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mathematics

A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole ?

Answer ∵ 8 m shadow means original height = 12 m ∴ 1 m shadow means original height = 12/8 m ∴ 100 m shadow means original height = (12/8) x 100 m = (6/4) x 100 = 6 x 25 = 150 m Correct Option: A The answer is: A

A

mathematics

The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?

Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B The answer is: B

B

mathematics

What will be the remainder when 8-3 + 3^5 + 2^10 is divided by 4?

The multiplication(e.g. 2^10) is done first and then the sum(e.g. 15+20) and subtraction (e.g. 8-3), and after all this expression it should be divided by 4 and the answer is 0, option D. The answer is: D

D

mathematics

How many quarters are equal to 2 dollars?

B. 8 quarters The answer is: B

B

mathematics

Insert the missing number. 2, 6, 12, 20, 30, 42, 56,72, 90, 110 (....)

Explanation: The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8,8 x 9, 9 x 10,10 x 11. So, the next number is 11 x 12 = 132. Answer: B) 132 The answer is: B

B

mathematics

Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?

1120 = P [1 + (5*12/5)/100] P= 1000 Answer:A The answer is: A

A

mathematics

If a2 - b2 = 10 and a*b = 5, find a4 + b4.

a2 - b2 = 10 : given a4 + b4 - 2a2b2 = 102 : square both sides and expand. a*b = 5 : given a2b2 = 52 : square both sides. a4 + b4 - 2(25) = 100 : substitute a4 + b4 = 150 correct answer C The answer is: C

C

mathematics

A certain deck of cards contains 2 white cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not white?

The question asks they will both be not white. Considering that these are draws without replacement there are following possibilities : draw 1, draw 2 ===== ===== 1) Not white, white; 2) white, Not white; 3) white, white; 4) Not white, not white; The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are white P(4) = 6/8*5/7=15/28 1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28 A The answer is: A

A

mathematics

If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 5x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?

The big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 2, and 5x – 2 are ALLintegers For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9. Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers When x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 2, and 5(3) – 2. When we evaluate these terms we get: 4, 6, 3, 5 and 13 Rearrange to get: 3, 4, 5, 6, 13. So, when x = 3, we get consecutive integers. In this case, the MEDIAN = 5 Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9) Answer: C The answer is: C

C

mathematics

A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Speed = 54 x 5/18 = 15 m/s Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/42 = 15 --> x + 300 = 630 x = 330m. Answer : C. The answer is: C

C

mathematics

WHEN A PERSON SELLS TWO ITEMS $800 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:

When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%. Answer : B The answer is: B

B

mathematics

A tortoise is making its way to eat a piece of lettuce at a constant speed. On its way to the lettuce, it takes 10 seconds to walk past a grain of sand. It then passes a piece of wood 20 cm long in 30 seconds to get to the lettuce. What is the length of the tortoise?

Sol. Let the length of the tortoise be x centimetres and its speed be y cm/sec. Then, x / y = 10 ⇒ y = x / 10 ∴ (x + 20) / 30 = x / 10 ⇔ x = 10 cm. Answer E The answer is: E

E

mathematics

A boy bought a pen at 40% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price?

Original price = 100 CP = 60 S = 60*(170/100) = 102 100 - 102 = 2% Answer: D The answer is: D

D

mathematics

A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream,it takes 4 hour.What is the speed of the boat in still water ?

Solution Rate downstream =(16/2) kmph = 8 kmph,Rate upstream = (16/4) kmph = 4 kmph. ∴ Speed in still water =1/2(8+4) kmph = 6 kmph. Answer B The answer is: B

B

mathematics

Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 23 items in the same time Machine Z produces 21 items. If machine Y takes 21 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

rate z/rate y=21/23 time z/time y=23/21 (23/21)*21=23 minutes E The answer is: E

E

mathematics

A is half good a work man as B and together they finish a job in 20 days. In how many days working alone B finish the job?

WC = 1:2 2x + x = 1/20 => x = 1/60 2x = 1/60 => 30 days Answer:B The answer is: B

B

mathematics

Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 24000, how much amount per month would he have spent on clothes and transport?

∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month ∵ Amount, spent on clothes and transport = 24000⁄12 = 2000 Answer A The answer is: A

A

mathematics

A man purchased a grinder for Rs. 660 and sold it at a profit of 10%. The selling price is:

s.p.=110/100 × 600 = 660 Answer: C The answer is: C

C

mathematics

From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a black and the second card is a spade is?

