Oral puzzles

Jai Ganesh · 2009-03-07 00:42:17

#643. If (x-a) is a factor of

,
then what is the value of b?

#644. What is the value of n if

?

#645. If the sum of the roots o an equation is-1 and the sum of their reciprocals is

, find the quadratic equation.

#646. What is the sum of the squares of the roots of the equation
x² - 3x + 1 = 0?

#647. If t² - 4t + 1 = 0, ten what is the value of

?

Jai Ganesh · 2009-03-07 01:51:57

#648. What is the Least Common Multiple of x²-1, x²+x, and (x+1)²?

#649. What are the factors of (x³-8y³)?

#650. When (x³ - 2x² + px - q) is divided by (x² - 2x - 3), the remainder obtained is (x-6). What are the values of p and q?

Jai Ganesh · 2009-03-07 03:02:01

#651. What is the solution for the following simultaneous equations?

.

#652. What is the Greatest Common Divisor of (x²-4), (x²-5x+6), and (x²+x-6)?

#653. What is the value of x² + y² if

?

Jai Ganesh · 2009-03-07 17:47:06

If xtan45°cos60° = sin60°cot60°, what is x equal to?

Jai Ganesh · 2009-03-07 18:05:45

#657. What is the value of

?

#658. What is the value of sin150°cos120° + cos330°sin660°?

#659. What is the value of tan(-585°)?

#660. If

, what is the value of tanA - cotA?

Jai Ganesh · 2009-03-08 02:52:44

#661. If the roots of the equation x²+px+q = 0 are 1, and 2, what are the roots of the equation qx²-px+1 = 0?

#662. Factorize:-

.

#663. What is the Greatest Common Divisor of

and ?

#664. If

,
what is the value of ?

#665. What is the value of

?

lady einstein · 2009-03-08 09:42:27

#642
7*25 = 175
3*20 = 60
3*28 = 84
60+84 = 144
175-144 = 31
is the remaining number 31?

Jai Ganesh · 2009-03-08 17:00:39

Answer to #642:-
Correct, lady einstein!

#666. The sum of squares of two consecutive positive integers is 61. What are the integers?

#667. A number consists of three digits. The numberobtained by writing the digits in the reverse order differs from the original number by a multiple of 5. What is the actual difference?

#668. What is the value of

?

#669. Which is the least perfect square that is divisible by 8, 10, 15, 26, and 36?

#670. What is the value of

?

Jai Ganesh · 2009-03-09 02:47:16

#671. The area of a rectangle is 12 sq.cm and its length is 3 times that of its breadth. What is the perimeter of the rectangle?

#672. The perimter of an isosceles triangle is 100 cms. If the base is 36 cms, find the length of the equal sides.

#673. Four equal sized circular plates are cut off from a square paper sheet of area 784 cm[sup]2[/sup]. What is the circumference of each circular plate?

#674. The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle.

#675. The base of a parallelogram is twice its height. if the area of the parallelogram is 72 cm[sup]2[/sup], find its height.

Jai Ganesh · 2009-03-11 01:43:04

#676. What would be the ratio of the area of a rectangle to the area of a triangle with one of the sides of the rectangle as the base and a vertext on the opposite sideof the rectangle?

#677. A square and an equilateral triangle have equal perimeters. if the diagonal of the square is 12√2 centimeters, what is the area of the triangle?

#678. The ratio of bases of two triangles is x:y and that of teir areas is a:b.What is the ratio of their corresponding altitudes?

#679. if the side of an equilateral triangle is decreased by 20%, by what percentage is the area decreased?

#680. If the height of a triangle is decreased by 40% and its base is increased by 40%, what would be the effect on its area?

#681. If every side of a traingle is doubled, the area of the new triangle is K times the area of the old one. What is the value of K?

#682. a traingle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 meters, then what is the altitude of the triangle?

#683. The area of a rhombus is 150 cm[sup]2[/sup]. The length of one of its diagonals is 10 centimeters. What is the length of the other diagonal?

#684. each side of a rhombus is 26 centimeters and one of its diagonals is 48 centimeters. What is the area of the rhombus?

#685. The area of a field is in the shape of a trapezium and measures 1440 m[sup]2[/sup]. The perpendicular distance between its parallel sides is 24 meters. If the ratio of the lengths of the parallel sides is 5:3, what is te length of te longer parallel side?

Jai Ganesh · 2009-03-11 02:56:49

#686. In measuring the sides of a rectangle, one side is taken 55 in excess and the other 4% in deficit. Find the rror percentage in the area calculated from these measurements.

