If, J, K, L, M, and N are positive integers in ascending ord

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If, J, K, L, M, and N are positive integers in ascending order, what is the value of L?

(1) The value of K is 3.
(2) The value of M is 7.

OA E

Source: Official Guide

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by Brent@GMATPrepNow » Fri Jan 25, 2019 5:17 am

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BTGmoderatorDC wrote:If, J, K, L, M, and N are positive integers in ascending order, what is the value of L?

(1) The value of K is 3.
(2) The value of M is 7.
Given: J, K, L, M, and N are positive integers in ascending order

Target question: What is the value of L?

Statement 1: The value of K is 3.
There are many scenarios that satisfy statement 1. Here are two:
Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the target question is L = 4
Case b: J = 1, K = 3, L = 5, M = 7, N = 8. In this case, the answer to the target question is L = 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The value of M is 7.
There are many scenarios that satisfy statement 2. Here are two:
Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the target question is L = 4
Case b: J = 1, K = 3, L = 5, M = 7, N = 8. In this case, the answer to the target question is L = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient.
So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the target question is L = 4
Case b: J = 1, K = 3, L = 5, M = 7, N = 8. In this case, the answer to the target question is L = 5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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BTGmoderatorDC wrote:If, J, K, L, M, and N are positive integers in ascending order, what is the value of L?

(1) The value of K is 3.
(2) The value of M is 7.
Source: Official Guide
$$1 \le J < K < L < M < N\,\,\,\,{\rm{ints}}$$
$$?\,\, = \,\,L$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,K = 3 \hfill \cr
\,M = 7 \hfill \cr} \right.\,\,\,\,\,\,:::\,\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {J,K,L,M,N} \right) = \left( {1,3,4,7,8} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 4 \hfill \cr
\,{\rm{Take}}\,\,\left( {J,K,L,M,N} \right) = \left( {1,3,5,7,8} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 5\, \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{E}} \right)$$


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

P.S.: if "ascending" is considered the same as "non-descending" (so that J <= K <= L , etc), the correct answer is still (E).
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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