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If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh

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If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh [#permalink] New post 03 Dec 2019, 02:31
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If 2, 4, 6, and 9 are the digits of two 2-digit integers, what is the least possible positive difference between the integers?


A. 28

B. 27

C. 17

D. 13

E. 9
[Reveal] Spoiler: OA

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Re: If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh [#permalink] New post 04 Dec 2019, 11:03
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If someone has a faster solution, please post so. Otherwise this was my method.

Utilizing the 4 digits, write down every combination of numbers possible.

24, 26, 29
42, 46, 49
62, 64, 69
92, 94, 96.

From here I tried subtracting numbers together. I looked at 62-49 and saw that the difference was 13. I tried to look for any other combination lower but I could not find anything.
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Re: If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh [#permalink] New post 05 Dec 2019, 07:54
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Carcass wrote:
If 2, 4, 6, and 9 are the digits of two 2-digit integers, what is the least possible positive difference between the integers?


A. 28

B. 27

C. 17

D. 13

E. 9


Let's first examine the tens digits.
To minimize the difference between our two numbers, we want the tens digits to be as close as possible.
There are two pairs of numbers that have a difference of 2. They are 2 & 4 and 4 & 6

This gives us two possible cases:
case i: The numbers are 2_ and 4_
case ii: The numbers are 4_ and 6_

case i: The numbers are 2_ and 4_
To minimize the difference between these two numbers, we need first unit's digit to be greater than the second units digit
We get: 29 and 46
Difference = 46 - 29 = 17

case ii: The numbers are 4_ and 6_
To minimize the difference between these two numbers, we need first unit's digit to be greater than the second units digit
We get: 49 and 62
Difference = 49 - 62 = 13

Answer: D

Cheers,
Brent
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Re: If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh [#permalink] New post 05 Dec 2019, 11:31
how do you know if you can repeat the numbers or not?....how do you know you cant use 22, or 44, etc.????? it does not specify, furthermore, it doesn't specify you can use 2 in two numbers....24,26, 29, etc…in my mind if you can use 24, 42, then you can use 22, 44.
can someone please explain?
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Re: If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh [#permalink] New post 07 Dec 2019, 10:20
D
Re: If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh   [#permalink] 07 Dec 2019, 10:20
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If 2, 4, 6, and 9 are the digits of two 2-digit integers, wh

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