get another prime

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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

MBM

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

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Source: Beat The GMAT — Problem Solving | Wed Apr 22, 2009 2:30 am

Sher1: Master | Next Rank: 500 Posts; Posts: 116; Joined: Fri Feb 20, 2009 9:26 am; Location: New Jersey; Thanked: 7 times; GMAT Score:660

by Sher1 » Wed Apr 22, 2009 3:04 am

I get 2

13 and 79

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

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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iamcste: Legendary Member; Posts: 940; Joined: Tue Aug 26, 2008 3:22 amFollowed by: 1 member; Thanked: 55 times

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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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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!

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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iamcste: Legendary Member; Posts: 940; Joined: Tue Aug 26, 2008 3:22 amFollowed by: 1 member; Thanked: 55 times

by iamcste » Thu Apr 23, 2009 2:10 am

Ops, I overlooked that, Go with 2

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

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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