacturer for $1200 dollars and marked up the price 10% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (10% off retail price) as opposed to the final retail price. Choices A) 122 B) 132 C) 142 D) 152 E) 162

Cost price=1200 Profit=10% =10% of 1200=120 selling price=CP+ Profit SP=1320 a Discount of 10% to employees means 10% off on 1320 so 10% of 1320= 132 Ans 132 <result>B</result>

B

A computer store offers employees a 10% discount off the retail price. If the store purchased a computer from the manufacturer for $1200 dollars and marked up the price 10% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (10% off retail price) as opposed to the final retail price.

aqua_rat__SOXHW3iDRYUC5Bvc

Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time T will the job be finished? Choose the correct choice from the following choices: A) Noon B) 12:30 p.m. C) 1:00 p.m. D) 1:30 p.m. E) 2:00 p.m.

Ans: C (1:00pm) From 9:00-11:00c(2 hrs) A can do 1/8 Job/hr. so in 2 hours he can do 1/4 job. B can do 1/10 job/hr so in 2 hrs. he can do 1/5 Job. C can do 1/12 job/hr so in 2 hours he can do 1/6 job. Total = 1/4+1/5+1/6 = 37/60 Job Now balance work needs to be done by B and C. Balance Work= 23/60 Job Combined rate of B and C = 1/10+1/12 = 11/60 job/hr. So they will do 22/60 work in 2 hrs (approx. to the balance work of 23/60) Hence the Job will be completed 2hrs. after 11:00 i.e. @ 1:00pm=T Ans: 1:00 p.m. (1:00pm) <result>C</result>

C

Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time T will the job be finished?

aqua_rat__I2Joi3VfTjx4myx6

If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 4? I. x^2 II. y^2 III. xy Choose the correct answer: A) I only B) II only C) III only D) I and II only E) I, II and III

4x^2 = 3y since x,y are positive integers, x^2 = x*x is divisible by 3 -&gt; x is divisible by 3 and y is divisible by x^2 -&gt; x^2 and y is divisible by 9 -&gt; y^2 is divisible by 9 (1),(2), and (3) must be true Answer is I and II only <result>D</result>

D

If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 4? I. x^2 II. y^2 III. xy

aqua_rat__UjfhggNLtsWCb4fn

The radius of a circle is increased by 1%. Find how much % does its area increases? Pick: A) 2.21% B) 2.07% C) 2.08% D) 2.01% E) 2.11%

r = 100 r = 101 r2 = 10000 r2 = 10201 10000 ---- 201 100 ---- ? =&gt; 2.01% Answer:2.01% <result>D</result>

D

The radius of a circle is increased by 1%. Find how much % does its area increases?

aqua_rat__RMsL5y8cgG0D6YjQ

Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P? Choose the correct choice A) 22 km/hr B) 70 km/hr C) 77 km/hr D) 66 km/hr E) 44 km/hr

Let their speed be x km/hr and y km/he respectively. Then, 120/(x + y) = 1 =&gt; x + y = 120 --- (i) Now, when they move in same direction: (Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km 6x - 6y = 120 =&gt; x - y = 20 --- (ii) Sloving (i) and (ii), we get x = 70, y = 50 P's speed = 70 km/hr. Answer:70 km/hr <result>B</result>

B

Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?

aqua_rat__F23sPqJtS0Z95JBk

A certain collage has total of 420 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects? Pick one. A) 100 B) 80 C) 75 D) 60 E) 50

Answer is A. Six majors are as follows: a + b + c + d + e + f Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20 4 of the majors have 300 seniors: a + b + c +d = 300 There are a total of 420 seniors. So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 100. 100 <result>A</result>

A

A certain collage has total of 420 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?

aqua_rat__BG7OCAH95ryAKT0a

By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? Select the correct option A) 100% B) 75% C) 60% D) 25% E) 50%

SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? =&gt; 25% Answer: 25% <result>D</result>

D

By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?

aqua_rat__FkxNPsqyekuTRC24

What is the average of xx,2x2x,and 66? Choose the correct choice from the following options. A) x+2 B) x+2x C) x+2x+2 D) 2x+2 E) x+2x-2

By the definition of an average, we get: x+2x+63=3x+63x+2x+63=3x+63 =3(x+2)3=x+2.=3(x+2)3=x+2. Hence, the answer is x+2x+2 or Option x+2x+2 <result>C</result>

C

What is the average of xx,2x2x,and 66?

aqua_rat__7FpCQxviUZZMtdDp

How many ways can 5 friends be arranged around a circular dinner table? Choose the most appropriate option: A) 24 B) 56 C) 108 D) 120 E) 132

The number of ways to order 5 people is 5! However, around a circular table, each pattern would be repeated 5 times. So the number of ways to seat 5 friends around a circular table is 4! = 24 The answer is 24. <result>A</result>

A

How many ways can 5 friends be arranged around a circular dinner table?

aqua_rat__OXMq63u50zbVf7TG

How much 60% of 50 is greater than 42% of 30? Choose one. A) 18 B) 91 C) 11 D) 17.4 E) 12

(60/100) * 50 – (42/100) * 30 30 - 12.6= <gadget id="calculator">30 - 12.6</gadget> <output>17.4</output> 17.4 Answer: 17.4 <result>D</result>

D

How much 60% of 50 is greater than 42% of 30?

aqua_rat__aCRBnuuef8xBiAWA

The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Choose the correct choice from the following options A) 388 B) 267 C) 225 D) 288 E) 261

Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==&gt; 2(150 + X) = 750 ==&gt; X = 225 m. Answer: 225 <result>C</result>

C

The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?

