Datasets:

VivekNaga

/

sampledata

like 0

If a survey conducted over consecutive years in the village reveals that after adding 6% more men and 10% more women to the population, the total population increases from 8000 to 8600, what was the initial number of men in the village?

Given, The initial population is 8000 So, let us consider Number of Men(M) + Number of Women(W) = 8000 (Equation 1) Now, after 6% men and 10% women getting added the population is 8600 Therefore, 1.06*M + 1.10*W = 8600 (Equation 2) Subtracting Equation 1 from Equation 2 we get 0.06*M + 0.10*W = 600 (Equation 3) Now Multiplying Equation 1 with 0.1 and subtracting Equation 3 from it we get, 0.1*M + 0.1*W = 800 (-) 0.06*M + 0.1*W = 600 0.04*M = 200 Therefore, Number of Men(M) = $\frac{200}{0.04}$ = 5000

The difference between the L.C.M. and the H.C.F. of two numbers is 60, and the sum of their L.C.M. and H.C.F. is 84. If one of the numbers is 24, find the other.

Given, LCM + HCF = 84 (Equation 1) LCM – HCF = 60 (Equation 2) Solving both equations, we get LCM = 72 and HCF = 12 We know that, LCM * HCF = Product of numbers Also, it is given that one of the numbers is 24 Let us consider the other number is x Now, LCM * HCF = 24 * x 72 * 12 = 24 * x x = 36 Therefore, the other number is 36

Length and breadth of a rectangle are directly proportional. If the length increases from 10 cm to 25 cm and if the breadth now is 15 cm, then what was the breadth before any change in the length occurred?

Given that the length and breadth of the rectangle are directly proportional, Let x be the initial breadth Therefore, $\frac{10}{25}$ = $\frac{x}{15}$ So, x = $\frac{10*15}{25}$ x = 6cm

A company makes a mixture that contains 5% alcohol and the remaining 95% water. If 20 liters of alcohol is added to the mixture, then the concentration of alcohol increases to 10%. What is the quantity of the mixture after adding extra alcohol in liters?

Given, Before adding the additional alcohol the concentration of alcohol is 5% Let us consider the total quantity before adding the alcohol as x Therefore, the quantity of alcohol before adding is 0.05*x After adding 20 liters of alcohol, the concentration increases to 10% So, 0.05*x + 20 = 0.10*(x+20) 0.10*x – 0.05*x = 20-2 = 18 x = 360 Therefore, after adding 20 liters of alcohol the total amount is 380

Find the largest 2-digit number dividing 578 and 753 and leave the remaining 3 in each case.

Given, The numbers 578 and 753 give 3 as the remainder when divided by a 2 digit number. To find the largest 2 digit number which gives 3 as a remainder we need to find the HCF of the numbers we get when subtracted by the respective remainder. So, the numbers are 578-3 = 575 and 753-3 = 750 HCF for numbers 575 and 750 First, let's find the prime factorization of each number: 575=5×5×23 750=2×3×5×5×5 Now, to find the HCF, we take the smallest power of each prime factor that appears in both factorizations: The common factor is 5×5=25 So, the HCF of 575 and 750 is 25

Solve: 2/3 * 63/40 * 5/9.

Given, $\frac{2}{3}$ * $\frac{63}{40}$ * $\frac{5}{9}$ To solve this let’s see the potential cancellations that can happen As 5*8 = 40 so, 40 goes 8 times with 5 and 9*7 = 63 so, 63 goes 7 times with 9 So, the resultant expression will be $\frac{2}{3}$ * $\frac{7}{8}$ Solving this expression we get 7/12 as the result

Find the unit digit of the sum 552+223+821+782:

Given, Sum of numbers 552, 223, 821, 782 To find the unit digit of the sum we need to add up all the unit places of numbers Unit place values of all numbers are 2,3,1,2 Therefore, 2+3+1+2 = 8 Unit digit of the given sum is 8

Out of the given three numbers, 7, 28, and 18, which 2 numbers are the co-prime numbers?

Co-primes are the numbers which have only ‘1’ as the common factor So, in the given numbers 7 and 28 have 7 as common factor And 28 and 18 have 2 as common factor But, when we check for common factors for 7 and 18 there are no other common factors except ‘1’ Therefore, 18 and 7 are co-primes

In a bag, there are 6 green balls and 30 red balls. If a person selects a green ball, they win, but if they pick a red ball, they lose. What is the probability of winning this game?

Given there are 6 green balls and 30 red balls Therefore, there are a total of 30+6 = 36 balls In order to win the game the person should pick green ball So, The probability of choosing a green ball is = $\frac{6}{36}$ = $\frac{1}{6}$

The largest 6-digit number that is exactly divisible by 4 is:

As per the divisibility rule of 4 the last two digits of the number should be divisible by 4 Therefore, 999996 is the largest 6-digit number divisible by 4 as the last two digits 96 is divisible by 4.

