Resolve into Factors

Resolve into Factors

X² + 2XY + Y² – 5X – 5Y + 6

HCF and LCM

The HCF of two numbers is 1/6th of the LCM of those two numbers. if one of the numbers is 15, find the other?

LCM and HCF

The product of 2 digit numbers is 2160 and their LCM is 180. Find the 2 numbers.

HCF

Find the HCF of 2923 and 3239

time and work

A certain number of men complete a piece of work in 60 days. if there were 8 men more, the work could be finished in 10 days less. How many men were there originally?

polygon

The sum measure of angles of a regular polygon is 68 rt angles. How many sides does this polygon have?

time and work

16 men can do a piece of work in 16 days. 4 days after they started the work, eight more men joined them. How many days will they take now to complete the work?

Average

The average age of 20 students in a class is 14 years. A student of age 16 leaves them and a new student joins them. Now their average age becomes 13.8 years. What is the age of the new boy?

distance and speed

Nanu travels at 54 km/hr excluding stoppages and at 45 km/hr including stoppages. How many minutes of stoppage is there in an hour?

Answer:

Basis : 1 hour

let distance to be covered be 54 km

so, distance covered with stoppages = 45 km

shortfall in distance covered = 54 - 45 = 9 km

time taken to cover 9 km = 9/54 = 1/6 hour

so, minutes of stoppage per hour = 60 x 1/6 = 10 mins

indices

If p =100.48, q =100.70 and pz = q2, then the value of z is:

JMO - miscellaneous examples

1.    Nanu was asked to divide a number by 6 and then add 12 to the quotient. She, however added 12 to the number first and then divided it by 6, getting an answer of 112. What was the correct answer?

2.    If Nanu travels at 40 km/hr speed, she reaches school from home at 9:30 am. If she travels at 50 km/hr speed, she reaches at 9:00 am. What is the distance from home to her school?

3.    Solve the alpha-numbers, given that each alphabet represents a unique digit.

                    S   E   N  D

 +    M  O   R  E

-----------------------------------------

            M   O   N  E  Y

factors

For the number 6¹⁰ x 7¹⁷ x 55²⁷, find

1.       The number of prime factors

2.       The number of all the factors.

tutorials -sum of factors

Sum of Factors

If a number N can be expressed as product of prime factors such that

N = p^a x q^b x r^c...............................

Write the power of each of the prime factors beginning with zero and going to thee highest power of the prime number.

Record the same for each prime number.

An example will help

64= 2⁶

Then the sum of factors (2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶) = 1 + 2 + 4 + 8 + 16 + 32 + 64 =  127

Another Example:

Find the total number of factors of 222.

222 = 2 x 3 x 37

Or, 222 = 2¹ x 3¹ x 37¹

then the sum of factors are (2⁰ + 2¹) (3⁰ + 3¹) (37⁰ + 37¹) = (1+2)(1+3)(1+37) = 3 x 4 x 38 = 456

We will check the answer

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222.

Sum of factors = 456

division

When we divide 333435 by 34 the remainder is a and when we divide 333534 by 34 the remainder is b. What is the value of b – a?

logarithm

clock puzzle

In an accident the minute arm and the second arm of the wrist watch is lost. The watch now has only the hour arm in the correct position.
What is the minimum time that can be measured accurately?

number puzzle

Number Puzzle

 

number puzzle

Number Puzzle

 

variation

The intensity of light is measured in Lux. It is found that the intensity of light varies as the inverse square of the distance between light source and point of measurement.
if at 10 meters, the intensity is 100 lux, what is the intensity of the light at 15 meter distance.

circle

 wooden cubes of unit cross section (1 cm x 1 cm) are used to keep the pipe in place as shown above. What is the horizontal distance between the two cubes.