aqua_rat__cSXqueX99DgL7UDt

Sarah, Fatima, Salma, and Lina all got tips during their waitressing shift. The average of Sarah, Fatima, and Salma's tips was $100. The average of Fatima, Salma, and Lina's tips was $90. If Lina earned $85, what did Sarah earn? Choose the correct option: A) 105 B) 108 C) 110 D) 113 E) 115

To solve: Average tips for Sarah, Fatima and Sarah = $100 Total tips = 3*100= <gadget id="calculator">3*100</gadget> <output>300</output> 300 Average tips for Fatima, Salma, and Lina= $90 Total tips = 3*90= <gadget id="calculator">3*90</gadget> <output>270</output> 270 Lina's tips= $85 Now, (Sarah+Fatima+Salma) - (Fatima+Salma+Lina) = 300-270= <gadget id="calculator">300-270</gadget> <output>30</output> 30 Sarah-Lina= 30 Sarah = Lina +30 = $115 Answer: Option 115 <result>E</result>

E

Sarah, Fatima, Salma, and Lina all got tips during their waitressing shift. The average of Sarah, Fatima, and Salma's tips was $100. The average of Fatima, Salma, and Lina's tips was $90. If Lina earned $85, what did Sarah earn?

aqua_rat__wfrllYZRvTwdutx7

mixture contains alcohol and water in the ratio 4 : 3. If 6.5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture. Choose one: A) 10 B) 99 C) 27 D) 22 E) 5.6

Let the quantity of alcohol and water be 4x litres and 3x litres respectively 26x = 4(3x+5) 14x = 20 x = 1.4 Quantity of alcohol = (4 x 1.4) litres = 5.6 litres. Answer: 5.6 <result>E</result>

E

mixture contains alcohol and water in the ratio 4 : 3. If 6.5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.

aqua_rat__zaHqSllcTGCMZIws

Which of the following expressions CANNOT be equal to 0 when x^2 − 2x = 3? Choose the correct choice from the following choices. A) x^2 − 6x + 9 B) x^2 − 4x + 3 C) x^2 − x − 2 D) x^2 − 7x + 6 E) x^2 − 9

E. Can x^2 − 9 = 0? Factor to get (x + 3)(x - 3) = 0 So, (x + 3) = 0 or (x - 3) = 0 ELIMINATE E D. Can x^2 − 7x + 6 = 0 Factor to get (x - 1)(x - 6) = 0 So, (x - 1) = 0 or (x - 6) = 0 Since we cannot conclude that (x - 3) = 0 or (x + 1) = 0, the correct answer must be x^2 − 7x + 6 <result>D</result>

D

Which of the following expressions CANNOT be equal to 0 when x^2 − 2x = 3?

aqua_rat__OoYiyWuyu9LHCyY8

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 12 hours. How many hours does it take machines X and Y , working simultaneously , to produce 24k bottles? Choices: A) 48 B) 42 C) 45 D) 98 E) 96

x rate = k/6 y rate = k/12 k/6 + k/12 = 24k / T solving T = 96 Answer 96 <result>E</result>

E

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 12 hours. How many hours does it take machines X and Y , working simultaneously , to produce 24k bottles?

aqua_rat__Xjs8vPXWe775g8bi

Find the wrong number below mentioned series 17, 600,6000,550,750 Options: A) 600 B) 6000 C) 17 D) 550 E) 750

17 is the only prime number or odd number in the series. ANSWER:17 <result>C</result>

C

Find the wrong number below mentioned series 17, 600,6000,550,750

aqua_rat__KrGpx1nRwU9RsbmA

Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in Choose the correct choice from the following options: A) 1 13/17 hours B) 2 8/11 hours C) 3 9/17 hours D) 5 1/7 hours E) None

Solution Net part filled in 1 hour = (1/9 + 1/6 -1/12) = 7/36. Therefore, the tank will be full in 36/7 hrs. ‹=› 5 1/7 hrs. Answer 5 1/7 hours <result>D</result>

D

Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in

aqua_rat__wNITwdmsOC3grggX

What is the area of a square with perimeter 16P ? Choose the correct choice from the following A) 16p^2 B) 4P C) P^2/4 D) P/16 E) P^2/16

Each side is 4p 16p^2 = (4p)^2 = 16(p^2) 16p^2nswer 16p^2 <result>A</result>

A

What is the area of a square with perimeter 16P ?

aqua_rat__dCpte697SSKGLLDi

A company received $2 million in royalties on the first $10 million in sales and then $8 million in royalties on the next $100 million in sales. By what percent did the ratio of royalties to sales decrease from the first $10 million in sales to the next $100 million in sales? Choose the correct choice from the following choices A) 30% B) 40% C) 50% D) 60% E) 70%

First find out (ratio of royalties to sales): 2:10 First 0.2 8:100 Second 0.08 Decrease = 0.2-0.08= <gadget id="calculator">0.2-0.08</gadget> <output>0.12</output> 0.12 Percent= (0.12/0.20) = 60%. ANSWER:60% <result>D</result>

D

A company received $2 million in royalties on the first $10 million in sales and then $8 million in royalties on the next $100 million in sales. By what percent did the ratio of royalties to sales decrease from the first $10 million in sales to the next $100 million in sales?

aqua_rat__g3zmu3bGzzIc5ulb

If the productivity of a brigade grows by 40% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade? Choose the correct answer: A) 1.51 B) 0.82 C) 1.2 D) 1.21 E) 1.44

B = 10-men brigade p = increase in the productivity = 40% Solution: B x p = B x 1.4 = 1.4B -------&gt; the productivity of 11 men brigade 1.4B x p = 1.4B x 1.1 = 1.51B -----&gt; the productivity of 12 men brigade The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.51B/B = 1.51 1.51 <result>A</result>