A sells a bicycle to B at a loss of 10%. B sells it to C at a profit of 33.33%. If C pays Rs. 240 for it, then the cost price of the bicycle for A is

Given, A sells a bicycle to B at a loss of 10% i.e. SP of A = CP of B = x - 0.1*x = 0.9*x B sells the same bicycle to C at a profit of 33.33% i.e SP of B = CP of C = 0.9*x + 0.9*x/3 = 1.2*x CP of C = 240 = 1.2*x x = 200

5.67 and -2.89 are 2 numbers on a real number line. If 1 is added to both numbers, then which of the following is true?

Given numbers 5.67 and -2.89, The distance between these numbers on the number line would be 5.67-(-2.89) = 5.67+2.89 = 8.56 After adding 1 to each of the numbers the numbers will become 6.67 and -1.89 The distance between these numbers on the number line would be 6.67-(-1.89) = 6.67+1.89 = 8.56 which is the same as the previous distance

The number 3482* is completely divisible by 6. The smallest value of * can be

Given number is 3482*, To be completely divisible by 6, the given number should be divisible by 2 and 3 When a number is even then it is said that the number is divisible by 2, therefore the digit * should be even. A number to be divisible by 3, the sum of the digits of the number should be divisible by 3. Therefore, 3+4+8+2+*= 17+* should be divisible by 3 So the nearest numbers to 17 which are divisible by 3 are 18 and 21, if we consider the sum as 18 the * digit would be 1 which is not even Therefore we have to consider 21 as the sum, * = 21-17 = 4

A number was supposed to be multiplied by 4/3​, but Saurabh mistakenly multiplied it by 3/4​ instead, resulting in a number that was 63 less than the correct one. What was the original number?

Let the number be x and the correct value is c, We know that, x * $ \frac{4}{3}$ = c (Equation 1) But Saurabh multiplied x by $ \frac{3}{4}$ which resulted in the result 63 less than the actual value Therefore, x * $ \frac{3}{4}$ = c – 63 (Equation 2) Subtract Equation 2 from Equation 1 We get, x * $\left (\frac{4}{3} - \frac{3}{4} \right )$ = 63 x * $ \frac{7}{12}$ = 63 x = 108

Swapna invested Rs. 10000 at 6% per annum. If the interest is compounded half-yearly, then the total interest earned by Swapna at the end of the year is

Given, Principle amount = 10000 Rate of Interest (per annum) = 6% It is said that the interest is compounded half-yearly so, the rate of interest for half year is 6/2 = 3% Interest for first 6 months = 10000 * 0.03 = 300 Principle amount for next 6 months = 10000+300 = 10300 Interest for next 6 months = 10300 * 0.03 = 309 Total Interest amount for the year = 300+309 = 609

An investment has done 5 paise per rupee invested. If, at the end of the year, the interest earned by the investment is Rs. 200, then the investment is equal to:

Given, The interest is 5 paise for every rupee of investment The total amount of interest gained by the end of the year is 200 rupees We know that 1 paise = 0.01 rupee, 5 paise = 5*0.01 = 0.05 rupees Therefore, dividing the interest gained with the rate of interest gives the total amount invested So, Principle amount = 200/0.05 = 4000 rupees.

What is the relationship between the fractions 13/14 and 15/16?

To compare two fractions the denominator should be the same then based on the numerator we will decide the relation between them. So, to do this we need to find the LCM of denominators i.e 14,16 First, let's factorize 14 and 16: 14 = 2 × 7 16 = $2^{4}$ Now, we take the highest power of each prime factor that appears in either number: The prime factor 2 appears as $2^{4}$ in 16, and 2^1 in 14. The prime factor 7 appears in 14 but not in 16. So, the LCM of 14 and 16 is $2^{4}$ * 7 = 112 Therefore, the fractions can be re-written as $\frac{13}{14}$= $\frac{13*8}{112}$ =$ \frac{104}{112}$ $\frac{15}{16}$ = $\frac{15*7}{112}$ = $\frac{105}{112}$ Comparing numerators 104<105 Therefore, $\frac{13}{14}$ < $\frac{15}{16}$

The ratio between the speeds of two trains is 5:4. If the first train covers a distance of 210 km in 3hrs, then what is the speed of the second train?

Given, Ratio of speeds = 5:4 Speed of first train = distance / time = 210/3 = 70 kms/hr Let the speed of second train is x Therefore, $\frac{3}{4}$ = $\frac{70}{x}$ x = $\frac{70*4}{5}$ x = 56 kms/hr

Ramana commutes daily by traveling 2/5 of the distance between his home and his office by bus, 3/10 by auto, and the remaining 3 km on foot. The distance between his home and his office is

Let us consider the total distance is x, Ramana travels 2/5 distance by bus = $\frac{4}{10}$*x 3/10 distance by auto = $\frac{3}{10}$*x 3 kms by walk Total distance x = $\frac{4}{10}$*x + $\frac{3}{10}$*x + 3 x - $\frac{7}{10}$*x = 3 $\frac{3}{10}$*x = 3 x = 10kms

A supplier supplies milk to the milk booths. He earns a profit of 20% by selling the milk packets for Rs.30/litre. Find the cost price of milk packets

Profit = SP – CP 0.2*(CP) = 30 – CP 1.2 *(CP) = 30 CP = 25

The number 45981*7 is completely divisible by 9. The smallest whole-digit number in place of * can be

According to the divisibility rule of 9, if the sum of digits of the number is divisible by 9 then the number is divisible by 9. Now, 4+5+9+8+1+*+7 = 34+* The nearest number to 34 which is divisible by 9 is 36 Therefore, * = 36-34 = 2 So, the smallest whole number in place of * can be 2

What is the interest rate provided by the bank if it promises to triple your investment in 20 years?