Probability of a black card= 26/52 = 1/12 Probability of a jack = 13/52 = 1/4 Probability of both = P1*P2 = 1/(2*4) = 1/8 Answer is B. The answer is: B

B

mathematics

A cube is divided into 729 identical cubelets. Each cut is made parallel to some surface of the cube . But before doing that the cube is coloured with green colour on one set of adjacent faces ,red on the other set of adjacent faces, blue on the third set. So, how many cubelets are there which are painted with exactly one colour?

total cubes created are 729 so a plane of big cube has 9*9 cubes out of that(n-2)*(n-2)=7*7=49 are painted only one side and a cube has six sides=6*49=294 ANSWER:B The answer is: B

B

mathematics

The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.

Let the diagonals of the squares be 2x and 5x respectively. Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2= 4x2: 25x2= 4 : 25. Option C The answer is: C

C

mathematics

Arrange the following in a logical order: 1. Birth 2. College 3. Marriage 4. School 5. Employment

Explanation: The given words when arranged in the order of various events as they occur in man's life, the sequence is : Birth, School, College, Employment, Marriage. Sequence is : 1, 4, 2, 5, 3. ANSWER B The answer is: B

B

mathematics

The compound interest on Rs.2800 for 1 1/2years at 10% per annum is

Explanation: Amount = Rs.[[2800×(1+10/100)](1+5/100)] = Rs.[2800×11/100×21/20]= Rs.3234 C.I = Rs.(3234-2800)= Rs.434 Correct Option: C The answer is: C

C

mathematics

At the store opening, Larry's Grocery had 50 Lemons and 60 Oranges. By closing, the store at 20 Lemons and 40 Oranges left. By approximately what percent did the ratio of Lemons to Orange decrease from opening to closing.

Opening: Lemons/Oranges = 50/60 =100/120 Closing: Lemons/Oranges = 20/40 =60/120 ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators. So, our ratio went from 100/120 to 60/120 Ignoring the denominators, we went from 100 to 60 The percent change = 100(difference in values)/(original value) = (100)(100-60)/100 = (100)(40)/100) = 40 Answer: B The answer is: B

B

mathematics

A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?

80* 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280 Answer: D The answer is: D

D

mathematics

Tough and Tricky questions: Number Properties. What is the smallest positive integer x such that 225x is the cube of a positive integer?

We want to know the smallest x that will make 225x a CUBE of some number. Let's call that number y. Let's first figure out what we're working with. The prime factorization of 225 can be visualized: ...........225 ......../.......\ ......25.......9 ...../..\....../...\ ...5....5...3.....3 So, we have 5 * 5 * 3 * 3 that can be multiplied together to get 225. Now we need to figure out what we need to make 225 * x into a cube of y (y^3=225*x). We have two 5s and two 3s. To arrange these numbers in identical sets (3,5), we need at least one more 5 and one 3. Each of these numbers will give us the value of y (3*5=15), which, multiplied by itself three times, gives us 225 * x. Looking at the factors we need to complete the triples, we get 5 * 3 = 15. We know this is the smallest number possible because prime factors by definition cannot be broken down any further. Therefore, we can go with answer choice B. If time permits, we can do a sanity check. We calculated that y should be 3 * 5, or 15. 15 * 15 * 15 = 3375. Also, 225 * 15 = 3375. Answer: B The answer is: B

B

mathematics

If |20x-10| = 190, then find the product of the values of x?

|20x-10| = 190 20x-10 = 190 or 20x-10 = -190 20x = 200 or 20x = -180 x = 10 or x = -9 product = -9*10 = -90 Answer is E The answer is: E

E

mathematics

If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many Q digits does this integer consists of?

Number of single digit integers = 9 Number of 2 digit integers = 99 - 10 + 1 = 90 Number of 3 digit integers = 150 - 100 + 1 = 51 Number of digits in the integer Q= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342 Answer: C The answer is: C

C

mathematics

In a mixture of 60 litres, the ratio of acid to base is 2 : 1. If this ratio is to be 1 : 2, then the quantity of base (in litres) to be further added is

Acid = 40 lts Base = 20 lts to make the ratio A:B = 1:2 , 60 lts of base should be added ANSWER:E The answer is: E

E

mathematics

If integers e and b are distinct factors of 30, which of the following CANNOT be a factor of 30? I. eb + b^2 II. (e + b)^2 III. e + b

Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. I. eb + b^2 --> if e=1 and b=2 then eb + b^2=6, which is a factor of 30. OK; II. (e + b)^2 --> (e + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD; III. e + b --> if e=1 and b=2 then e + b=3, which is a factor of 30. OK. Answer: B. The answer is: B

B

mathematics

the cyclist walking at a constant rate of 15 miles per hour is passed by a car traveling in the same direction along the same path at 60 miles per hour. the car stops to wait for the cyclist for 6 minutes after passing her, while the cyclist continues to go at her constant rate, how many minutes must the car wait until the cyclist catches up?