A

If the productivity of a brigade grows by 40% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?

aqua_rat__fQFAQh4AGsI8SrUr

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 9 km/hr completes one round in 5 min, then the area of the park (in sq. m) is? Choose the correct choice from the following answers: A) 337500 m B) 300000 m C) 153600 m D) 33750 m E) 9000 m

Perimeter = Distance covered in 5 min. = (9000 x 5)/60 m = 750 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 750 or x = 75. Length = 225 m and Breadth = 150 m. Area = (225 x 150) m2 = 33750 m 33750 m <result>D</result>

D

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 9 km/hr completes one round in 5 min, then the area of the park (in sq. m) is?

aqua_rat__7UC1sxS0qElfxhfV

If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? Choose the most appropriate option: A) 5 minutes B) 10 minutes C) 8 minutes D) 14 minutes E) 20 minutes

5 minutes 5 minutes <result>A</result>

A

If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ?

aqua_rat__3wkab7a9PUm2X4vX

In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive? Select. A) None B) One C) Two D) Three E) Four

Non - Negative ( zero to positive infinity ) Solution to the question : -4,-3,-2,-1,0 , 1,2,3 Hence ans is 3 ..option Three <result>D</result>

D

In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive?

aqua_rat__LNckfABUAuFUqz0t

Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 22 white marbles. How many red marbles could be in bag A? Answers A) 1 B) 3 C) 4 D) 2 E) 8

# of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D. Bag A: R:W:B = 2:6:9 Bag B R:W = 1:4 6X + 4Y = 22 i.e 3X + 2Y = 11 X has to be odd to make an odd sum from the eq. X = 1 , Y = 4 OR X = 3, Y = 1 So R can be 2X i.e 2 or 6. Answer 2 <result>D</result>

D

Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 22 white marbles. How many red marbles could be in bag A?

aqua_rat__KE9C3zzleyIk0Ocv

A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 7 minutes? Choices: A) 36 B) 54 C) 108 D) 216 E) 378

ON378 Veggiematik machine can chop 36 carrots in 4 minutes So, ON378 Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes In other words, ON378 Veggiematik machine can chop 54 carrots in7minutes So,SIXVeggiematik machines can chop (7)(54) carrots in6minutes In other words, SIX Veggiematik machines can chop 378 carrots in7minutes Answer 378 <result>E</result>

E

A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 7 minutes?

aqua_rat__SKKpQvnE29ea6acX

A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? Select: A) 33 B) 77 C) 48 D) 99 E) 22

D = 540 + 180= <gadget id="calculator">540 + 180</gadget> <output>720</output> 720 S= 54 * 5/18= <gadget id="calculator">54 * 5/18</gadget> <output>15</output> 15 mps T= 720/15= <gadget id="calculator">720/15</gadget> <output>48</output> 48 sec Answer:48 <result>C</result>

C

A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?

aqua_rat__ZA3kGenEOyoUDKKc

The ratio of the incomes of Chetan and Dinesh is 3:4. The ratio of their expenditures is 5:7. If each of them saves Rs.200, find the incomes of both? Answers: A) 1977 B) 1892 C) 2928 D) 2791 E) 1600

The savings of Chetan and Dinesh are 3x - 5y and 4x - 7y respectively. 3x - 5y = 200 --- (1) 4x - 7y = 200 --- (2) Multiplying (1) by 7 and (2) by 5 and subtracting the resultant equation (2) from resultant equation (1), we get x = 400. The incomes of Chetan and Dinesh are 3x = Rs.1200 and 4x = Rs.1600 respectively. Answer: 1600 <result>E</result>

E

The ratio of the incomes of Chetan and Dinesh is 3:4. The ratio of their expenditures is 5:7. If each of them saves Rs.200, find the incomes of both?

aqua_rat__0nrV45EgpGTATHgM

Three candidates contested an election and received 1136, 7636 and 15000 votes respectively. What percentage of the total votes did the winning candidate get? Choose the correct choice. A) 46% B) 63% C) 74% D) 63% E) 68%

63% 15000/(1136 + 7636 + 15000) = 63%. <result>B</result>

B

Three candidates contested an election and received 1136, 7636 and 15000 votes respectively. What percentage of the total votes did the winning candidate get?

aqua_rat__E4oMPPOoGBRUxDCE

If 20 percent of the members of a certain organization are women and 2/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of unmarried men in the organization is greater than the number of married men in the organization. Answers A) III B) II C) I D) I,II E) II,III

2/10 (20%) of the members are women and 2/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 2/10*80= <gadget id="calculator"> 2/10*80</gadget> <output>16</output> 16 women; 80 - 16= <gadget id="calculator"> 80 - 16</gadget> <output>64</output> 64 men; 2/8*64= <gadget id="calculator"> 2/8*64</gadget> <output>16</output> 16 married men; 64 - 16= <gadget id="calculator"> 64 - 16</gadget> <output>48</output> 48 unmarried men. So, only option III is true. IIInswer: III <result>A</result>

A

If 20 percent of the members of a certain organization are women and 2/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of unmarried men in the organization is greater than the number of married men in the organization.

aqua_rat__suEc1IcaxndXdVmI

A and B are two stations 125km apart. A train starts from A at 6a.m. and travels towards B at 50kmph. Another train starts from B at 7a.m. and travels towards A at 25kmph. At what time do they meet? Pick one: A) 7a.m. B) 8a.m. C) 9a.m. D) 9.30a.m. E) 10a.m.