Given, The investment will be tripled in 20 years Let us assume that the amount invested initially is P So, the interest gained in 20 years would be, 3*P-P = 2*P We know that, Simple Interest = $\frac{P*T*R}{100}$ 2*P = $\frac{P*20*R}{100}$ Rate of Interest (R) = $\frac{100}{10}$ = 10%

The product of a number and its multiplicative inverse is 25% of the number. What is the number?

Let us consider the number as x, Given that product of number and its multiplicative inverse is 25% of the number So, x * $\frac{1}{x}$ = $\frac{25}{100}$*x 1 = $\frac{1}{4}$*x Therefore, x = 4

Train A takes 9 hours to reach Hyderabad from Chennai, while Train B takes 12 hours. The ratio of the speeds of both trains is ______.

We know that, Speed = Distance/time Here the distance is same for both the trains. So, the ratio of speeds of train A and B = $\frac{ \frac{D}{9}}{\frac{D}{12}}$ = $\frac{12}{9}$ = $\frac{4}{3}$ Therefore, the ratio is 4:3

Satya travels from Hyderabad to Vijayawada in 5 h at a speed of 70 km/h. How long will it take if she averages her speed to 50 km/h during her drive?

We know that, Speed = Distance/time Given speed at a speed of 70km/hr she will cover the distance in 5hrs Now let’s find the distance covered, Distance = time*speed = 5*70 = 350km If the average speed is 50km/hr time taken is, Time = Distance/Speed = 350/50 = 7hrs

What is the largest power of 7 in 200!?

To find the highest power of a number in the factorial of a given number we divide the consecutive powers of the number with the factorial number and consider the integral part and add them. Given, we have to find the highest power for number 7 in 200! So, power is = $\frac{200}{7}$+ $\frac{200}{7^{2}}$ + $\frac{200}{7^{3}}$ + ..... = 28 + 4 + 0 = 32 Therefore, the highest power of 7 in 200! Is 32

A water pump takes 5 hrs to fill an overhead tank. The standby pump takes 10 hrs to fill the same overhead tank. If the first pump fails after 1 hrs of running, how long will the standby pump take to fill the remaining volume of the overhead tank in hrs?

Given a pipe can fill the tank in 5hrs and the standby pipe can fill the tank in 10hrs, So, the amount of tank can be filled in 1hr by normal pipe is = 1/5 By standby pipe = 1/10 So, if the normal pipe stops running after 1hr now the tank is already 1/5 full We have to fill the remaining 4/5 of tank with standby pipe Therefore, time required is = $\frac{ \frac{4}{5}}{\frac{1}{10}}$ = $\frac{4*10}{5}$ = 8hrs

How many ways can the letters of the word 'Toothpaste’ be arranged so that the two O's are not consecutive?

Given word is ‘toothpaste’ If we observe the word we have 3 t’s and 2 o’s repeating So, total number of arrangements would be = 10!/(2!*3!) = 3,02,400 Now, to find the number of arrangements with no two o’s together we subtract all the arrangements where o’s are together from total arrangements. So, total number of arrangements where o’s are together = (8+1)!/3! = 60,480 Therefore, total number of arrangements with no two o’s together are = 3,02,400 - 60,480 = 2,41,920

Nandan reaches his office late by 30 min if he drives at 30 km/h. He is on time if he drives at 40 km/h. What distance does he have to travel daily from home to the office and back in kms?

To solve this question, we need to first find the actual time he takes to reach home Let the time be x If the speed is 30km/hr he reaches home 30 minutes late i.e. 0.5 hrs late = x+0.5 By equating the distances we can find x, 30*(x+0.5) = 40*x 10*x = 15 x = 3/2 hrs Therefore, Distance = speed*time = 40*(3/2) = 60kms

A rectangle’s length is 2 times its breadth. It has an area of 5000 $yd^{2}$. What is the length of the rectangle in yds?

The formula for the area of a rectangle is length times breadth. The area of the rectangle is given as 5000 $yd^{2}$. We express the length in terms of the breadth: L=2*B. Substitute the expression for length into the area formula: 5000=(2*B)×B. 2* $B^{2}$ = 5000 $B^{2}$ = 2500 B = 50 L = 2*(50) = 100

Aditi can finish a job in 8 hrs and Bala in 12 hrs. Aditi and Bala work alternatively, starting with Aditi. If Aditi earns Rs. 60/hr, then how much does Aditi earn in total through this job in Rs.?

