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get another prime

by sanju09 » Wed Apr 22, 2009 2:30 am
In a two-digit prime number, if 18 is added, we get another prime number with reversed digits. How many such numbers are possible?
A. 5
B. 4
C. 3
D. 2
E. 1


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by Sher1 » Wed Apr 22, 2009 3:04 am
I get 2

13 and 79
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by scoobydooby » Wed Apr 22, 2009 11:36 pm
get 2 as well. had to resort to algebra, as am very bad with numbers :(

let the prime number be 10x+y

10x+y+18=x+10y
=>y-x=2 (the units digit must be 2 greater than the tens digit)

10-19: only 13 satisfies
20-29, 30-39, 40-49, 50-59, 60-69: do not give primes satisfying this criterion

70-79: only 79 satisfies.
80-99: do not give 2 digit primes with the y=x+2

so only 2 primes, 13 and 79
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by iamcste » Thu Apr 23, 2009 1:42 am
IMO C

10x+y+18=10y+x

10x+y-10y-x+18=0

9x-9y=-18


x-y=-2
xy
13+18=31

79+18=97

so we have 2 such pairs
Last edited by iamcste on Thu Apr 23, 2009 2:11 am, edited 1 time in total.
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by sanju09 » Thu Apr 23, 2009 2:08 am
iamcste wrote:IMO C

10x+y+18=10y+x

10x+y-10y-x+18=0

9x-9y=-18


x-y=-2
xy
13+18=31

35+18=53

79+18=97

so we have 3 such pairs
but 35 is not prime :( iamcste!
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by iamcste » Thu Apr 23, 2009 2:10 am
Ops, I overlooked that, Go with 2
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by shibal » Mon Apr 27, 2009 4:54 am
i didn't use algebra but also got 2 (13 and 19)
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