Suppose they meet x hours after 6 a.m. Distance moved by first train in x hours + distance moved by 2nd train in x-1 hrs = 125 50x+25(x-1) = 125 x = 2hr So they meet 2hr after 6a.m. is at 8a.m. Answer is 8a.m. <result>B</result>

B

A and B are two stations 125km apart. A train starts from A at 6a.m. and travels towards B at 50kmph. Another train starts from B at 7a.m. and travels towards A at 25kmph. At what time do they meet?

aqua_rat__TsmMAOlocG4V4827

In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A rectangle has a center at (1, 2) and width (x), length (y), 6", 4", respectively. Some points, such as the center (1, 2), are inside the rectangle, but a point such as (4, 2) is on the rectangle, but not in the rectangle. How many lattice points are in the rectangle? Choose the correct choice: A) 7 B) 71 C) 72 D) 17 E) 27

The lattice points that are in the rectangle can be calculated as follows: divide the rectangle into 4 quadrants. Now we solve for one quadrant, multiply by 4, and subtract the repeating points along the vertical and horizontal lines that lie along the center point. For one quadrant we have: vertical = (1, 2), (1, 3), horizontal = (2, 2), (3, 2), (don't count center again), others = (2, 2), (3, 3). There are 6 points. So, 6 * 4 = 24. Subtract repeating points, 7, we get 17. There are a total of 17 lattice points in the square. Answer: 17 <result>D</result>

D

In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A rectangle has a center at (1, 2) and width (x), length (y), 6", 4", respectively. Some points, such as the center (1, 2), are inside the rectangle, but a point such as (4, 2) is on the rectangle, but not in the rectangle. How many lattice points are in the rectangle?

aqua_rat__t1QWe4Dca7OFvopm

A password of a computer used three digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero? Choose the correct choice from the following options. A) 1/32 B) 1/16 C) 1/8 D) 2/5 E) 1/2

We have three digits can be used for password -0,2,3,5,7. Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9) So, 5/10 * 5/10 * 5/10 =1/8 (1/8) <result>C</result>

C

A password of a computer used three digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

aqua_rat__4rOHvjFHRj4Bxxhu

A boy can reach a certain place in 30 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed. Select. A) 3 km/hr. B) 6 km/hr C) 8 km/hr D) 14 km/hr E) None of these

Explanation : Solution: Let the speed be x km/hr. then, 30x - (30 * 29x/30) = 3 =&gt; x = 3 km/hr. 3 km/hr.nswer : 3 km/hr. <result>A</result>

A

A boy can reach a certain place in 30 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed.

aqua_rat__56ZiMs9xh1amVMmE

A money lender lent a total of $1400 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1400, how much did he lend to each of the two customers? Choose the correct choice from the following answers: A) 700; 1100 B) 938; 462 C) 1000; 800 D) 1200; 800 E) None of the above

The method given above is the one given in the book. However the method I used was (1*x*5)/100 + (1400-x)*6/100 = 1400*5.67/100 Simplifying we get x=462 938; 462 <result>B</result>

B

A money lender lent a total of $1400 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1400, how much did he lend to each of the two customers?

aqua_rat__rIlg0EpyAwrnWtRz

A man can row with a speed of 20 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is? Choose the correct choice from the following answers: A) 28 B) 26 C) 31 D) 87 E) 24

M = 20 S =11 DS = 20 + 11= <gadget id="calculator">20 + 11</gadget> <output>31</output> 31 Answer: 31 <result>C</result>

C

A man can row with a speed of 20 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?

aqua_rat__tfDVYDLRVKJVwF23

A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit Choose the correct choice from the following choices: A) 3 B) 4 C) 5 D) 6 E) 7

954 -459 --------- 495 Rearrenge=954 ANSWER:4 <result>B</result>

B

A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit

aqua_rat__JRiajtPSqPF8NPxq

Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest. Choose the correct choice: A) 40% B) 30% C) 20% D) 10% E) 15%

Explanation: Let the sum be x Simple interest on x for 2 years = Rs.2000 Simple interest = PRT/100 2000 = x × R × 2100 ⇒ x R = 100000 --- (1) Compound Interest on x for 2 years = 2400 P(1+R/100)T − P = 2400 x (1+R/100)2 − x = 2400 x (1 +2R/100+R210000)−x=2400x(2R100+R210000)=2400 2xR/100 + xR2/10000 = 2400--- (2) Substituting the value of xR from (1) in (2) ,we get (2×100000)/100 + 100000 × R10000 = 2400 2000+10R = 2400 10R=400 R=40% 40%NSWER IS 40% <result>A</result>

A

Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.

aqua_rat__0BxyIc0YXQn5jDVG

The 100-milliliter solution of sugar and water is 21% sugar. How much water (in milliliters) must be added to make a solution that is 12% sugar? Choose the correct choice from the following: A) 55 B) 60 C) 65 D) 70 E) 75

In the original solution the amount of sugar is 0.21*100= <gadget id="calculator">0.21*100</gadget> <output>21</output> 21 ml. Let the volume of the new solution be V. 0.12V=21 ml. V=175 ml. The amount of water we need to add is 175 - 100= <gadget id="calculator"> 175 - 100</gadget> <output>75</output> 75 ml. The answer is 75. <result>E</result>

E

The 100-milliliter solution of sugar and water is 21% sugar. How much water (in milliliters) must be added to make a solution that is 12% sugar?

aqua_rat__oHLVXmKoBGFAQugP

In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x. Select the correct option. A) 3 B) 4 C) 5 D) 6 E) 7

(x+2)×60+x×120+(x−2)×180 /(x+2)+x+(x−2)=100 ⇒ 360x−240 /3x = 100 ⇒ 60x = 240 ⇒ x = 4 Answer 7 <result>E</result>

E

In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.