Aditi can complete the task in 8 hrs Bala can complete the task in 12 hrs Let us assume the total task as LCM(8,12) - 24 units Aditi’s efficiency is 3 units/ hr Bala’s efficiency is 2 units/ hr, As they are working alternatively, they can finish 5 units of work in 2hrs So, 20 units of work would be done by Aditi and Bala alternatively in 2*4 = 8hrs and Aditi would do remaining 4 units of work in 4/5 hrs Therefore total amount earned by Aditi is = (4+(4/5))*60 = Rs.288

What is the value of $2-\frac{1}{3}*\log_{3}27$ ?

Given $2-\frac{1}{3}*\log_{3}27$ We can write 27 as $3^{3}$ $2-\frac{1}{3}*\log_{3}3^{3}$ We can write it as $2-\frac{3}{3}*\log_{3}3$ We know that $ log_{3}3$ = 1 So, by solving accordingly we get = 2-1 = 1

Arrange the following in ascending order:3/15, 19/30, 8/19, 11/89.

By calculating the decimal values of the corresponding fractions, we can arrange them in ascending order 3/15 = 0.2 19/30 = 0.63 8/19 = 0.42 11/89 = 0.12 By taking a glance at the decimal values, 0.12 < 0.2 < 0.42 < 0.63 Therefore, 11/89 < 3/15 < 8/19 < 19/30

The simple interest earned on a certain amount is the same as money invested when invested at an interest rate 10% per annum. What is the period of investment in years?

Given, Rate of interest = 10% Let us consider the invested amount is P So, the simple interest = P We know that, simple interest = P*T*R/100 P = P*T*10/100 T = 100/10 = 10yrs

Every year before the festive season, a shopkeeper increases the price of a product by 40% and then introduces two successive discounts of 10% and 10%. What is the percentage loss or percentage gain?

Let the initial price be x, increased price is = x + (40/100)*x = 1.40*x After the first discount of 10% the price is = 1.40*x - (10/100)*(1.40*x) = 1.26*x After the second discount of 10% the price is = 1.26*x - (10/100)*(1.26*x) = 1.134*x Therefore, the gain is = 1.134*x – x = 0.134 The percentage gain is 13.4%

A dealer marks his goods 10% above the cost price but allows a discount of 5% for cash payment. What is the percentage of gain?

Let the initial price be x, increased price is = x + (10/100)*x = 1.10*x After the discount of 5% on the cash payment price is = 1.10*x - (5/100)*(1.10*x) = 1.045*x Therefore, the gain is = 1.045*x – x = 0.045 The percentage gain is 4.5%

If the sum of the two numbers is 30 and their HCF and LCM are 4 and 20 respectively then the sum of the reciprocal of the two numbers is?

Let the two numbers be x and y Given, x + y = 30 And LCM(x,y) = 20 and HCF(x,y) = 4 We know that LCM*HCF = x*y so, x*y = 20*4 = 80 Now, sum of reciprocals = (1/x)+(1/y) = (x+y)/(x*y) = 30/80 = 3/8

What is the value of $\log_{3}27 - \log_{5}125 + \log_{2}16$ ?

Given, $\log_{3}27 - \log_{5}135 + \log_{2}16$ We can write 27 as $3^{3}$, 125 as $5^{3}$, 16 as $2^{4}$ $\log_{3}3^{3} - \log_{5}5^{3} + \log_{2}2^{4}$ We can write it as $3*\log_{3}3 – 3*\log_{5}5 + 4*\log_{2}2$ We know that $ log_{x}x$ = 1 So, by solving accordingly we get = 3-3+4 = 4

If 564*32 is divisible by 3, then what could be the minimum value of *?

Divisibility rule of 3: If the sum of digits of a number is divisible by 3 then the number is divisible by 3 Given number = 564*32 Sum of digits = 5+6+4+*+3+2 = 20+* Nearest number for 20 which is divisible by 3 is 21 So, minimum value of * = 21-20 = 1

Ravi and Edward are working on an assignment. Ravi takes 6 h to type 30 pages on a computer, while Edward takes 5 h to type 35 pages on a computer. How much time will they take, working together on two different computers to type an assignment of 126 pages?

Typing Speed of Ravi = 30/6 = 5 pages/hr Typing Speed of Edward = 35/5 = 7 pages/hr When they both work together the speed will be = 5 + 7 = 12 pages/hr To complete the assignment of 126 pages time taken will be = 126/12 = 10.5 hrs i.e. 10 Hours 30 Minutes

What is the rate of simple interest at which a certain amount will increase to 5 times its original value in a span of 24 years?

Given, the amount will increase to 5 times the original investment Let the invested amount is P So, Simple Interest is = 5*P – P = 4*P Therefore, 4*P = P*24*R/100 R = 100/6 = 16.67%

In a farm, 50 cows give 300 liters of milk in 2 days. In how many days will 30 cows give 270 liters of milk?

