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Distance

by shashank.ism » Mon Feb 15, 2010 10:57 pm
A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining
distance, where q is a natural number. During the third day, it travelled 1/p of the distance remaining
after the second day, and during the fourth day, 1/q of the distance remaining after third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.
The value of p + q is:
A) 4
B) 5
C) 6
D) 7
E) 8
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by komal » Wed Feb 17, 2010 4:43 am
shashank.ism wrote:A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining
distance, where q is a natural number. During the third day, it travelled 1/p of the distance remaining
after the second day, and during the fourth day, 1/q of the distance remaining after third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.
The value of p + q is:
A) 4
B) 5
C) 6
D) 7
E) 8
Since it is given that distance travelled is 3 / 4 and p and q are natural numbers, the distance has to be a multiple of 7.
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by ajith » Wed Feb 17, 2010 4:56 am
komal wrote:
shashank.ism wrote:A truck travelled from town A to town B over several days. During the first day, it covered 1/p of the total distance, where p is a natural number. During the second day, it travelled 1/q of the remaining
distance, where q is a natural number. During the third day, it travelled 1/p of the distance remaining
after the second day, and during the fourth day, 1/q of the distance remaining after third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.
The value of p + q is:
A) 4
B) 5
C) 6
D) 7
E) 8
Since it is given that distance travelled is 3 / 4 and p and q are natural numbers, the distance has to be a multiple of 7.
I couldnt quite follow that logic - could you explain it to me?
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by komal » Wed Feb 17, 2010 5:02 am
ajith wrote: Since it is given that distance travelled is 3 / 4 and p and q are natural numbers, the distance has to be a multiple of 7.
I couldnt quite follow that logic - could you explain it to me?[/quote]

This is an alternate solution mentioned here https://www.complore.com/testSolution.php?id=1045. I was hoping someone would come up with a different approach.
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