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Number Properties

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Number Properties

by komal » Wed Jun 16, 2010 1:13 am
If a and b are odd integers such that a - b > 7, what is the smallest possible positive difference between a and an even number less than b ?

a. 7
b. 8
c. 9
d. 10
e. 11

My Problem : I could not fully understand the question itself !!. Any help will be greatly appreciated.

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by kvcpk » Wed Jun 16, 2010 1:26 am
let a and b be 2m+1,2n+1

(2m+1)-(2n+1)>7
2m-2n>7

even number less than b is 2n

diff = 2m+1 -(2n)
diff-1 = 2m-2n

diff-1 >7
diff>8

therefore diff is 9

hope this helps!!
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by amising6 » Wed Jun 16, 2010 2:26 am
good explaination given by kvcpk
but let me try by plugging some number
a-b>7
so the minimum value which a can take will be 9 and in that case b will take 1
now an even number less than b will be 0
so minimum possible positive difference will be
9-0=9
answer will be 9
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