Given that, 50 cows give 300 liters of milk in 2 days Let’s calculate how many liters a cow will give in a day on an average = 300/(50*2) = 3 liters/day Now according to this, 30 cows will give 30*3 = 90 liters/day So, to get 270 liters of milk we need 270/90 = 3 days

If a content developer can typically create 5 questions per hour on average, how many developers should the resource manager recruit to finish a project consisting of 1600 questions within a timeframe of 10 hours?

Given, The rate at which the content developer can create questions is = 5 questions/hr To finish a project requiring creation of 1600 questions in the timeframe of 10hrs, the rate of question creation should be = 1600/10 = 160 questions/hr So, the manager should recruit 160/5 = 32 content developers to complete the project

After purchasing a watch for Rs. 8,000, Rahul sells it to Manoj with a 20% profit. Later, Manoj sells it back to Rahul at a 10% loss. Determine the overall outcome of these transactions.

Given, Rahul sells the watch to Manoj at 20% profit = 8000 + (20/100)*8000 = 8000+1600 = 9600, Then Manoj sells it to Rahul at a loss of 10% = 9600 – (10/100)*9600 = 9600-960 = 8640 Therefore, Rahul gains = 9600 – 8640 = Rs. 960

The value of x in the following expression is: 631.28 - 342.32 = 804.84 - x

Given expression, 631.28 - 342.32 = 804.84 - x So, x = 804.84+342.32-631.28 x = 515.88

The total number of prime factors of $243^{5}$ is

Given number is $243^{5}$ Let us prime factorize the base number 243 = 3*3*3*3*3 = $3^{5}$ Therefore, $(3^{5})^{5}$ = $3^{25}$ So, there is only one prime factor which is 3

A total profit of Rs. 54,000 is to be distributed among Aman, Bharath, and Chandra, such that Aman and Bharath share in the ratio 3:5, while Bharath and Chandra share in the ratio 10:11. What is the share of Bharath?

Given ratios are Aman : Bharath = 3 : 5 and Bharath : Chandra = 10 : 11. To make Bharath’s share consistent, multiply the first ratio by 2. This gives, Aman : Bharath = 6:10 , Bharath : Chandra = 10:11 The combined ratio Aman : Bharath : Chandra = 6 : 10 : 11 Therefore, 6x+10x+11x = 27x = 54,000 , x = 54,000/27 = 2000 So, share of Bharath is 10x = 10*2000 = 20,000

Raghav has a bag containing 9 red and 7 blue chocolates. If he draws 2 chocolates randomly from the bag, what is the probability that he will select at least 1 red chocolate?

Find the probability of drawing a blue flower on the first draw: 7/16. Since one blue flower has been drawn, there are 6 blue flowers left out of 15. Calculate the probability of drawing a blue flower on the second draw given that the first draw was blue: 6/15. Multiply the probabilities of the individual draws to find the probability of not getting any red flowers: (7/16) × (6/15) = 7/40. Use the complement rule: Subtract the probability of not getting any red flowers from 1 to find the probability of getting at least one red flower: 1 - 7/40 = 33/40.

Find the value of: 0.00003 + 0.000003 + 0.00030 + 0.00300

0.003 0.0003 0.00003 +0.000003 ----------------- 0.003333

The ratio of 2 numbers is 4:7 and their H.C.F. is 3. Their L.C.M. is

Given ratio is 4:7 Let us assume the numbers are 4x and 7x So, the HCF of these numbers = x But we know that the HCF of numbers is 3 so, x=3 Therefore, the numbers are 4*3=12 and 7*3=21 LCM(12,21) = 3*4*7 = 84

A watch store advertises a 'Buy 1, Get 1 Free' deal. The selling price of a watch is Rs. 6000, and the store claims to make a profit of 25%. What is the approximate cost price of one watch?

Given, the selling price of watch is Rs.6000 As there is buy 1 get 1 offer running, let us assume the selling price of one watch is 6000/2 = Rs.3000 We know that, SP = CP + Profit 3000 = CP + (25/100)*CP 3000 = (5/4)*CP CP = 3000*(4/5), CP = 2400 Therefore, Cost price of each watch is Rs.2400

If Mohan downloads 4 more movies on his Laptop, he will have songs worth 210 GB on his mobile. On average, each movie is 2.5 GB. How many movies did he initially have on his laptop, before downloading those 4 movies?

Present movies data - 210 GB Given, each movie average size = 2.5GB So, size of 4 Movies would be - 4*2.5=10GB Therefore, initial movie data = 210-10 = 200GB So, total movies before downloading = 200/2.5 = 80 movies

A train leaves Hyderabad at 7:00 a.m. and reaches Shirdi at 11:00 a.m. Another train leaves Shirdi at 9:00 a.m. and reaches Hyderabad at 12:30 a.m. When do the two trains cross each other if the distance between Delhi and Agra is 280 km?

Given, the distance between Hyderabad and Shirdi is 280 km. Then speed of first train = 280/4= 70 kmph The speed of 2nd train = 280/3.5= 80 kmph If trains met after t hours from 7 AM, then So, the distance travelled by the first train is =70t km Distance travelled by the second train is =80(t−2) km as it starts at 9 AM So, total distance, 70t+80(t−2) = 280 15t = 44 ⇒ t=44/16 hours. =2*(12/16) t=2 hrs 45 mins. ((12/16)*60 = 45 mins) So the trains meet at 9:45 AM

If an integer k is divisible by 2, 3, and 7, then what is the next largest number that is divisible by all the 3 given numbers?