aqua_rat__Kw3YqaXeRYmuTwHw

Reena took a loan of 1200 with simple interest for as many years as the rate of interest. If she paid 432 as interest at the end of the loan period, what was the rate of interest? Choose the correct choice from the following answers: A) 3.6 B) 6 C) 18 D) Cannot be determined E) None

Explanation: Let rate = R% and time = R years. Then, (1200 x R x R)/100 = 432 12R² = 432 R² = 36 R = 6. Answer: Option 6 <result>B</result>

B

Reena took a loan of 1200 with simple interest for as many years as the rate of interest. If she paid 432 as interest at the end of the loan period, what was the rate of interest?

aqua_rat__x26xqVGO6vOqQvFE

Three candidates contested an election and received 1136, 7636 and 12628 votes respectively. What percentage of the total votes did the winning candidate got? Choose the most appropriate option. A) 55% B) 56% C) 57% D) 58% E) 59%

Total number of votes polled = (1136 + 7636 + 12628)= <gadget id="calculator">(1136 + 7636 + 12628)</gadget> <output>21_400</output> 21400 So, Required percentage= 12628/21400 * 100 = 59% ANSW59%R : 59% <result>E</result>

E

Three candidates contested an election and received 1136, 7636 and 12628 votes respectively. What percentage of the total votes did the winning candidate got?

aqua_rat__fi5nvpAziWkPtF6u

Tough and Tricky questions: Exponents. If 3^(x+1)*5^(y-1) = 9^x*125^y, then 2x + y = Choose the correct answer A) -3/4 B) -2/5 C) -5/2 D) 2/5 E) 5/2

Here is my solution. 3^(x+1)*5^(y-1) = 9^x*125^y Here RHS 9^x*125^y= 3^(2x)*5^(3y) Equating powers on both sides--&gt; x+1=2x , thus x=-1 and y-1=3y giving y=-1/2 So, x+y=-5/2 Option: -5/2 <result>C</result>

C

Tough and Tricky questions: Exponents. If 3^(x+1)*5^(y-1) = 9^x*125^y, then 2x + y =

aqua_rat__EcIXunIaKXaHdUFG

Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture? Answers A) 3 gallons B) 4 gallons C) 5 gallons D) 10 gallons E) 12 gallons

Let A = number of gallons on Mixture A in 15 gallon mixture B = number of gallons on Mixture B in 15 gallon mixture (20/100)A + (50/100)B= (30/100)(A+B) --1 A+B=15 -- 2 On solving equations 1 and 2 , we get A=10 B=5 Answer 10 gallons 10 gallons <result>D</result>

D

Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

aqua_rat__DZR0RNx4mFjgwIEd

A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram? Choices: A) 835 1/3 grams B) 833 1/3 grams C) 833 1/9 grams D) 836 1/3 grams E) 843 1/3 grams

If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120. If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%. How many grams he has to give instead of one kilogram(1000 gm). 120 gm ------ 100 gm 1000 gm ------ ? (1000 * 100)/120 = 2500/3 = 833 1/3 grams. Answer: 833 1/3 grams <result>B</result>

B

A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?

aqua_rat__6q63aK5WSdpuDx1v

Calculate 56581 ÷ ? = 137 Answers. A) 113 B) 213 C) 413 D) 417 E) 414

Answer Let 56581/X = 137 Then X = 56581/137= <gadget id="calculator">56581/137</gadget> <output>413</output> 413 Option: 413 <result>C</result>

C

Calculate 56581 ÷ ? = 137

aqua_rat__27DTEycMidn8QpXw

If 60 honey bees make 60 grams of honey in 60 days, then 1 honey bee will make 1 gram of honey in how many days? Choose the correct choice from the following choices: A) 1 B) 3.5 C) 20 D) 49 E) 60

Explanation : Let the required number days be x. Less honey bees, More days (Indirect Proportion) Less honey, Less days (Direct Proportion) Honey bees 1 : 60 :: 60 : x Honey 60 : 1 =&gt; 1 x 60 x x = 60 x 1 x 60 =&gt; x = 60. Answer : 60 <result>E</result>

E

If 60 honey bees make 60 grams of honey in 60 days, then 1 honey bee will make 1 gram of honey in how many days?

aqua_rat__luRsgix4QrR4XzdB

The average earning of a mechanic for the first-four days of a week is Rs. 16 and for the last four days is Rs. 24. If he earns Rs . 27 on the fourth day, his average earning for the whole week is ? Choose the correct choice from the following answers. A) Rs . 18.95 B) Rs 16 C) Rs. 19 D) Rs. 25.71 E) None of these

Answer Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day = 4 x16 + 4 x 24 -27 = Rs. 133 ∴ Average earning = 133 / 7 = Rs. 19 Rs. 19orrect Option: Rs. 19 <result>C</result>

C

The average earning of a mechanic for the first-four days of a week is Rs. 16 and for the last four days is Rs. 24. If he earns Rs . 27 on the fourth day, his average earning for the whole week is ?

aqua_rat__RH0u4yeSXB6CX2gF

A can do a piece of work in 3 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it? Choose the correct choice from the following answers. A) 12 B) 9 C) 8 D) 6 E) 5

A's 1 hour's work = 1/3; (B + C)'s 1 hour's work = 1/3 ; (A + C)'s 1 hour's work = 1/2 . (A + B + C)'s 1 hour's work = ( 1/3 + 1/3 ) =2/3 . B's 1 hour's work = ( 2/3 - 1/2 ) = 1/6. Therefore A alone will take 6 hours to do the work. 6 <result>D</result>

D

A can do a piece of work in 3 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

aqua_rat__Zz4n90CqnQK7E9Fk

Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number? Choose the correct choice from the following answers: A) 4/7 B) 1/2 C) 1/3 D) 1/7 E) 2/7

