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## #226 2009-01-22 02:48:57

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#131.Without actual division, find the remainder when

is divided by 2x+3.

#132. A business organization declares an annual dividend of 6%. Rose owns 325 shares (par value #75). How much divided would she receive?

#133. The sum of squares of three numbers which are in the ratio 2:3:4 is 725. What are the three numbers?

#134. Ten years ago, a father was seven times as old as his son. Two years hence, twice his age would be equal to five times his son's age. What are the present ages of the father and the son?

#135.Two places A and B are 200 kilometers apart. A person travels from A to B at the speed of 60 kilometers/hour by a car. At the same time, another person starts from B to A on a motorbike riding at the speed of 40 kilometers per hour. After how much time from the start would the two persons meet?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #227 2009-01-22 05:46:28

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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## #228 2009-01-22 05:54:04

careless25
Real Member
Registered: 2008-07-24
Posts: 559

### Re: *** Problems

for 131 do you mean synthetic division is allowed?:)

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## #229 2009-01-22 08:02:25

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: *** Problems

I think Ganesh means

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## #230 2009-01-22 19:09:56

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

Answers to #131, #133, #134, and #135:
Very well done!

careless25,
Synthetic Division wasn't allowed. The solution is  given by Jane Fairfax in post #230, using the Remainder theorem.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #231 2009-01-22 19:52:12

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#136. The diameter of a circle is

units. What is the length of a saide of a square inscribed in it?

#137. All the surfaces of a cube are colored. If a number of smaller cubes are taken out from it, each smaller cube having a side one-fourth of the original cube's side, what is the number of cubes which would have only one side colored?

#138.
(a) What is the difference in area of a circle of diameter 2x units and square of side 2 units?

(b) What is the perimeter of a rectangle of area 60 square meters and whose diagonal is 13 meters long?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #232 2009-01-28 03:19:16

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#139. Two trains start from stations M and N and travel towards each other at speeds of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 kilometers more than the first. What is the distance between stations M and N?

#140. A man can row 5 km/hour in still water. If the river flows at 1 km/hour, it takes him 75 minutes to row to a place and breturn. How far is the place?

#141. A container contains 40 kilograms of milk. From this container, 4 kilograms of milk was taken out and replaced by water. This process was repeated two more times. What is the content of milk in the container after these processes?

#142. An investor invested

of his capital at 7%,
at 8% and the remaining at 10%. What is his capital if his annual income is \$561?

#143. A cone of height 7 cm and base radius 3 cm is carved from a rectangular block of wood 10 cm x 5 cm x 2 cm. What is the percentage of wood wasted?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #233 2009-01-28 11:17:50

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: *** Problems

Last edited by JaneFairfax (2009-01-29 06:45:43)

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## #234 2009-01-29 04:46:59

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

Both the answers are correct, JaneFairfax!

#144. In a race of 200 meters, A can beat B by 31 meters and C by 18 meters. By what distance can C beat B in a race of 350 meters, assuming the three runners run at uniform speed the entire distance?

#145. If 18 persons can build a wall 140 meters long in 42 days, how many days would it take 30 persons to build a similar wall 100 meters long?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #235 2009-01-30 03:55:03

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#146. The property of a person was divided among his wife, son and daughter according to his will, in the following manner. The wife's share was 6/7 of the son's share and the daughter's share was 4/7 of that of the son. If the son and the daughter together got \$102300, how much did his wife get?

#147. A earns 10% more than B, and 15% less than C. If B earns \$85 a day, what is C's earning?

#148. What is the 16th term of the series 1, 3, 6, 10, 15, ...?

#149. A and B can do a work in 6 days, and the same work can be done by B and C in 10 days. A and C can finish the samw work in 12 days. In how many days can the three working together complete the work?

#150. If 81 be divided in the proportion

,
what is the value of the largest part?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #236 2009-01-30 09:01:42

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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## #237 2009-01-30 19:39:49

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

Answers to #144, #145, #148, and #149:-
All correct, JaneFairfax!

#151. In a square ABCD of side 28 centimeters, four quadrants are drawn inside the circle from the vertices A, B, C, and D of radius 14 centimeters. A square EFGH is constructed joining the midpoints of sides AB, BC, CD, and DA. The area of the quadrants overlapping with the smaller square are painted red. What is the total area of the painted region?

