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Challenging Problem Solving

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Challenging Problem Solving

by thedude232 » Wed Dec 29, 2010 3:40 pm
If each term in the sum a-1 + a-2 + ... + a-n is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

a) 38

b) 39

c) 40

d) 41

e) 42

The correct answer is "C" but I have been banging my head trying to figure out why. Thanks!
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by anshumishra » Wed Dec 29, 2010 4:01 pm
thedude232 wrote:If each term in the sum a-1 + a-2 + ... + a-n is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

a) 38

b) 39

c) 40

d) 41

e) 42

The correct answer is "C" but I have been banging my head trying to figure out why. Thanks!
7x + 77 y = 350 ; x+y = ?
=> x+11y = 50

possible solutions (y=1, x = 39 , hence x+y = 40)
(y=2, x = 28, x+y = 30)
(y=3, x=17, x+y = 20)
(y=4, x =6, x+y = 10)

There are multiple solutions , but we found our answer as 40 in the options given.
Thanks
Anshu

(Every mistake is a lesson learned )
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by Anurag@Gurome » Wed Dec 29, 2010 10:33 pm
thedude232 wrote:If each term in the sum a-1 + a-2 + ... + a-n is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

a) 38
b) 39
c) 40
d) 41
e) 42
Units digit of each term in the sum is 7 and the sum ends in 0.
This is possible only when the number of terms is a multiple of 10. Only such option is 40.

The correct answer is C.
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