Let A be the event ‘the number on the card drawn is even’ and B be the event ‘the number on the card drawn is greater than 3’. We have to find P(A|B). Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Then 4/7 = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10} and 4/7 n B = {4, 6, 8, 10} 4/7lso P(4/7) = 5/2, P(B) = 7/10 and P(4/7 n B) = 4/10 Then P(4/7|B) = P(4/7 n B)/P(B) = (4/10)/(7/10) = 4/7 4/7 <result>A</result>

A

Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

aqua_rat__bMiTWauNROIyvv09

A pair of prime numbers that can be expressed in the form W{p, (p + 6)} is defined as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT Choose the correct answer A) 11 B) 13 C) 17 D) 19 E) 23

definetly a sitter.plug in the values for middle term and calculate.We can see clearly that W for 19 , 19+6 gives 25 which is not a prime therefore correct answer 19 <result>D</result>

D

A pair of prime numbers that can be expressed in the form W{p, (p + 6)} is defined as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT

aqua_rat__PNJBZUGRaG5NePEO

If the radius of a circle is decreased 30%, what happens to the area? Pick A) 51% decrease B) 20% decrease C) 36% decrease D) 40% decrease E) 50% decrease

51% decreaserea of Square = Pi* radius^2 New Radius = 0.7 * old radius so new area = (0.7)^2 old area =&gt; 0.49 of old area =&gt; 49% old area 51% decreasens : 51% decrease <result>A</result>

A

If the radius of a circle is decreased 30%, what happens to the area?

aqua_rat__VCNWprThFG38IJ4N

Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops? Choose the correct choice from the following options A) white − wheat − wheat B) wheat − wheat − rye C) rye − white− wheat D) rye − rye − rye E) rye − rye − white

In a single round Lucy drops 6 morsels. Remainder (2000/6) = 2 Final action = 2 drops of Wheat --&gt; Options B, C, D and E can be eliminated white − wheat − wheatnswer: white − wheat − wheat <result>A</result>

A

Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?

aqua_rat__IYw1dRLfDv5pEnRj

The angles of a triangle have ratios 3:4:5 relative to each other. Determine which angle below corresponds to one of the angles of this triangle. Choose the correct choice from the following choices: A) 40° B) 60° C) 80° D) 100° E) 120°

The three angles of a triangle add up to 180°. Knowing the ratios, we can formulate this expression: 3x + 4x + 5x = 180° 12x = 180° x = 15° Now, find the angles within the triangle. 3x = 3(15°) = 45° 4x = 4(15°) = 60° 5x = 5(15°) = 75° Therefore, the answer is 60°, or 60°. <result>B</result>

B

The angles of a triangle have ratios 3:4:5 relative to each other. Determine which angle below corresponds to one of the angles of this triangle.

aqua_rat__toHZGyKvSDkofOze

What is the sum of the greatest common factor and the lowest common multiple of 16 and 72? Select A) 142 B) 152 C) 124 D) 160 E) 184

Prime factorization of 16 = 2 x 2 x 2 x 2. Prime factorization of 72 = 2 x 2 x 2 x 3 x 3 GCF = 8 LCM = 144 Sum = 152. Answer 152. <result>B</result>

B

What is the sum of the greatest common factor and the lowest common multiple of 16 and 72?

aqua_rat__Vu3Y1WAM9bZldEVd

Fred and Sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 2 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet? Choose the correct choice from the following answers: A) 5 B) 9 C) 25 D) 30 E) 45

relative distance =35 miles relative speed =2+5= <gadget id="calculator">2+5</gadget> <output>7</output> 7 miles per hour time taken=35/7= <gadget id="calculator">35/7</gadget> <output>5</output> 5 hours distance travelled by sam=5*5= <gadget id="calculator">5*5</gadget> <output>25</output> 25 miles=25 <result>C</result>

C

Fred and Sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 2 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?

aqua_rat__gJnzjn7NLR3eESIi

At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? Choose one: A) 62.5 B) 62.8 C) 62.1 D) 62.9 E) 32.5

Explanation: CP = 47.50 SP = 47.50*(125/100)= <gadget id="calculator">47.50*(125/100)</gadget> <output>59.375</output> 59.375 MP*(95/100)= 59.375 MP = 62.5 62.5nswer: 62.5 <result>A</result>

A

At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?

aqua_rat__fRQoY0lRD1z9AhWX

In how many ways, a committee of 6 members can be selected from 7 men and 4 ladies, consisting of 4 men and 2 ladies? Pick: A) 210 B) 180 C) 200 D) 310 E) 250

(4 men out 7) and (2 ladies out of 4) are to be chosen Required number of ways = 7C4*4C2 = 210 210nswer is 210 <result>A</result>

A

In how many ways, a committee of 6 members can be selected from 7 men and 4 ladies, consisting of 4 men and 2 ladies?

aqua_rat__jQEoPCMrjF7qJXY8

A Table is bought for Rs.1600/- and sold at a loss of 20% find its selling price? Choose the correct answer: A) s.1280/- B) s.1560/- C) s.1580/- D) s.1250/- E) s.1300/-

100 % ------&gt; 1600 (100 * 16 = 1600) 80 % ------&gt; 1280 (80 * 16 = 1280) Selling price = Rs.1280/- Option 's.1280/-' <result>A</result>

A

A Table is bought for Rs.1600/- and sold at a loss of 20% find its selling price?

aqua_rat__vnTCAfr4IcmkQGcv

What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261? Pick one A) Rs.8000 B) Rs.8400 C) Rs.7500 D) Rs.7800 E) None of these

Explanation: 8820 ---- 441 100 ---- ? =&gt; 5% x *105/100 * 105/100 = 8820 x*1.1025=8820 x=8820/1.1025= <gadget id="calculator">8820/1.1025</gadget> <output>8_000</output> &gt; 8000 Rs.8000nswer is Rs.8000 <result>A</result>