For the 6 minutes the car continues to overtake the cyclist, she is going at 45 miles per hour faster than the cyclist. Once the car stops, the cyclist is going at 15 miles per hour while the car is at rest So the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds. 45/15 * 6 or 18 minutes Answer is (E) The answer is: E

E

mathematics

5 blue marbles, 3 red marbles and 4 purple marbles are placed in a bag. If 4 marbles are drawn without replacement, what is the probability that the resu lt will not be 2 blue and 2 purple marbles?

Answer is 29/33. The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33. Subtracting the above from 1 we get 29/33 E The answer is: E

E

mathematics

The average of 11 observations is 60. If the average of first five observations is 58 and that of the last five is 56, then the sixth observation is.

Explanation : Sixth observation=[60*11 - (58*5 + 56*5)] = 90. Answer : B The answer is: B

B

mathematics

If the sum of a number and its square is 182, What is the number?

Explanation: Let the integer be x. Then, x + x2 = 182 x2 + x - 182 = 0 (x + 14) (x – 13) = 0 x = 13 ANSWER: E The answer is: E

E

mathematics

E=√[2√63 + 2/(8+3√7)] =

In these type of question u multiply the nominator and denominator with conjugate...Conjugate of 8 +3sqrt(7) is 8 -3sqrt(7) sqrt[2sqrt(63) + 2 { 8 - 3sqrt(7)}/{64 - 63}] E=sqrt[2sqrt(63) +16 - 2sqrt(63)] =4 Answer is 4.D The answer is: D

D

mathematics

The marks obtained by Vijay and Amith are in the ratio 6:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?

6:5 3:2 ------- 18:15:10 18:10 9:5 ANSWER:C The answer is: C

C

mathematics

The speed of a boat in still water in 22 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:

Explanation: Speed downstream = (22 + 4) = 26 kmph Time = 24 minutes = 24/60 hour = 2/5 hour Distance travelled = Time × speed = (2/5)×26 = 10.4 km Answer: Option A The answer is: A

A

mathematics

When 0.232323..... is converted into a fraction, then the result is

0.232323... = 0.23 = 23/99 Answer is A. The answer is: A

A

mathematics

nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 12 cm?

Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (12) = 228 cm2 Answer:E The answer is: E

E

mathematics

If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?

A particular players is never chosen, it means that 11 players are selected out of 14 players. => Required number of ways = 14C11 = 14!/11!x3! = 364 C The answer is: C

C

mathematics

Guadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters?

One is 300 m by 500 m and the other is 250 m by 630 m : (300*500)+(250*630) = 150000+157500 307500 ANSWER:B The answer is: B

B

mathematics

The dimensions of a rectangular solid are 4 inches, 5 inches, and 12 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?

Answer: E. The answer is: E

E

mathematics

14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish

14 men make toy in 5 days after 1 day 14 more worker join m1/m2=d2/d1 14/28=d2/4 =2 day ANSWER:B The answer is: B

B

mathematics

At a party, there were five times as many girls as boys and three times as many adults as children. Which of the following could NOT be the number of people at the party?

Five times as many girls as boys --> F = 5M. Three times as many adults as children --> (F + M) = 3C. The number of people at the party = F + M + C = 3C + C = 4C. The number of people at the party must be a multiple of 4. The only answer choice which is NOT a multiple of 4 is A. Answer: A. The answer is: A

A

mathematics

The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?

Explanation: Given that the area of the square = 1225 sq.units => Side of square = √1225 = 35 units The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units Given that breadth = 10 units Area of the rectangle = lb = 14 * 10 = 140 sq.units ANSWER IS A The answer is: A

A

mathematics

An article costs Rs. 600. What should be the marked price of an article so that after 10% discount, the trader makes 20% profit?

