A two-digit even number

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deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

by deepoe » Sun Mar 01, 2009 10:18 am

A two-digit even number is such that reversing its digits creates an odd number greater than
the original number. Which one of the following cannot be the first digit of the original number?

(A) 1 (B) 3 (C) 5 (D) 7 (E) 9

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Source: Beat The GMAT — Problem Solving | Sun Mar 01, 2009 10:18 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sun Mar 01, 2009 10:28 am

My answer would be E, 9, simply because 9 is the greatest of digits. If the first digit of the initial number is 9, then the second will be from 2 to 8 (0 is eliminated, since you have to flip the digits and obtain an odd number):
92 vs. 29
94 vs. 49
96 vs. 69
98 vs. 89
As you can see, all the numbers on the left are greater than the numbers on the right.
A counter example for why 3, for instance, cannot be the first digit of the required number would be 36. Flip the digits and you get an odd number, 63, that is greater than the original number.

Last edited by DanaJ on Sun Mar 01, 2009 11:47 am, edited 1 time in total.

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deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

by deepoe » Sun Mar 01, 2009 11:42 am

Ah ok ok so just fill those digit in a ten digit numer like:

21
23
25
27
29

I misunderstand the question:$

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sun Mar 01, 2009 2:54 pm

Pick an original even number starting with each of the answer choices and only when the first digit of the original even number is 9 will the reversed number not be odd number greater than the original number.

Since 9 is highest single digit place value possible the even number's 2nd digit will always be less than 9.

If this is flipped the resulting number will always be smaller.

Hence E

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lax: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun Nov 23, 2008 4:43 am

by lax » Sun Mar 01, 2009 4:42 pm

consider 8 in the units place. for all the first four choices, reversal of digits makes the new no greater whereas for 9, it is the opposite.

89<98.

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welcome: Master | Next Rank: 500 Posts; Posts: 137; Joined: Thu Jan 08, 2009 1:27 am; Thanked: 7 times

by welcome » Sun Mar 01, 2009 5:31 pm

Consider this...

No is 10x+y , where x and y are 1st and second digit.

Resverse no. 10y+x should be less that original no. so

10x+y < 10y+x
x-y<0

so we need to find out 2 digis for which x-y>=0, for this relation 9-anyDigit will work.##Answer E.

Shubham.
590 >> 630 >> 640 >> 610 >> 600 >> 640 >> 590 >> 640 >> 590 >> 590

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