Digits Interchanged

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 am; Location: India; Thanked: 64 times; Followed by:6 members; GMAT Score:760

Digits Interchanged

by harsh.champ » Wed Feb 17, 2010 4:25 am

A number has 2 digits whose sum is 9.If 27 is added to the number,its digits get interchanged.How many prime divisors of that number are there ?

(A)1
(B)2
(C)3
(D)4
(E)5

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Source: Beat The GMAT — Problem Solving | Wed Feb 17, 2010 4:25 am

money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pm; Location: New Jersey; Thanked: 109 times; Followed by:79 members; GMAT Score:640

by money9111 » Wed Feb 17, 2010 8:49 am

i'm going to say A.

I made a table for the digits...

10's digit = X
1's digit = y

XY

X+Y=9

1 + 8 = 9 number would be 18 -> + 27 = 45 does not switch original numbers
2 + 7 = 9 number would be 27 -> + 27 = 54 does not switch original numbers
3 + 6 = 9 number would be 36 -> + 27 = 63 DING DING switches original numbers
4 + 5 = 9 number would be 45

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Wed Feb 17, 2010 8:55 am

harsh.champ wrote:A number has 2 digits whose sum is 9.If 27 is added to the number,its digits get interchanged.How many prime divisors of that number are there ?

(A)1
(B)2
(C)3
(D)4
(E)5

let 'ab' be the number

a+b=9
10a+b +27 = 10b+a
b-a =3

b=6
a= 3
36 = 2^2*3^2 there are 2 prime divisors

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pm; Location: Gandhinagar; Thanked: 41 times; Followed by:2 members

by shashank.ism » Wed Feb 17, 2010 8:55 am

harsh.champ wrote:A number has 2 digits whose sum is 9.If 27 is added to the number,its digits get interchanged.How many prime divisors of that number are there ?

(A)1
(B)2
(C)3
(D)4
(E)5

Let the number be XY
X+Y=9---(i)
10X+Y+27=10Y+X --> 9X+27 = 9Y --> Y-X=3 ---(ii)
Adding we get 2Y= 12 Y=6
X=3
so the no,. is 36 = 2x2x3x3 so no. of prime divisors = 2Ans B

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pm; Location: New Jersey; Thanked: 109 times; Followed by:79 members; GMAT Score:640

by money9111 » Wed Feb 17, 2010 9:01 am

i like your answers better

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pm; Location: Gandhinagar; Thanked: 41 times; Followed by:2 members

by shashank.ism » Wed Feb 17, 2010 9:09 am

money9111 wrote:i like your answers better

Thanks money1119. i think there are times when you solve problem in general way rather than plugin and eliminationand you u reach to the answer much faster ....

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pm; Location: New Jersey; Thanked: 109 times; Followed by:79 members; GMAT Score:640

by money9111 » Wed Feb 17, 2010 9:11 am

yeah the way you guys did it is much more concise... i've done it like that before, but in this case it slipped my mind

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pm; Location: Gandhinagar; Thanked: 41 times; Followed by:2 members

by shashank.ism » Wed Feb 17, 2010 9:14 am

money9111 wrote:yeah the way you guys did it is much more concise... i've done it like that before, but in this case it slipped my mind

I think similar questions have been posted in this forum now and then and I have posted the solution in the general way.. i hope you have gone thru those answers.
Well don't use plug in method for this question next time . You will certainly loose some of yor precious seconds...

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pm; Location: New Jersey; Thanked: 109 times; Followed by:79 members; GMAT Score:640

by money9111 » Wed Feb 17, 2010 9:16 am

i think the real issue here isn't the approach I took, but the fact that I got the same numerical answer and didn't put 2 and 2 together to realize that there are 2 prime divisors!!! lol

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pm; Location: Gandhinagar; Thanked: 41 times; Followed by:2 members

by shashank.ism » Wed Feb 17, 2010 9:19 am

money9111 wrote:i think the real issue here isn't the approach I took, but the fact that I got the same numerical answer and didn't put 2 and 2 together to realize that there are 2 prime divisors!!! lol

yeah u were surely wrong at that point .. Be careful on the D day...

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pm; Location: New Jersey; Thanked: 109 times; Followed by:79 members; GMAT Score:640

by money9111 » Wed Feb 17, 2010 9:21 am

i'll be sure to be careful! thanks for the tip

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 am; Location: India; Thanked: 64 times; Followed by:6 members; GMAT Score:760

by harsh.champ » Wed Feb 17, 2010 11:26 pm

Hey Guys,
It is better to go by the formal approach rather than by plugging no.s as it takes approx. the same time.
Now,Let no. be 10x + y[xy].Now ,after adding 27 the digits are reversed.10y + x[yx]
So,we get the equation:-10x + y + 27 = 10y + x
=>9(x-y) + 27 = 0
=>x-y + 3 =0
=>y-x=3 [so,we check for "y" 4....5.....6 voila!! Now that makes x=3 ]
So, the no. is 36.
36 can be written as 2^2 x 3^2
So,we have 2 prime divisors.
The OA hence is B.

I hope the method is clear now.

P.S:-36 can straightaway strike your mind if you have done lot of problems regarding the digits reversal.

It takes time and effort to explain, so if my comment helped you please press Thanks button

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