Explanation: Cost price of article = Rs. 600 Profit % = 20% Therefore, selling price of article = 120% of C.P. = (120 / 100) * 600 = Rs. 720 Marked price = ? Discount % = 10% S.P. = Rs. 720 90% of M.P. = S.P. 90/100 * M.P. = 720 M.P. = 720 * (100/90) = Rs. 800 ANSWER A The answer is: A

A

mathematics

When all the students in a school are made to stand in rows of 46, 36 such rows are formed. If the students are made to stand in rows of 42, how many such rows will be formed ?

Explanation: Total number of students = 46 x 36 When arranged in rows of 42, number of rows formed are, = 39. Answer: D The answer is: D

D

mathematics

If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?

A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer:B The answer is: B

B

mathematics

A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different R arrangements of plays can be run, if the same play can’t be run more than once?

Number of R ways to choose the first play: 9 Second play: 8 Third:7 9*8*7= 504.D The answer is: D

D

mathematics

Three years ago, the ratio of ages of P and Q was 4:3. Six years from now, the ratio of their ages will be 7:6. What is P's age at present?

3(P-3)/4 = (Q-3). Then Q = 3(P-3)/4 + 3 6(P+6)/7 = Q+6 6(P+6)/7 = 3(P-3)/4 + 9 24P+144 = 21P + 189 3P = 45 P = 15 The answer is C. The answer is: C

C

mathematics

At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?

A B C D 90 100 80 100 A D 90 ----- 100 360 ------ ? = 400 500 ------ 400 100 ------- ? => 80% Answer: C The answer is: C

C

mathematics

Jerry, an electrician, worked 8 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth) What percent 12 is 8? 12 months = 1 year

1. Multiply the opposites 8 x 100 = 800 100=8/12 Divide by the remaining number 66.67% (rounded to hundredth) correct answer B The answer is: B

B

mathematics

In six successive games, a baseball team scored 1 runs once, 4 runs twice, and 5 runs three times. What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?

1 runs once (one game) 4 runs twice (two game) 5 runs three times (three games) SO we have (1*1 + 4*2 + 5*3)/6 = 24/6 = 4. ANS: E. The answer is: E

E

mathematics

What is the maximum number of pieces that a circular pie can be divided into by four linear cuts?

Such kind of combinations problems are always about a pattern recognition. Maximum pieces: 0 line gives 1 whole piece; 1 line will gives 2 pieces: 1+1=2; 2 lines will give 4 pieces: 2+2=4; 3 lines will give 7 pieces: 4+3=7; 4 lines will give 7+4=11 pieces. ANSWER:E The answer is: E

E

mathematics

852.68 − 4.5 + 288.98 = ? − 2132.54

Option 'C' The answer is: C

C

mathematics

The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?

A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 5 years, their ages will be 45 and 25. Sum of their ages = 45 + 25 = 70. ANSWER A The answer is: A

A

mathematics

What percent of the different arrangements of the letters of the word AKACUL are those in which the vowels appear together?

let's determine the number of total possibilities in arranging the letters. There are six spaces, so the total number of arrangements is 6!, or 360. Next, we need to figure out how to determine the number of ways that we can arrange the 3 vowels together - simply place them together (as in AAU) and call that a single place. Next, we must determine the number of ways to arrange the now 4 units (i.e., AAU, B, C, S). Like above, there are 4 units and 4 places so the number of arrangements is 4!, or 24. Finally, we need to account for the number of ways we can arrange AAU. We can either write out each unique iteration (AAU, AUA and UAA) or calculate as 3!/2! and get 3. Putting this all together, we get the number of ways to arrange the letters so that the vowels are together is 4! x 3 ==> 72 the number of total arrangements of all the letters is 6! ==> 360 72/360 = 1/5, or 20% Correct answer is E The answer is: E

E

mathematics

Four friends, Patricia, Melyssa, Tania, and Cassandra, are pooling their money to buy a $1100 item. Patricia has twice as much money as Melyssa. Tania has $10 more than Patricia. Cassandra has 20% more than Tania. If they put all their money together and spend the $1100, they will have $32 left. How much money does Patricia have?

P= 2M ; T= P+10 ; C= 1.2(T) P+M+T+C-1100=32 P+0.5P+P+10+1.2(P+10) = 1132 P+0.5P+P+10+1.2P+12=1132 P+0.5P+P+1.2P+22=1132 P+0.5P+P+1.2P=1110 3.7P=1110 P=300 Answer:C The answer is: C

C

mathematics

Sanjay invested an amount of ` 16,000 for two years on compound interest and received an amount of ` 17,640 on maturity. What is the rate of interest per annum?

