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Tough and Tricky questions: Exponents. If a and b are positive integers and x = 24^a and y = 9^b, which of the following is a possible units digit of xy?
Alex has $246,713 dollars in his savings account. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among his 6 children?
An inspector rejects 0.008% of the meters as defective. How many will be examine to project ?
In a school of 850 boys, 44% of Muslims, 32% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
An office supply store stocks two sizes of notebooks, each in six colors: orange, blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors a...
On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis? I. (1, 1) II. (4, 4) III. (6, 6)
Bradley owns b video game cartridges. If Bradley’s total is one-fifth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3 ♠0.098 - ♠1.125 =
A customer pays 20 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffee maker?
John makes $60 a week from his job. He earns a raise and now makes $90 a week. What is the % increase?
How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?
The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 30 and n is not prime, what is the greatest possible value of f(n)?
On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders Q will be:[/b]
One-fourth of a tank holds 135 litres of water. What part of the tank is full if it contains 180 litres of water?
?⁄50 = 60.5⁄?
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
The average of 35 students in a class is 18 years. The average age of 25 students is 16. What is the average age of remaining 10 students?
What is the median from the below series 93, 88, 95, 88, 97, 87, and 98
There are 380 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
What is the greatest 6-digit number when divided by 7 ,8 , 9, and 10 leaves a remainder of 5, 6, 7, and 8 respectively?
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed R of the train.
Find the average of all the numbers between 6 and 34 which are divisible by 5
In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at T mile/month . One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship fro...
After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 200 billion gallons, the reservoir was approximately what percentage full before the storm?
A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
By selling 15 pens for a rupee a woman loses 25%. How many for a rupee should he sell in order to gain 25%?
James started from his house headed North. After walking a distance of 50 m. He turned to the left and walked 60 m. He then made a right turn and walked 30 m. After this he is to turn left at 90o degrees and to cover another 40 m. How many meters did James walk in total and what direction was he headed in when he left ...
By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article?
What is the area of square field whose side of length 13 m?
If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
A circular rim A having a diameter of 24 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 32 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.
An employer has 7 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is less than 5?
If each edge of cube increased by 25%, the percentage increase in
A circular rim 20 inches in diameter rotates the same number of inches per second as a circular rim 15 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
36 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 0.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
Express a speed of 36 kmph in meters per second?
The sum of two number is 120 and their difference is 30. Find the numbers.
Eight years ago Anita was P times as old as Ben was. If Anita is now 27 years old, how old is Ben now in terms of P ?
There are three prizes to be distributed among seven students. If no students gets more than one prize, then this can be done in?
A CHOCOLATE manufacturer produces 400 units of a certain model each month at a cost to the manufacturer of £40 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these...
What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
One hour after Matthew started waking from t to y, a distance of 45km, Johnny started walking along the same road from y to t. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny walked when they met?
In an election, 68% of the voters exercised their franchise. Of these, 48% were women. The number of males exercising their franchise was 53,040. How many eligible voters were there in all?
The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day Rs. 1,325 were collected from the passengers travelling between these stations, then what was the amoun...
If rupee one produces rupees nine over a period of 30 years, find the rate of simple interest?
In a college the ratio of the numbers of boys to the girls is 8:5. If there are 135 girls, the total number of students in the college is?
The average height of 15 girls out of a class of 60 is 138 cm. and that of the remaining girls is 142 cm. The average height of the whole class is :
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is
The distance from City A to City B is 100 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?
The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
If a class of 10 students has seven men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is?
Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 135 mangoes.
A train running at the speed of 45 km/hr crosses a pole in 16 seconds. Find the length of the train.
If (a-5)(b+2) = 0 which of the following must be true?
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?
If r = 199,999 and s = 991,999, which of the following is the units digit of r^3 + s^3?
Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 10 minutes ...
10^185 - 10^30 = Which of the following best approximates the value of the expression above?
A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.
A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 25%?
A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
What least fraction should be added to 1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ....... + 1/(21 × 22) so that the result is unity?
In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Q that the worker is under 25 years old?
How many 4-digit numbers can be formed by using the digits 0-9, so that the numbers contains exactly 3 distinct digits?
If the sides of a triangle are 31 cm, 29 cm and 15 cm, what is its area?
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
Employees of a certain company are each to receive a unique 9-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
The food in a camp lasts for 40 men for 20 days. If 10 more men join, how many days will the food last?
If A's height is 25% less than that of B, how much percent B's height is more than that of A?
The radius of a cylinder is 10 m, height 14 m. The volume of the cylinder is:
A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money T did Bob receive?
A certain car dealership offers its newest model in ten exterior and ten interior colors. If the eight interior colors are identical to the eight exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different c...
The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3?
If a is a positive integer, and if the units digit of a^2 is 4 and the units digit of (a+1)^2 is 1, what is the units digit of (a+2)^2?
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?
The sum of the squares of three numbers is 241, while the sum of their products taken two at a time is 100. Their sum is:
The average of ten numbers is 8. If each number is multiplied by 11, then what is the average of the new set of numbers?
What percentage of numbers from 1 to 100 have cube that end in the digit 5?
Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and U. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of U if J is negative?
If X, Y and Z are digits and 7XYZ is a 4-digit number that is divisible by 2, which of the following is a possible product of X, Y and Z?
A sales executive gets 20% bonus of the total sales value and 10% commission besides the bonus on the net profit after charging such commission. If the total sales value be Rs. 10 lakh per annum and the total profit of the company be Rs. 1.32 lakh, then his total earning per annum will be, given that he is not entitled...
If a × b = 2a - 3b + ab, then 3 × 2 + 2 × 3 is equal to :
A sum of money deposited at compound interest (compounded yearly) amounts to $600 in 2 years and to $624 in 3 years. What is the interest rate?
In expressing a length 810472 km as nearly as possible with three significant digits , find the percentage error
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 60 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?