#152. A rectangular lawn measures 100 meters x 80 meters. It has two roads each 10 meters wide running in the middle of it, one parallel to the length of the rectangular region and the other parallel to its width. What is the cost of levelling the roads if the unit cost of levelling is \$5 per square meter?

#153. In a rectangle of length 35 centimeters and breadth 14 centimeters, 10 circles of equal area are drawn, 5 along the length and two along the breadth. What is approximate percentage of the area of the rectangle which is not covered by the circles, as compared to the total area of the rectangle?

#154. In a rectangle of length 28 centimeters and breadth 14 centimeters, Two semicircles touching each other at a point are drawn on the two sides along the lenght and one each along the breadth. What is the total area of the shape so formed?

#155. In a semicircle of radius a, a triangle ABC is constructed with the diameter AC as the base and OB as the altitude where O is the center of the circle. What is the area of the semicircle outside the triangle ABC?

#156. 8 men and 12 children can do a work in 9 days. A child takes double the time taken by the adult to do the work. In how many days can 12 men complete double the work?

#157. A is three times as efficient as B and is, therefore, able to complete a work in 60 days. What is the number of dys A and B together would take to complete the work?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #238 2009-01-31 03:05:01

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#158. From each of the two given numbers, half of the smaller number is subtracted. Of the resulting numbers, the greater number is three times the lesser number. What is the ratio of the two original numbers?

#159. Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #239 2009-02-04 03:42:54

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#160. What is the value of

?

#161. Let N = 1421 x 1423 x 1425. What is the remainder when N is divided by 12?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #240 2009-02-04 04:23:25

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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## #241 2009-02-04 16:59:02

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

Answers to #159, #160, and #161:-
All the answers are correct, JaneFairfax!!!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #242 2009-02-07 01:35:35

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#162. Solve:-

.

#163. Solve

.

#164. Three numbers are in a Geometric Progression and the middle number is 16. If the sum of the first and third numbers is 130, find the numbers.

#165. If m and n are the roots of

, find the value of
.

#166. Find the value of C if the roots of

are consecutive integers.

#167. Find the value of k if the following equation has equal roots:

.

#168. Find the quotient and the remainder when

is divided by
.

#169. What is the value of a if (x + 6) is a factor of

?

#170. A sheet is in the form of a rhombus whose side is 5 meters and one of the diagonals is 8 meters. Find the cost of painting both the sides of the sheet if the painting cost is \$2.50 per square meter.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #243 2009-02-07 17:51:55

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#171. A vessel is 50% full containing a certain solution. Another vessel with twice the capacity as the first vessel is 25% full containing the same solution. Water is added to the two vessels till the vessel are full. The contents of both the vessels are then poured into a large empty container, which is large enough to hold the contents of both the vessels. What percentage of the contents in the container is the solution?

#172. How many three digit numbers begin and end with digits that are prime numbers?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #244 2009-02-07 18:16:51

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#173. ABCD is a rectangle in which AB = 6 centimeters and AD = 10 centimeters. A rhombus EFGH is formed by joining the midpoints of AB, BC, CD, and DA. What is the area of the rhombus?

#174. If the area of an equilateral triangle is

, what is the perimeter of the triangle?

#175. What is the value of

?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #245 2009-02-11 11:52:30

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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## #246 2009-02-12 02:20:23

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

Both correct, JaneFairfax!
Very good!

#176. What is the value of

?

#177. A cradboard is in the form of a square of side 20 centimeters. Semicircular portions drawn inside the circle with two opposite sides of the square as diameter are cut off. What is the area of the remaining portion?

#178. If

and
leave the same remainder when divided by
, what is the value of m?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #247 2009-02-14 23:36:58

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#179. What is the digit in the unit's place of

?

#180. What is the digit in the unit's place of

?

#181. How many consecutive zeros would the following product end in?

.

#182. How many consecutive zeros would

end in?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #248 2009-02-14 23:42:08

ganesh
Registered: 2005-06-28
Posts: 23,084

### Re: *** Problems

#183. Find (i) the number of factors of the number 621 and (ii) the sum of all the factors.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #249 2009-02-15 00:52:33

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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## #250 2009-02-15 01:11:29

ganesh
Registered: 2005-06-28
Posts: 23,084