#687. The perimeters of two squares are 40 centimeters and 32 centimeters. Find the perimeter of a third square whose area is equal to the difference of th areas of the two squares.

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

#689. The difference between two parallel sides of a trapezium is 4 centimeters. The perpendicular distance between them is 19 centimeters. If the area of the trapezium is 475 cm[sup]2[/sup], find the lengths of the parallel sides.

#690. Fin the length of the rope by which a cow must be tethered such that it may be able to graze an area of 9856 m[sup]2[/sup].

Jai Ganesh · 2009-03-11 17:49:32

#691. A tyre has two punctures. The first puncture alone would have deflated the tyre in 9 minutes and the eond alone would have done it in 6 minutes. If air leaks out at a constant rate, how long would it take both the punctures together to deflate the tyre?

#692. A, B, and C can complete a work in 24 days, 6 days, and 12 days respectively. Working together, in how many days would they complete the same work?

#693. A man can do a job in 15 days. His father takes 20 days to complete the work and his son would take 25 days to finish it. How long would it take to complete the work if the three work together?

#694. A person can complete a work in 5 days, but with the help of his son, he can complete it in 3 days. In what time can the son alone complete the work?

#695. A and B can do a work in 12 days, B and C in 15 days, and A and C in 20 days. If A, B, and C work together, in how many days would they finish the work?

#696. P and Q can do a work in 8 days, Q and R can do the same work in 12 days. P, Q, and R together can finish the work in 6 days. In how many days would P and R complete the work?

#697. U and V can do a work in 72 days, V and W can do it in 120 days, and U and W can do it in 90 days. In what time can U alone do it?

#698. The salaries of Desmond, Michael and Robert are in the ratio 2:3:5. If they are sanctioned annual increments of 15%, 10%, and 20% of their salaries, what would the new ratio of their salaries be?

#699. If $1210 were divided among X, Y, and Z in the ratio X:Y = 5:4 and Y:Z = 9:10, then what would Z get?

#700. In a bag, there ate coins of a certain currency k in the denomination 25k, 10k, and 5k in the ratio 1:2:3. If the amount in the bag is 300k, how many 5k coins are there in it?

Jai Ganesh · 2009-03-12 07:27:01

#701. In a fraction, if the nuerator is increased by 40% and the denoominator is increased by 80%, then what fraction ofthe original fraction is thenew fraction?

#702. The price of wheat falls by 16%. By what percentage can a person increase the consumption of wheat in order to maintain the same expenditure?

#703. The price of television sets decreased by 25% as a result of which the sale increased by 20%. What is the effect on the total revenue for the seller?

#704. In the year 2000, a businessman earned a profit of 20% of his investment in the business. In the year 2001, his investment was lesser by $5000, yet he had the same income as that in 2000. (Income = Investment + profit). The profit percent earned in 2001 increased by 6%. What was his investment in the year 2000?

#705. The total population of avillage is 5000. The number of males and females increases by 10% and 15% respectively and consequently, the population of the village becomes 5600. What was the number of males in the village?

Jai Ganesh · 2009-03-12 10:12:05

#706. What is the value of

?

#707. What is the value of

?

#708. what is the value of n if

?

#709. What is the value of m if

?

#710. What is the value of x if

?

Jai Ganesh · 2009-03-12 11:40:37

#711. A hemispherical bowl is filled to the brim with a liquid. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is the same for both the bowl and the cylinder, what percentage of the cylindrical vessel is filled with the liquid?

#712. A metallic hemisphere is melted and recast in the shape of a cone with the same base radius, R, as that of the hemisphere. If H is the height of the cone, express H in terms of R.

#713. A hemisphere and a cone have equal bases. If their heights are also equal, then what would the ratio of their curved surface areas be?

#714. A cone of height 9 centimeters and diameter of its base 18 centimeters is carved out from a wooden solid sphere of radius 9 centimeters. What is the percenage of wood wasted?

#715. A solid metallic spherical ball of diameter 6 centimeters is melted and recast into a cone with diameter of base 12 centimeters. What is the height of the cone?

Jai Ganesh · 2009-03-14 22:33:59

#716. Find the value of x if the distance between the points (x, -1) and (3, 2) is 5 units.

#717. Find a point of the x-axis which is equidistant from the points
A(2, -5) and B(-2, 9).

#718. Find a point on the y-axis which is equidistant from the points
A(6, 5) and B(-4, 3).

#719. Do the points A(3,2), B(-2,-3), and C(2,3) for a triangle? if so, what kind of triangle?