The extra money for two years is 1,640. This can be broken up as 800 + (800 + 40). Since 40 = 5% of 800 and 800 = 5% of 16000 So, r = 5%. Answer: B The answer is: B

B

mathematics

The S.I. on a certain sum of money for 4 years at 12% per annum is half the C.I. on Rs. 6000 for 2 years at 15% per annum. The sum placed on S.I. is?

C.I. = [6000 * (1 + 15/100)2 - 6000] = (6000 * 23/20 * 23/20 - 6000) = Rs. 1935. Sum = (967.5 * 100)/(4 * 12) = Rs.2015.625 Answer:D The answer is: D

D

mathematics

In a certain parking lot, 3% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What % of cars in the parking lot are parked illegally.'

So Total no. of cars parked illegally: 300 Total no. of cars: 2000 300/2000*100, So 15% ANSWER:C The answer is: C

C

mathematics

A rectangular-shaped carpet that measures x feet by y feet is priced at $46. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)

The area of the carpet in feet is xy. The area in square yards is xy / 9. The price per square yard is 46 / (xy/9) = 414/(xy). The answer is E. The answer is: E

E

mathematics

A number x is multiplied by 3, and this product is then divided by 7. If the positive square root of the result of these two operations equals x, what is the value of x if x≠0 ?

sqrt(3x/7) to be perfect square x has to 3/7 Ans: B The answer is: B

B

mathematics

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?

A 833 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. The answer is: A

A

mathematics

If 7^k + 7^k = (7^9)^(7^9) - 7^k, then k = ?

7^k + 7^k = (7^9)^7^9 - 7^k 7*(7^k) = 7 ^ (49 * 7^9 ) = 7^(7^2 * 7^9) = 7^(7^11) 7^k+1 = 7^(7^11) So k+1 = 7^11 So k = 7^11 -1 Answer is E The answer is: E

E

mathematics

P alone can complete a job in 12 days. The work done by Q alone in one day is equal to one-half of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?

P's rate is 1/12 Q's rate is 1/24 The combined rate is 1/12 + 1/24 = 1/8 If they work together, the job will take 8 days. The answer is D. The answer is: D

D

mathematics

A straight line has a slope of 1/2 and a y-intercept of -2. On this line, what is the x-coordinate of the point whose y-coordinate is 10?

For the point intercept form of a line y=mx+b ; m is the slope and (b=y when x=0) Slope=y2−y1/ x2−x1 we are given slope =1/2 y intercept is always equal to b when x = 0 (therefore at origin we can always write any (x,y) pair as (0,b) y intercept hence (b) is given -2 now we have got all the values that we want to calculate slope 1/2=10−(−2)/x−0 1/2=10+2/x==>1/2=12/x==>x=24 CORRECT ANSWER IS E The answer is: E

E

mathematics

The sum of the mean, the median, and the range of the set {1, 2, 9} equals which one of the following values?

set {1, 2, 9} Mean = (1+2+9)/3 = 4 Meadian = Middle term = 2 Range = Highest - Lowest = 9-1 = 8 Mean+Median+Range = 4+2+8 = 14 Answer: Option B The answer is: B

B

mathematics

Simran started a software business by investing Rs.50,000. After six months, Nanda joined her with a capital of Rs.80,000. After 3 years , they earned a profit of Rs.24,500. What was Simran's share in the profit?

Solution Simran : Nanda =(5000x36):(80000x30) = 3 : 4. Simran's share = Rs.(24500x3/7) = Rs.10,500. Answer C The answer is: C

C

mathematics

A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?

This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B The answer is: B

B

mathematics

How many three letter words are formed using the letters of the word GAMER?

The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is 5P3 = 5 * 4 *3 = 60. Answer: A The answer is: A

A

mathematics

In a triangle, one side is 6 Cm and another side is 8 Cm. which of the following can be the perimeter of the triangle?

Given : one side is 6 Cm and another side is 8 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 22. Hence A. The answer is: A

A

mathematics

A motor car starts with a speed of 70km/hr with its speed increasing every 2hours by 10kmph. In how many hours will it cover 345kms?