A

What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?

aqua_rat__VwiIakzCDAt17fTF

The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is? Choose the correct choice from the following answers: A) 3 B) 4 C) 5 D) 6 E) 8

2x 3x 8x cube + 27x cube = 945 35x cube = 945 x cube = 27 =&gt; x = 3.3nswer: 3 <result>A</result>

A

The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is?

aqua_rat__sRbCiDO1gVoNhteo

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be: Answers A) 18 cm B) 28 cm C) 30 cm D) 38 cm E) 42 cm

l2 + b2 = 41. Also, lb = 20. (l + b)2 = (l2 + b2) + 2lb = 41 + 40= <gadget id="calculator">41 + 40</gadget> <output>81</output> 81 (l + b)= 9. Perimeter = 2(l + b) = 18 cm. 18 cm) <result>A</result>

A

The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

aqua_rat__nQnQldO8korT2sQ5

At the starting of 2012, 60% of the population of Town Y lived in the north and the rest lived in the south. During the year 2012, the population of Town Y grew by 5.5%. If the population in the north grew by 4.5%, by how much did the population in the south grow? Pick one. A) 7% B) 9% C) 1% D) 1.5% E) 3.8%

Here I prefer the weighted average method over dealing with creating and solving the algebraic expression: Ratio of population in the Town Y -North:South :: 60%:40% = 3:2 Mean growth = 5.5% South Growth: 4.5% North Growth = ?? North-------------7%verage--------------South 4.5% __(2n)_____5.5%_____(3n)_____?? Since: 4.5 + 2n = 5.5 n = 1/2 (this is the multiplier of the ratio) Therefore: South = 5.5 + 3n South = 5.5 + 3(0.5) = 7% <result>A</result>

A

At the starting of 2012, 60% of the population of Town Y lived in the north and the rest lived in the south. During the year 2012, the population of Town Y grew by 5.5%. If the population in the north grew by 4.5%, by how much did the population in the south grow?

aqua_rat__BbcW13hqVJuo3Epk

Three 6 faced dice are thrown together. The probability that all the three show the same number on them is? Pick A) 1/39 B) 1/36 C) 1/32 D) 1/31 E) 1/30

Explanation: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= <gadget id="calculator">6 * 6 * 6</gadget> <output>216</output> 216 ways. Hence the probability is 6/216= 1/36 Answer: 1/36 <result>B</result>

B

Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?

aqua_rat__JOuxujhPjDs1m6nJ

A started a business with Rs.25000 and is joined afterwards by B with Rs.30,000. After how many months did B join, if profit per annum is divieded equally? Choose the most appropriate option: A) 2 months B) 4 months C) 5 months D) 7 months E) 9 months

Given their profits are equal per annum so 25000*12=30000*x x=10 months 12-10= <gadget id="calculator"> 12-10</gadget> <output>2</output> 2 months 2 monthsNSWER:2 months <result>A</result>

A

A started a business with Rs.25000 and is joined afterwards by B with Rs.30,000. After how many months did B join, if profit per annum is divieded equally?

aqua_rat__SmSEo9uy8XbEh7vP

If k is a non-negative integer and 15^k is a divisor of 759,325 then 3^k - k^3 = Choose the correct choice from the following options A) 0 B) 1 C) 37 D) 118 E) 513

At first we should understand whether 759325 divisible by 15. 15 is equal to 3 * 5 so 759325 should be divisible on these integers 759325 is divisible by 5 because of last digit 5 but not divisible by 3 because sum of its digits doesn't divisible by 3: 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 doesn't divisible by 3 so 759325 can be divisible by 15^k only if k = 0 and 15^k = 1 so 3^k - k^3 = 1 - 0= <gadget id="calculator">1 - 0</gadget> <output>1</output> 1 Answer is 1 <result>B</result>

B

If k is a non-negative integer and 15^k is a divisor of 759,325 then 3^k - k^3 =

aqua_rat__Z9WFG7TJ5Hda1wZV

Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 10 hours and 8 hours respectively. The ratio of their speeds is Choose the correct choice from the following: A) 4 : 9 B) 4 : 3 C) 4 : 12 D) 4 : 8 E) 4 : 5

Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 10 = 4 : 5. Answer: 4 : 5 <result>E</result>

E

Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 10 hours and 8 hours respectively. The ratio of their speeds is

aqua_rat__MoTcsVQdI2xQ7xzj

J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 2 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance? Choose the correct choice from the following answers: A) a)4y B) b)5y C) c)6y D) d)11y E) e)10y

J and M were both paid x dollars If M gave Y dollars from her X to J then at the end J will have X+Y dollars M will have X- Y dollars Now since the hourly wages have to be same then Hourly wage of J = (X+Y) / 12 (Since J worked for 12 hrs) Hourly wage of M = (X-y) /10 (Since M worked 2 hrs less than J) Equating both (X+Y)/12=(X-Y)/10 on simplifying X=11y Answer d)11y <result>D</result>

D

J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 2 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?

aqua_rat__a7vxVdaXvL6ONJQM

A bowl contains pecans, cashews, and almonds in a ratio of 7 : 12 : 18, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10 Pick one A) I only B) III only C) I,II only D) II only E) II,III only

i. The ratio 2 : 3 is the same as the given ratio 12 : 18. If one pecan were removed, the new ratio would be 6 : 12 : 18, or 1 : 2 : 3. ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio. iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio. I onlynswer : I only <result>A</result>

