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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]

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01 Apr 2012, 12:33
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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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01 Apr 2012, 12:56
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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.

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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink]

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28 May 2013, 05:28
Bumping for review and further discussion.
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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink]

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28 May 2013, 15:42
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]

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16 Jan 2014, 04:36
I use this pattern:
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

(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.

I basically followed the same approach as bunuel, but simplified the expressions first. Hope it's clear!

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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink]

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11 Aug 2015, 11:24
Hello from the GMAT Club BumpBot!

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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink]

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11 Aug 2016, 18:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero [#permalink]

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18 Nov 2016, 22:41
Great Question
Here y=0.jklm
To get y we need j,k,l,m
Statement 1
using test cases
y=0.9876
y=0.8765
Clearly not sufficient
Statement 2
This statement looks interesting
Here j>1
and a=> (1,j)
so least possible value of j is 3
a=2
=> y=0.3579
Hmmm
let j=4
a=2
=> y=0.468[10]=> not posible as m is a single digit integer.
hence the only possible value of y is 0.3579

Hence Sufficient
Hence B
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Re: If y = 0.jkmn, where j, k, m, and n each represent a nonzero   [#permalink] 18 Nov 2016, 22:41
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