If a given number is divisible by a set of numbers, then it is either the LCM or a multiple of the LCM of the set of numbers. So, k should be LCM or multiple of LCM of 2, 3 and 7 LCM(2,3,7) = 2*3*7 = 42 Therefore the next largest number should be k+42

A car is 300 m behind the bus. The car and the bus are moving at 50 km/h and 20 km/h, respectively. The car will be ahead of the bus by 200 m in:

Car will be ahead of the bus by 200 m when it travels a distance of 300+200 = 500 m by relative speed. Relative speed of car with respect to bus = 50-20 = 30km/hr = 30000m/3600s = 25/3 m/s Time=distance/speed Time = 500/(25/3) = (500×3)/25 = 60s

The value of $\log_{7}\frac{1}{243}$

Given, $\log_{7}\frac{1}{243}$ We can write $\frac{1}{243}$ as $243^{-1}$ We also know that 243 = $7^{3}$ So, the resultant expression would be $\log_{7}7^{-3}$ = $-3*\log_{7}7$ = -3 (Since, $\log_{x}x$ = 1)

Riya can finish one-fourth of her homework in 1 h. Nandana can finish three-fifths of her homework in 1 h 30 min, and Sandhya can finish five-sixths of her homework in 3 h 30 min if all of them start their homework at noon and can go to play as soon as they all finish their homework. When can they start to play together if they take a break at 2:30 p.m. for 15 min?

Riya can finish her entire homework assignment in 4*1 = 4 hrs Nandana can complete her entire homework in (5/3)*(1.5) = 2.5 hrs = 2 hrs 30 min Sandhya can conclude her homework in (6/5)*(3.5) = 4.2 hrs = 4 hrs 12 min Therefore, they all started their work at 12 p.m. and took a 15-minute break around 2.30 p.m. Riya can begin playing at 12 p.m. + 4 hrs + 15 min break = 4.15 p.m. Nandana can begin playing at 12 p.m. + 2hrs 30min = 2:30 p.m. Sandhya can begin playing at 12 p.m. + 4hrs 12 min + 15 min break = 4:27 p.m. So, all can play together from 4.27 p.m.

If the principal increases to 125/64 times its initial value in 3 years at a certain compound interest rate, then a principal of Rs. 16000 loaned for a year at the same interest rate will amount to

We know that, Amount of Compound Interest = $ P*\left ( 1+\frac{r}{100} \right )^{nT}$ (125/64)*P = $ P*\left ( 1+\frac{r}{100} \right )^{3}$ Solving this we get, r = 25 Now at the same interest rate, the investment of 16000 in 1 year will amount to = $ 16000*\left ( 1+\frac{25}{100} \right )$ = 20,000

The product of 2 numbers is 1728. If the L.C.M. of the numbers is 144, what is their H.C.F.?

We know that, LCM * HCF = Product of two numbers So, 1728 = 144*HCF HCF = 1728/144 = 12

The average age of the national-level football team of 11 is 23 years. The average age increases by 2 years when the coach’s age is also included. What is the age of the coach?

Given, The average age of the football team of 11 is 23 Sum of ages = avg*no.of.players = 23*11 = 253 Let the coach age is x, after adding coach age the average would be 23+2 = 25 (253+x)/12 = 25, x = 300-253 = 47

Select the term that is unrelated to the other:

Geography : Studies Earth's features and populations. History : Examines past events and civilizations. Mathematics : Focuses on numbers and patterns. Civics : Deals with citizenship and government. But,Mathematics is unrelated because it doesn't study Earth, history, or social structures; it's focused on abstract concepts like numbers and patterns

What is the next number in the sequence:96, 48, 24, 12, ...

Starting with 96: 96÷2=48 48÷2=24 24÷2=12 So, the next number in the sequence is obtained by dividing 12 by 2: 12÷2=6 Therefore, the next number in the sequence is 6.

Select the term that does not belong to the same category as the others:

The terms "Year," "Date," and "Month" refer to specific units of time, while "Calendar" encompasses the entire system for organizing time. Therefore, "Calendar" is distinct from the others in its broader scope

Haiku is to poem as fable is to?

A Haiku is a form of poem, and a fable is a form of story. Haikus are short poems that traditionally consist of three lines with a 5-7-5 syllable count, often capturing a moment in nature. Similarly, fables are short stories, typically featuring animals as characters and conveying a moral lesson.

If DOLPHIN is written as 'FQNRJKP', then what is written as 'RGPIWKP'?

If "DOLPHIN" is written as 'FQNRJKP', it appears that each letter is shifted by 2 positions to the right in the alphabet. Let's apply the same pattern to 'RGPIWKP': R (shifted 2 positions) -> P G (shifted 2 positions) -> E P (shifted 2 positions) -> N I (shifted 2 positions) -> G W (shifted 2 positions) -> U K (shifted 2 positions) -> I P (shifted 2 positions) -> N So, the correct corresponding word for 'RGPIWKP' is 'PENGUIN'

When the time is 6:40, then what is the angle b/w the hour hand & the minute hand of a clock?