A

A bowl contains pecans, cashews, and almonds in a ratio of 7 : 12 : 18, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10

aqua_rat__AdNu2fVWSom7XoRH

Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.2 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas’s current age in years? Choose the correct choice from the following options: A) 24 years B) 44 years C) 34 years D) 64 years E) 16 years

16 years If current ages of Rahim and Thomas be 5A years and 4A years correspondingly Then, 5A + 2 = 11 4A + 2 = 9 9(5A + 2)=11(4A + 2) A = 4 Thomas’s current age = 4A = 16 years. 16 years <result>E</result>

E

Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.2 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas’s current age in years?

aqua_rat__VIOERSk5pGxTxL8r

Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 2160, find the total rent of the field. Select. A) 3750 B) 3550 C) 4250 D) 9750 E) 3250

Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63. Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325 (72x)/325=2160 = x=(2160 x 325)/72 = 9750 Hence, total rent of the field is Rs. 9750. Answer is 9750. <result>D</result>

D

Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 2160, find the total rent of the field.

aqua_rat__t0Z5ClkgF2bjSBWM

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is ? Choose the correct answer. A) 45 kmph B) 25 kmph C) 30 kmph D) 50 kmph E) None of these

Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) x (18/5)] km/hr = 45 km/hr. Let the speed of the train be 'S' km/hr. Then, relative speed = (S - 5) km/hr. S - 5 = 45 =&gt; S = 50 km/hr. ANSWER IS 50 kmph <result>D</result>

D

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is ?

aqua_rat__JDofS8lYidRjJuxY

Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days? Choose the correct choice from the following choices: A) 22 B) 26 C) 48 D) 77 E) 12

Sravan's one day's work = 1/25 - 1/75 = 2/75 Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75 Sravan completed 16/75th of total work. So, his share is 16/75 * 225 = Rs. 48. Answer:48 <result>C</result>

C

Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?

aqua_rat__8g1yuFtoCm8zCuEY

An examiner rejects 0.16% of the meters as defective. How many will be examine to reject 4? Choose the correct choice from the following answers A) 500 B) 4000 C) 2500 D) 5500 E) None of these

Explanation : Solution: let the number of meters to be examined be x. then, 0.16% of x = 4 =&gt;(16/100 * 1/100 * x) = 4 =&gt;x = (4*100*100)/16= <gadget id="calculator">(4*100*100)/16</gadget> <output>2_500</output> 2500. Answer : 2500 <result>C</result>

C

An examiner rejects 0.16% of the meters as defective. How many will be examine to reject 4?

aqua_rat__kAjLYQVK1ZpmCdG1

An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height? Choose the correct choice from the following answers. A) 80 B) 88 C) 94 D) 112 E) 124

We see that h will be a maximum h=150 when t-3=0, that is when t=3. At t=5, h = -14(5-3)^2 + 150 = -14(4) + 150 = 94 The answer is 94. <result>C</result>

C

An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?

aqua_rat__yjR0cqc9LcZi0ENh

In a forest 150 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 10 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 correct choice A) 150 B) 750 C) 3,000 D) 1,500 E) 2,500

The percentage of tagged deer in the second sample = 10/50*100= <gadget id="calculator">10/50*100</gadget> <output>20</output> 20%. So, 150 tagged deers comprise 10% of total # of deers --&gt; total # of deers= 150*20 = 3,500. Answer: 3,000 <result>C</result>

C

In a forest 150 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 10 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?

aqua_rat__mrTAutMSvF6JPvh7

There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'Y', then how many triangles can be determined with the 15 points that contain the point Y? Choose the correct choice from the following choices: A) 91 B) 105 C) 182 D) 210 E) 455

Fist point is A which is fixed so can be selected in 1 way Second point can be selected in 14 ways Third point can be selected in 13 ways so total ways = 1x14x13 = 182 but answer is 91 which is 182/2=182 <result>C</result>

C

There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'Y', then how many triangles can be determined with the 15 points that contain the point Y?

aqua_rat__HtBKO4h8e5YsOP0h

if 70% of (x-y) = 30% of (x+y) then what percent of x is y? Choose the correct choice from the following answers: A) 2.5% B) 40% C) 5% D) 15% E) 25%

70% of (x-y)=30% of(x+y) (70/100)(x-y)=(30/100)(x+y) 7(x-y)=3(x+y) 4x=10y x=5/2y therefore required percentage =((y/x) X 100)% = ((y/(5/2)y) X 100) =40% Answer is 40%. <result>B</result>

B

if 70% of (x-y) = 30% of (x+y) then what percent of x is y?

aqua_rat__UhY8WUyuuIwJaPAt

A and B can do a work in 8 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed? Select the correct option: A) 9.6 days B) 7.6 days C) 4 days D) 8.6 days E) 6.6 days

Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/8+ 1/12 = 5/24. Total time required to complete the work = 2 * 24/5= <gadget id="calculator">2 * 24/5</gadget> <output>48/5 = around 9.6</output> 9.6 days. 9.6 daysNSWER:9.6 days <result>A</result>

A

A and B can do a work in 8 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?

aqua_rat__xc7j4TCd0FhkcVaa

If KING is coded as 17 and DON is coded as 18 Then MASS is coded as Answers. A) 21 B) 20 C) 19 D) 29 E) None

KING = 11+9+14+7= <gadget id="calculator">11+9+14+7</gadget> <output>41</output> 41 i.e (4*4)+(1*1)=17 MASS = 13+1+19+19= <gadget id="calculator">13+1+19+19</gadget> <output>52</output> 52 i.e (5*5)+(2*2)=29 29ON = 4+14+15= <gadget id="calculator">4+14+15</gadget> <output>33</output> 33 i.e(3*3)+(3*3)=18 ANSWER:29 <result>D</result>

D

If KING is coded as 17 and DON is coded as 18 Then MASS is coded as