Distance covered in first 2hours = 70*2 = 140km Distance covered in next 2hours = 80*2 = 160km remaining distance = 345- (140+160) = 45km speed in the fifth hour = 90km/hr total time to cover 45km = 45/90 = 1/2 hr total time taken = 4+(1/2) = 4hours 30minutes. correct option is D The answer is: D

D

mathematics

The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?

(30 * 30)/100 = 9% decrease ANSWER C The answer is: C

C

mathematics

How many five-digit numbers exist such that the product of their digits is 400?

We're asked to name all of the 5-digit numbers whose product-of-digits is 400. We can use prime-factorization to figure out the digits, BUT this comes with a "twist".....NOT ALL of the digits have to be primes.... 400 = (25)(16) The 25 = (5)(5) and there's no way around that. Every option MUST have two 5s as two of the digits. The 16 can be broken down in a few different ways though: 16 = (1)(2)(8) 16 = (1)(4)(4) 16 = (2)(2)(4) Each of those options has to be accounted for. So, we have 3 sets of 5 digits: 1) 1, 2, 8, 5, 5 --> This gives us 5!/2! arrangements = 120/2 = 60 different 5-digit numbers. 2) 1, 4, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements = 120/4 = 30 different 5-digit numbers. 3) 2, 2, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements = 120/4 = 30 different 5-digit numbers. 60 + 30 + 30 = 120 different 5-digit numbers Final Answer:B The answer is: B

B

mathematics

Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?

Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 120 + 280 = 400 m. The time required = d/s = 400/20 = 20 sec.Answer: D The answer is: D

D

mathematics

Calculate f(3), given that f(x) = x3 + f0(-1)x2 + f00(1)x + f0(-1)f(-1).

Differentiating, we compute f0(x) = 3x2 + 2f0(-1)x + f00(1) f00(x) = 6x + 2f0(-1): Plugging in x = -1 into the first equation and x = 1 into the second, we obtain a system of equations in f0(-1) and f00(1): f0(-1) = 3 - 2f0(-1) + f00(1); f00(1) = 6 + 2f0(-1): Denoting f0(-1) and f00(1) by a and b respectively, we have a = 3 - 2a + b b = 6 + 2a: Plugging the second equation into the first, we get a = 3 - 2a + (6 + 2a) = 9: Thus, b = 6 + 2a = 24, so f(x) = x3 + ax2 + bx + af(-1) = x3 + 9x2 + 24x + 9f(-1): Finally, plugging x = -􀀀1 into this equation, we get f(-1) =-1 + 9-24 + 9f(-1) -8f(-1) = -16 f(-1) = -2 We conclude that f(x) = x3 + 9x2 + 24x + 18 f(3) = 33 + 9* 32 + 24 *3 + 18 = 27 + 81 + 72 + 18 = 198 correct answer A The answer is: A

A

mathematics

The average weight of A, B and C is 60 kg. If the average weight of A and B be 70 kg and that of B and C be 50 kg, then the weight of B is:

EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (60 x 3) = 180 …. (i) A + B = (70 x 2) = 140 …. (ii) B + C = (50 x 2) = 100 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 240 …. (iv) Subtracting (i) from (iv), we get : B = 60. B’s weight = 60 kg. Answer B The answer is: B

B

mathematics

The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?

Explanation : In alphabetical order : A D O P S T A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A. A D _ _ _ _ : empty places can be filled in 4!=24 A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24 this total crosses 42. So We should not consider all the words starting with AO. A O D _ _ _ : 3!= 6 A O P _ _ _ : 3!=6 Till this 36 words are obtained, we need the 42nd word. AOS _ _ _ : 3!= 6 Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD. So given word is AOSTPD Answer : D The answer is: D

D

mathematics

A person can row upstream 2 kmph and downstream 8 kmph. Find the rate of the stream and person rate in still water.

Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(8-2) = 3 kmph => Rate in still water = 1/2(8+2) = 5 kmph Option D The answer is: D

D

mathematics

Find the value of * in the following (1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)

3.6 Option 'C' The answer is: C

C

mathematics

A can do a piece of work in 10 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?

B (x – 5)/10 + x/20 = 1 x = 10 days The answer is: B

B

mathematics

Arun has 13 boxes of chocolates with him, with an average of 17 chocolates per box. If each box has at least 11 chocolates and no two boxes have equal number of chocolates, then what can be the maximum possible number of chocolates in any box?

