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

Question

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.

Bunuel · Answer

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.

unceldolan · Answer

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!

stonecold · Answer

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 => not posible as m is a single digit integer.
hence the only possible value of y is 0.3579

Hence Sufficient
Hence B

kokus · Answer

1) Insufficient as it could be 2<3<4<5 or 3<4<5<6 or 4<5<6<7 etc 2) j+a=k k+a=m m+a=n j>a>1 a=2 ;j=3 3+2=k -> k=5 5+2=m -> m=7 7+2=n -> n=9 jkmn=3759 -> y=0.3579 -> Statement 2 is sufficient -> B

CEdward · Answer

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

Clearly insufficient.
j = 1, k = 2, m = 3, n = 4
j = 2, k = 3, m = 4, n = 5

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

Sufficient.
j = 3, a = 2, m = 7, n = 9 YES
j = 4, a = 2, m = 8, n = 10 NO (n cannot be a two-digit integer)

B.

sahuanamika · Answer

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

Clearly insufficient.
j = 1, k = 2, m = 3, n = 4
j = 2, k = 3, m = 4, n = 5

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

Sufficient.
j = 3, a = 2, m = 7, n = 9 YES
j = 4, a = 2, m = 8, n = 10 NO (n cannot be a two-digit integer)

B.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards