Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#739. The product of two numbers is 120 and the sum of their squares is 289. What is the sum of the numbers?

#740. The product of two numbers is 45 and the sum of their squares is 106. What are the numbers?

#741. The difference between two positive integers is 3. If the sum of their squares is 369, what is the sum of the numbers?

#742. The sum of two numbers is 22 and the sum of their swuares is 404. What is the product of the numbers?

#743. The product of two numbers is 9375 and the quotient, when the larger number is divided by the smaller, is 15. What is the sum of the numbers?

#744. The product of two numbers is 192 and the sum of the two numbers is 28. What is the smaller of the two numbers?

#745. The difference between two integers is 5 and their product is 500. Find their sum.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

JohnnyReinB

Member

Registered: 2007-10-08

Posts: 453

Re: Oral puzzles

I'll be honest, Ganesh, I didn't actually answer them orally, haha.
I'm really bad with big numbers
Peace V

---

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

Answers to #739, #740, #741, #742, #743, #744, and #745:-
All correct, JohnnyReinB!

These questions are to test whether you can solve the problems mentally. Hence, no calculator or paper/pencil please.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#746. If the sum of the roots of a quadratic equation is 5 and the sum of their cubes is 35, then find the quadratic equation.

#747. What is the value of

?

#748. If A = {0,1,2} and B = {2,4,6}, then what is

?

#749. What is the value of n if

?

#750. If p and q are the roots of the equation

,
find the equation whose roots are

.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#751. What is the greatest coefficient in the expansion of

?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#752. What is the value of n if

?

#753.

#754. What is the value of m if

?

#755. What is the  value of a if

?

#756. What is the value of q if

?

#757. What is the value of b is

?

#758. What is the value of

?

#759. What is the value of

?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#760. The radius of a cone is 20 cm and the slant height is 29 cm. What is the height of the cone?

#761. The center of a circle is at (4, -1). If one end of a dimaeter is (9,7), find the other end.

#762. The sum of three numbers in Geometric progression is 26. Their product is 216. Find the numbers.

#763. The perimeter of a rectangle is 36 cm and its area is 80 sq. cm. Find its dimensions.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#764. Solve:-
2x + y = 8, 3y = 4 + 4x

#765. Find x and y if

.

#766. If 2x + 3y = 29 and y = x + 3, what is the value of x?

#767. If 3xs + 7y = 75 and 5x - 5y = 25, then what is the value of (x+y)?

#768. What are the values of a and b if

?

#769. What is the condition for the system of equation
2x + ky = 11 and
5x - 7y = 5 having no solution?

#770. Under what condition does the system of equations kx - y = 2 and 6x - 2y = 3 has no solution?

#771. Under what condition does the system of equations 4x + 7y = 10 and 10x + ky = 25 has infinite number of solutions?

#772. If 3x - 5y = 5 and

,
what is the value of (x-y)?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#773. If P(A) = 0.37, P(B) = 0.42,

,
then what is the value of

?

#774. The variance of 5 values is 16. If each value is doubled, then what is the new Standard Deviation?

#775.  24 sided regular polygon is inscribed in a circle of radius 1 meter. What is the angle subtended by each side at the center of the circle?

#776. What is the value of (tan 7°) x (tan 23°) x (tan 60°) x (tan 67°) x (tan 83°) ?

#777. What is the area of the triangle formed by the points (0,4), (4,0) and the origin?

#778.What is the x-intercept of the line 4x - 7y + 28 = 0?

#779. If the straight line 5x + 4y = k passes through (2, -10, then what is the value of k?

#780. What is the value of

?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#781. The ages of Sam and Tim are in the ratio 8:15. After 9 years, the ratio of their ages would be 11:18. What is the difference between their ages?

#782. The ratio of the ages of Adam and Wilfred is 3:4. After 5 years, the new ratio of their ages would be 4:5. What is the age of Wilfred at present?

#783. The sum of the ages of a father and his son is 100 years now. Five years ago, their ages were in the ratio 2:1. What would the ratio of the ages of the father and son be after 10 years?

#784. The ratio of the ages of a father and his son 10 years hence would be 5:3, while 10 years ago, it was 3:1. What is the ratio of the age of the son to his father
today?

#785. The ratio of the present ages of two brothers is 1:2 and 5 years back, the ratio was 1:3. What would be the ratio of their ages after 5 years?

#786. The ratio of Stefanie's age to the age of her mother is 3:11. The difference between their ages is 24 years. What would the ratio of their ages after 3 years be?

#787.fifteen years hence, a man would be four times as old as he was 15 years ago. What is his present age?

#788. The ages of two persons are in the ratio 5:7. Sixteen years ago, their ages were in the ratio 3:5. What are their present ages?

#789. three years ago, the average age of A, and B was 18 years. With C joining them, the average age now becomes 22 years. How old is C now?

#790. The age of a man ten years ago was thrice the age of his son. Ten years hence, the man's age would be twice that of his son's. What is the ratio of their present ages?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#791. If the cost of x meters of wire is d Dollars, then what is the cost of y meters of wire at the same rate?

#792. A pole 17.5 meters high casts a shadow of length 40.25 meters. What would be the height of a building which casts a shadow 28.75 meters under similar condfitions?

#793. 36 men can complete a work in 18 days. In how many days would 27 men complete the same work?

#794. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the samller wheel has made 21 revolutions, how many revolutions would tehe larger wheen have made?

#795. 4 weavers can weave 4 mats in 4 dys. At the same rate, how many mats would be woven by 8 weavers in 8 days?

#796. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles would 10 such machines produce in 4 minutes?

#797. 10 men working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the same work in 12 days?

#798. 39 persons can repair a road in 12 days, working 5 hours a day.In how many days would 30 persons, working 6 hours a day, complete the work?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#799. What is the value of

?

#800. What is the value of

?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#801. What is the value of

?

#802. f(x) = 3 + x, g(x) = x - 4, find the value of fog.

#803. Find the value of

.

#804. Form the quadraratic equations whose roots are

.

#805. The ratio of corresponding sides of two similar triangles is 2:5. What is the ratio of their areas?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#806. The curved surface area of a cylindrical pillar is 264 m[sup]2[/sup] and its volume is 924 m[sup]3[/sup]. Find the ratio of its diameter to its height.

#807. Two right circular cylinders of equal volumes have their heights in the ratio 1:2. What is the ratio of their radii?

#808. A cylindrical tank of diameter 35 centimeters is full of water. if 11 liters of water is drawn off, by what level would the water in the tank drop by?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#809. A class starts at 10.00 a.m. and lasts till 1.27 p.m. Four periods are held during this interval. After every period, a break of 5 minutes is given. What is the exact duration of each period?

#810. What is the value of

?

#811. What is the difference between

and its reciprocal?

#812. A total of 324 coins of a particular currency X of value 0.2X and 0.25X make a sum of X71. What is the number of 0.25X coins?

#813. How many digits are required for numbering the pages of a book having 300 pages?

#814. In an examination containing objective type questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attmepting all the 90 questions, a student got a total of 387 marks. How many questions did he answer wrongly?

#815. Each boy contributed as many Dollars as there were number of girls in the class and each girl contributed as many Dollars as there were number of boys in the class, n a class of 60 students. If the total contribution is $1600, how many boys are there in the class?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

#816. determine whether (x-1) is a factor of

.

#817. Find the value of a if

is divisible by (x+3).

#818. Find the value of p if (x+1) is a factor of

.

#819. Find the value of m if (x+5) is a factor of

.

#820. Find the value of q if

is divisible by (x-1).

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Last edited by bobbym (2009-08-16 13:56:10)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

Hi bobbym,

The solutions 816, 817, 818, 819, and 820 are all correct. Outstanding!

#821. Find the value of

.

#822. Find the value of

if

.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

Hi bobbym,

The solutions to 821 and 822 are perfect. Neat work!

#823. Find the Standard Deviation of the first n natural numbers.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

Hi bobbym,

The solution to 823, as per my note, is

.

#824. The mid point of AB is (-2,3). If A is (4,5), what is B?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Oral puzzles

Hi bobbym,

The solution to 824 is perfect. Neat work!

#825. Find the centroid of triangle ABC where A(3,-2), B(-7,5), and C(-2,0).

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.