#720. Find the values of x, y if the distances of the point (x,y) from
(-3,0) as well as from (3,0) are 4.

Devantè · 2009-03-15 04:06:32

Again... shame no one answers these. Maths Is Fun homepage could have a link to these or something.

Last edited by Devantè (2009-03-15 04:30:48)

Jai Ganesh · 2009-03-15 06:53:51

Answers to #641, #644, #659, #665, #709, #716, #719, and #720:-
Devantè , Please check your answers to #644, #709, #716, and #720. Regarding #719, the answer is partly right.
The others are correct!
Well done!!!

Jai Ganesh · 2009-03-17 07:41:56

#721. If m and n are the roots of the equation 3x² - 6x + 1 = 0, find the value of m²n + mn².

#722. For what value of m is 2x³ - x² - 3mx - 24 divisible by (x-2)?

#723. Find the remainder when the Polynomial P(x) = x[sup]4[/sup] - 3x[sup]2[/sup] + 2x + 1 is divided by (x-1).

#724. Find the difference between Compound Interest and Simple Interest on $15,000 for 2 years at 8% per annum.

#725. Find the sum 5 + 10 + 15 + 20 + ...... + 250.

Jai Ganesh · 2009-03-18 22:04:58

#726. What is the sum of 1+ 3 + 5 + 7 + 9 ..... 20 terms?

#727. If A = {3, 4, 5, 6}, B = {5, 7, 8}, then what is A - B equal to?

#728. Simplify :

.

#729. If f(x) = x + 5, g(x) = x[sup]2[/sup], then find the value of f o g.

#730. Find the coordinates of the point which divides the line segment joining the points (2,6), and (3,4) in the ratio 3:1 internally.

Jai Ganesh · 2009-03-20 03:42:08

#731. If j and k are the roots of x[sup]2[/sup] + 8x - 14 = 0. find

.

#732. Find the range of f fiven

with domain {-3, 0}.

Jai Ganesh · 2009-03-20 03:50:39

#733. Find the 11[sup]th[/sup] term of the Arithmetic Progression
3, 8, 13, .............

#734. Solve:

.

Jai Ganesh · 2009-03-20 03:54:44

#735. The radius and a height of a cone are 7 cm mand 24 cm respecrively. Find the volume of the cone.

#736. Find the point which divides the linesegment joining the points (-1,10) and (4,5) internally in the ratio 2:3.

#737. Find the equation of a staight line parallel to the y-axis and passing through the point (-7,5).

#738. Determine the length of the tangent of a circle of radius 6cm from a point at a distance 10 meters from the center of the circle.

JohnnyReinB · 2009-03-21 03:08:54

Last edited by JohnnyReinB (2009-03-21 03:11:51)

Jai Ganesh · 2009-03-21 05:33:11

Answers to #725, #726, #727, #728, #729, #733, #735, #736, and #737:-
All correct, JohnnyReinB!

Math Is Fun Forum

#326 2009-03-07 00:42:17

Re: Oral puzzles

#327 2009-03-07 01:51:57

Re: Oral puzzles

#328 2009-03-07 03:02:01

Re: Oral puzzles

#329 2009-03-07 17:47:06

Re: Oral puzzles

#330 2009-03-07 18:05:45

Re: Oral puzzles

#331 2009-03-08 02:52:44

Re: Oral puzzles

#332 2009-03-08 09:42:27

Re: Oral puzzles

#333 2009-03-08 17:00:39

Re: Oral puzzles

#334 2009-03-09 02:47:16

Re: Oral puzzles

#335 2009-03-11 01:43:04

Re: Oral puzzles

#336 2009-03-11 02:56:49

Re: Oral puzzles

#337 2009-03-11 17:49:32

Re: Oral puzzles

#338 2009-03-12 07:27:01

Re: Oral puzzles

#339 2009-03-12 10:12:05

Re: Oral puzzles

#340 2009-03-12 11:40:37

Re: Oral puzzles

#341 2009-03-14 22:33:59

Re: Oral puzzles

#342 2009-03-15 04:06:32

Re: Oral puzzles

#343 2009-03-15 06:53:51

Re: Oral puzzles

#344 2009-03-17 07:41:56

Re: Oral puzzles

#345 2009-03-18 22:04:58

Re: Oral puzzles

#346 2009-03-20 03:42:08

Re: Oral puzzles

#347 2009-03-20 03:50:39

Re: Oral puzzles

#348 2009-03-20 03:54:44

Re: Oral puzzles

#349 2009-03-21 03:08:54

Re: Oral puzzles

#350 2009-03-21 05:33:11

Re: Oral puzzles

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