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If y = 0.jkmn, where j, k, m, and n each represent a nonzero

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If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink] New post 01 Apr 2012, 11:33
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If y = 0.jkmn, where j, k, m, and n each represent a nonzero digit of y, what is the value of y ?

(1) j < k < m < n
(2) j + a = k, k + a = m, and m + a = n, where j > a > 1.
[Reveal] Spoiler: OA

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Re: Value of y [#permalink] New post 01 Apr 2012, 11:56
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If y = 0.jkmn, where j, k, m, and n each represent a nonzero digit of y, what is the value of y ?

(1) j < k < m < n. Many combinations are possible: 1<2<3<4, 2<3<4<5, 1<3<4<5, ... Not sufficient.

(2) j + a = k, k + a = m, and m + a = n, where j > a > 1.

Since j+a=k and j and k represent digits then a must be an integer.

Next, since j > a > 1 then the least value of a is 2 and the least value of j is 3.

So, from j+a=k the least value of k is 3+2=5, from k + a = m the least value of m is 5+2=7 and from m + a = n the least value of n is 7+2=9.

Now, if our initial number, a, is more than 2, 3 for example, then the values of all other variables will increase and n will become more than 9, which is not possible since each variable represents a single nonzero digit.

Hence: j=3, k=5, m=7, and n=9. Sufficient.

Answer: B.
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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink] New post 28 May 2013, 04:28
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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink] New post 28 May 2013, 14:42
Bunuel wrote:
Bumping for review and further discussion.


I love the way you always able to pull numbers out of thin air and make the equation work so good
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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink] New post 16 Jan 2014, 03:36
I use this pattern:
AD
BCE

cross out what's incorrect.

(1) j<k<m<n --> could be 1,2,3,4 or 2,3,4,5 hence IS --> cross out AD

possible answers left: BCE

(2) j + a = k, k + a = m, and m + a = n, where j > a > 1

Since we're talking about units digit, every variable here is an integer. hence a is at least 2 and j at least 3. If you simplify the given expressions you get j+3a = n. If j = 3 and a = 2 we get n = 9, which is the highest possible value (0 is not an option). Hence you can calculate the other numbers. SUFFICIENT. Cross out C and E.

Left with answer B.

I basically followed the same approach as bunuel, but simplified the expressions first. Hope it's clear!
Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero   [#permalink] 16 Jan 2014, 03:36
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