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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Administrator**- Registered: 2005-06-28
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Answer to #67:

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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**ganesh****Administrator**- Registered: 2005-06-28
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#72. An aeroplane left 30 minutes later than its scheduled time, and in order to reach its destination 1,500 kilometers away in time, it has to increase its speed by 250 kilometers per hour from its usual speed. Determine its usual speed.

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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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Administrator**- Registered: 2005-06-28
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Answer to #72 :-

JaneFairfax,**Very Good! You are correct!!!**

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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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Administrator**- Registered: 2005-06-28
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Answers to #57, #58, #59, #60, and #64:-

All correct, JaneFairfax!

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

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**ganesh****Administrator**- Registered: 2005-06-28
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#73. If (a + b + c) = 0, then what is a³ + b³ + c³ equal to?

#74. What is the Least Common Multiple of

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**JaneFairfax****Member**- Registered: 2007-02-23
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*Last edited by JaneFairfax (2009-01-09 09:39:13)*

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**JaneFairfax****Member**- Registered: 2007-02-23
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#74

Do you have a special definition of least common multiple for rational numbers?

Otherwise, I find the question meaningless. The rational numbers form a field; therefore every rational number is a multiple of any nonzero rational number whatsoever. Divisibility in the rationals is totally trivial. Moreover, since there is no such thing as a least positive rational, there is no such thing as a least common multiple (as I understand it) among rational numbers.

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**ganesh****Administrator**- Registered: 2005-06-28
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Answer to #73.

Hence, the answer is 3abc.

Answer to #74:

Haven't you learned finding Least Common Multiples and Greatest Common Divisors of fractions?

LCM of

GCD of

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**JaneFairfax****Member**- Registered: 2007-02-23
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I have never heard of such a thing before.

Nevertheless, as long as you clearly define what you are doing, and your definition makes sense, then everything is fine.

Well, then. LCM of the four fractions is

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**ganesh****Administrator**- Registered: 2005-06-28
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Answer to #174:

Perfectly right, JaneFairfax!

As can be seen, 140/3 divided by 2/3 is 70;

140/3 divided by 4/9 is 105;

140/3 divided by 5/6 is 56;

and 140/3 divided by 7/12 is 80.

All the resultants are whole numbers!

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

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**JaneFairfax****Member**- Registered: 2007-02-23
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ganesh wrote:

As can be seen, 140/3 divided by 2/3 is 70;

140/3 divided by 4/9 is 105;

140/3 divided by 5/6 is 56;

and 140/3 divided by 7/12 is 80.

All the resultants are whole numbers!

Oh I see! Now I understand the logic behind the definition. Thank!

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**ganesh****Administrator**- Registered: 2005-06-28
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#75. Find the Greatest Common Divisor of

#76. Find the Greatest Common Divisor of 108, 288, and 360.

#77. Find the Least Common Multiple of

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**ganesh****Administrator**- Registered: 2005-06-28
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#78. Find the Greatest Common Divisor and the Least Common Multiple of 0.63, 1.05, and 2.10.

#79. Find the greatest number which on dividing 1657 and 2037 leaves remainders of 6 and 5 respectively.

#80. Find the largest number which divides 62, 132, and 237 to leave the same remainder in each case.

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

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Administrator**- Registered: 2005-06-28
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Answers to #75, #77, #79, and #80:

All correct, JaneFairfax!

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

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**ganesh****Administrator**- Registered: 2005-06-28
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#81. An officer's pension on retirement of services is equal to half the average monthly salary during the last 36 months of his service. His salary from Jan 01, 1954 was $380 per month with increments of $40 as from Oct 01, 1954, Oct 01, 1955 and Oct 01, 1956. If her retired on Jan 01, 1957, how much pension does he draw?

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

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**ganesh****Administrator**- Registered: 2005-06-28
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#82. Eleven persons contributed a certain sum. Nine of them gave $2 each and the other two gave $2 and $2.50 more respectively than the average of all the eleven persons. Find out the sum contributed by the two persons who contributed more.

#83. In a business, A and B received some amount in a certain ratio. B and C received the profits in the same ratio as A and B. If A received $2,500 and C received $3,600, what is the amount received by B?

#84. The ratio of prices of two cars was 16:23. Two years later, when the price of the first had risen by 10% and that of the second by $477, the ratio of their prices became 11:20. Find the original prices of the two cars.

#85. A person is standing on a railway bridge which is 50 meters long. He finds that a train crosses the bridge in 4½ seconds and crosses him in 2 seconds. Find the length of the train and its speed in kilometers per hour.

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

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**ganesh****Administrator**- Registered: 2005-06-28
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#86. Two persons ride towards each other 55 kilometers apart, one riding at 12 kilometers per hour and the other at 10 kilometers per hour. When would they first be 11 kilometers apart? If they continue riding, after how much time would they again be 11 kilometers apart?

#87. Walking at 4 kilometers per hour, a clerk reaches his office 5 minutes late. If he walks at 5 kilometers per hour, he would be 2½ minutes early. Find the distance of his office fromhis home.

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

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**ganesh****Administrator**- Registered: 2005-06-28
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#88. A alone can reap a certain field in 15 days and B alone in 12 days. If A begins alone, and after a certain interval, B joins him, the field is reaped in 7½ days. How long did A and B work together?

#89. Three persons A, B and C finished a work. A worked at it for 5 days, B for 7 days and C for 9 days. Their daily wages were in the ratio 4:3:2 and the total earnings amounted to $118.What was the daily wage of each of them?

#90. P, Q, and R can do a piece of work in 6, 8, and 10 days respectively. They begin to work together. A continues to work till it is finished, B leaves off 1 day before and C leaves off ½ day before the work is finished. In what time is the work finished?

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

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**JaneFairfax****Member**- Registered: 2007-02-23
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#90

Who are A, B and C?

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**mathsyperson****Moderator**- Registered: 2005-06-22
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I think it's safe to assume that PQR = ABC.

My guess is supported by the nice answer that follows.

Why did the vector cross the road?

It wanted to be normal.

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**JaneFairfax****Member**- Registered: 2007-02-23
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