θ=(11/2)M ~30H H= 6 , M= 40 Required angle, θ=(11/2)40 ~(30×6) = 40 degrees

What is the succeeding number in the sequence 11, 13, 17, 19, 23, 29, _?

The given series consists of consecutive prime numbers in increasing order. So the next prime number will be 31.

In the sequence U, O, I, _, A.what is the missed letter?

The series of vowels in reverse order, U, O, I, E, A. So, the missing letter is E.

If ARMY is written as ASOB in a certain code, how is the word JUDGE represented in the same code?

The first letter in the word ARMY remains same and the second, third and fourth letters are moved one, two and three steps forward respectively. Following the same coding, J will be coded as J, U as V, D as F, G as J and E as I. So, the JUDGE is written as JVFJI .

If "Wings" is related to "Fan," then find the term which relates to "Wheel".

Here Fan : Wings" indicates that a fan is operated by wings. Applying the same logic, for Wheel,the relationship would involve a part or component of a wheel. Among the options: Spokes are components of a wheel, just as wings are components of a fan. Therefore, the correct answer is Spokes

What is the next number in the sequence 21, 35, 56, 91, 154, ?

Here for the given patern: 21 × 2 – 7 = 35 35 × 2 – 14 = 56 56 × 2 – 21 = 91 91 × 2 – 28 = 154 154 × 2 – 35 = 273 So the next number in the given sequence is 273.

If today is Monday, what day of the week will it be 61 days from now?

To find out the day after 61 days, we need to consider that there are 7 days in a week and 61 is divisible by 7 (61 = 8 * 7 + 5). Adding 5 days to Monday: Monday + 5 days = Saturday So, after 61 days, it will be Saturday.

Which of the following words cannot be formed using the letters of "ASTRONOMY"?

The letter 'E' is not available in "ASTRONOMY," so "ASTER" cannot be formed using the given letters.

Complete the analogy:If ______ is to Zenith as Fear is to Composure.

The analogy compares two pairs of opposite terms: Zenith and Nadir: Zenith represents the highest point, and Nadir represents the lowest point. They are antonyms, describing opposite extremes. Fear and Composure: Fear is an emotional state of being afraid or anxious, while composure refers to a state of calmness or self-control. Again, these are antonyms. Therefore, to maintain the pattern, the word that corresponds to Zenith in the same way that Fear corresponds to Composure is Nadir

What comes next in the sequence 0, 1, 1, 2, 3, 5?

Here in the series,it follows the pattern of adding the two previous numbers to get the next number. 0 + 1 = 1 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 So, the next number will be 3 + 5 = 8.

Find the next alphabet in the sequence A, C, G, O,?

Here in the given series: A +2 = C C +4 = G G +8 = O O +16 = U

Select the pair where the words have similar meanings:

Here lets go with options: A) Love: Hate - Opposites (Love is the opposite of Hate) B) Smart: Intelligent - Synonyms (Smart and Intelligent are synonyms, meaning they have similar meanings) C) Brave: Cowardly - Opposites (Brave is the opposite of Cowardly) D) Bright: Dull - Opposites (Bright is the opposite of Dull) So, the odd one out is B) Smart: Intelligent because it's the only pair where the words are synonyms (having similar meanings), while the others are pairs of opposites.

If January 1, 2006 fell on a Sunday, what day of the week would January 1, 2010 will be?

On 31st December,2005 it was saturday Number of odd days from 2006 to 2009 = (1+1+2+1) = 5 days On 31st december 2009,it was Thursday. So on 1st Jan,2010 it was Friday

If the word ROYAL is represented by the numbers 18, 15, 25, 1, 12, what word do the numbers 12, 15, 7, 9, 3, 1, 12 represent?

To get the word, we need to convert the numbers to their corresponding letters in the alphabet. 12 corresponds to "L" 15 corresponds to "O" 7 corresponds to "G" 9 corresponds to "I" 3 corresponds to "C" 1 corresponds to "A" 12 corresponds to "L" Putting these letters together, we get the word LOGICAL

If ARMY is assigned the code as 2, 19, 14, 26.Then what is the corresponding code for POLICE?

If ARMY is coded as 2, 19, 14, 26, one possible coding scheme could be adding 1 to the position of each letter in the alphabet. Applying the same coding to POLICE: P (16) + 1 = 17 O (15) + 1 = 16 L (12) + 1 = 13 I (9) + 1 = 10 C (3) + 1 = 4 E (5) + 1 = 6 So,POLICE could be coded as 17,16,13,10,4,6.

What is the numerical difference between the second highest and second lowest numbers when the digits within each number are arranged in ascending order from left to right in the given sequence: 578, 679, 249, 568, 489?