DETAILED SOLUTION Total number of chocolates = 13 x 17 = 221 For one box to have maximum number of chocolates, the other boxes need to have minimum number of chocolates i.e. 11, 12, ………………….., 22 Total = 11 x 12 + (0+1+2+……………+11) = 132 + 66 = 198 Therefore, maximum possible chocolates = 221 – 198 = 23 CORRECT ANSWER A. The answer is: A

A

mathematics

How many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph?

Explanation: D = 70 + 80 = 150 S = 36 * 5/18 = 10 mps T = 150/10 = 15 sec Answer: Option D The answer is: D

D

mathematics

The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate Y of movement for his trip along the moving walkway?

A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average Y MUST bebetween3-6 ft per second or the Earth is FLAT!!!. So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible. The answer is: E

E

mathematics

In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?

P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E ∩ H) = (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5 C The answer is: C

C

mathematics

The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 2500?

To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^11 = 2048 < 2500, then the greatest possible length of integer z is 11. The answer is C. The answer is: C

C

mathematics

Mane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Mane or Thomas is to be selected?

Ans:C Solution: M+T+6 = total 8 , we need to select at least one of the M and T or both= total 4 out of 8 - 4 out of 6 8C4 - 6C4 =55 The answer is: C

C

mathematics

If a*b*c=195, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ?

Explanation : a∗b∗c/b∗c∗d= 195/65 => a/d = 3 d∗e∗f/c∗d∗e= 250/1000 => f/c = 1/4 a/d* f/c = 3 * 1/4 = 3/4 Answer : C The answer is: C

C

mathematics

A soft drink company had 6000 small and 15000 big bottles in storage. If 12% of small 14% of big bottles have been sold, then the total bottles remaining in storage is

6000 + 15000 - (0.12*6000 + 0.14*15000) = 18180. Answer: C. The answer is: C

C

mathematics

P, Q and R can do a piece of work in 20, 30 and 60 days respectively. In how many days can P do the work if he is assisted by Q and R on every third day?

P's 2 day's work = 1/20*2=1/10 P+Q+R)'S 1 DAY'S WORK = 1/20+1/30+1/60 = 6/60 = 1/10 WORK IN DAYS = 1/5 NOW 1/5 DONE IN 3 DAYS WHOLE WORK WILL BE DONE IN(3*5) = 15 DAYS ANSWER A The answer is: A

A

mathematics

Calculate the HCF of 64, 592, 960

Explanation: Lets solve this question by factorization method. The factors of 64 are: 1, 2, 4, 8, 16, 32, 64 The factors of 592 are: 1, 2, 4, 8, 16, 37, 74, 148, 296, 592 The factors of 960 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 Then the greatest common factor is 16. Answer: Option B The answer is: B

B

mathematics

A watch was sold at a loss of 36%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?

64% 104% -------- 40% ---- 140 100% ---- ? => Rs.350 Answer: A The answer is: A

A

mathematics

If a number 105 divides into n with no remainder, which of the following must be a factor of n?

105 / n = k (with k an integer) (7)(5)(3) / n = k n must have a 7 in his prime factorization to divide 105 without remainder. answer D The answer is: D

D

mathematics

What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 3 Years?

160 = (800*3*R)/100 R = 6.6% Answer: B The answer is: B

B

mathematics

How much interest can a person get on Rs. 8200 at 10.5% p.a. simple interest for a period of six years and six months?

I = (8200 * 6.5 * 10.5)/100 = (8200 * 13 * 21)/(100 * 2 * 2) = Rs. 5596.5 Answer: A The answer is: A

A

mathematics

If |5x-20| = 100, then find the sum of the values of x?

|5x-20| = 100 5x-20 = 100 or 5x-20 = -100 5x = 120 or 5x = -80 x = 24 or x = -16 sum = 24-16 = 8 Answer is C The answer is: C

C

mathematics

A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?

100*(20/100) = 20 --- 10 ? --- 1 => Rs.2 100 --- 80 ? --- 2 => Rs.2.5 Answer:C The answer is: C

C

mathematics

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 20.25, the number of the member is the group is:

Money collected =(20.25 x 100) paise = 2025 paise numbers of members = 2025 squareroot = 45 Answer C The answer is: C

C

mathematics

Salesperson A's compensation for any week is $300 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

300+0.06(x-1000) = 0.08x 0.02x = 240 x = $12,000 The answer is C. The answer is: C

C