The given sequence: 578,796,429,685,849 Arranging all the digits in increasing order from left to right within the number, we get: 578,679,249,568,489 Second highest number = 578 Second lowest number = 489 Required Difference = 578 – 489 = 89

Pen:Poet::Needle:?

A pen is a tool used by a poet. A needle is a tool used by a tailor.

In a coding scheme where "SAND" is coded as "UCPF".What would be the code for "STONE" when applying the same logical rule?

Here there is a consistent pattern of shifting each letter 2 positions forward in the alphabet. Now, let's apply the same pattern to the word "STONE": S + 2 = U T + 2 = V O + 2 = Q N + 2 = P E + 2 = G After following the same coding pattern, "STONE" would be coded as "UVQPG".

Given the series 5, 9, 18, 34, 59, 95,144,what pattern defines the sequence?

The series 5, 9, 18, 34, 59, 95,144 follows the pattern of adding consecutive square numbers: 5 + (2^2) = 9 9 + (3^2) = 18 18 + (4^2) = 34 34 + (5^2) = 59 59 + (6^2) = 95 95 + 49 (7^2) = 144

If "23" is related to "12167" in a certain way, which of the following pairs has a similar relationship?

If "23" is related to "12167" in a certain way, it indicates a cubing relationship, as 23^3 equals 12167 From the options: 6 : 36,Here 36 is the square number of 6 10 : 100,Here 36 is the square number of 6 15:225,Here 225 is the square number of 225 5:125,Here 125 is the cube number of 5 So the correct option is 5:125

which day of the week did January 1 - 1997 fall ,If January 1 - 1996 was a Monday?

The year 1996 is divisible by 4, so it is a leap year with 2 odd days. As per the question, the first day of the year 1996 was Monday, so the first day of the year 1997 must be two days after Monday. So, it was Wednesday.

Complete the anology: Computer: ? :: Human: Heart

As the heart is related to humans, a CPU is related to a computer. CPU is known as the heart of a computer.

Arrange the following words in decreasing order based on size, forming a meaningful sequence: 1. Room 2. Building 3. Society 4. Flat 5. City

In terms of decreasing order based on size: The proper order is city, society, building, flat, and room

Find the missing number in the series:4096,3375,2744,___,1728,1331

The pattern here involves perfect cubes. Each term is the cube of a specific number. 4096 is (16^3) 3375 is (15^3) 2744 is (14^3) 1728 is (12^3) 1331 is (11^3) The number 13 is missed in between So the missed number in the series 2197, which is (13^3)

Arrange the given words in a meaningful sequence: 1.Exam 2.Probationary Period 3.Formal Appointment 4.Screening Interview 5.Application Submission 6.Job Advertisement 7.Interview selection

It shows the sequence of hiring a candidate in companies which is Job posting,Application Submission,Exam,Screening interview,Interview selection, Formal Appointment,Probationary Period

Identify the incorrect number in the series: 2, 6, 15, 31, 56, 93.

the series: 2, 6, 15, 31, 56, 93. In this series, the difference between the two consecutive numbers is 4, 9, 16, 25, and 37 6-2 = 4 = 2^2 15-6 = 9 = 3^2 31-15 = 16 = 4^2 56-31 = 25 = 5^2 93-56 = 37 which is not a square number. So, after 25 there should be 36, not 37 And after 56 there should be 92 (56+36) not 93.

What is the next term in the series:PAF, PEF, PIF, POF,___.

The middle letters which are vowels have an increasing trend of A, E, I, O, U and remaining letters have been retained as it is. So answer is PUF

In the course of 24 hours, how many instances can be observed on a 12-hour analogue clock where the clock hands form right angles?

In a 12-hour time frame, the clock hands align at right angles 22 times. Extending this to a 24-hour period, they form right angles exactly 44 times.

If "Book" is to "Author" as "Movie" is to _____, what word completes the analogy?

An author writes a book, and a director oversees the creation of a movie.

Find the odd one out:

Except Cashew, all others are fruits

Organize the given words alphabetically and select the appropriate option: a. Rank b. Rain c. Rare d. Rackle e. Ravish

Arranging the words in alphabetical order: d.Rackle b.Rain a.Rank c.Rare e.Ravish So the correct option is : d,b,a,c,e

Find the odd one out:

"Fox" is different from the rest is that it is not a domesticated animal.Rest all Cat,Dog,Goat are domestic animals.

In a clock it is showing 4 o'clock, what is the angle between the hour and minute hands?

At four o’clock, the minute hand is on the 12 and the hour hand is on the 4. The angle formed between them is 4/12 of the total number of degrees in a circle, which is 360 degrees Angle = (4/12)*360 degrees = 120 degrees

Complete the anology:December: ? :: May: Summer

May is the month of the summer season. December is the month of the winter season.

What is the missing number in the series 4,11,19,41, __,161

Here for the given series,the pattern involves multiplication by 2 and alternating addition or subtraction of 3. 4 × 2 + 3 = 11 11 × 2 – 3 = 19 19 × 2 + 3 = 41 41 × 2 – 3 = 79 79 × 2 + 3 = 161 So the missing number in the sequence is 79.