List A consists of 10 distinct integers arran...

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List A consists of 10 distinct integers arranged in ascending order. Is the difference between the sixth term and the fifth term of list A greater than 5?
(1) The difference between any two integers in list A is a multiple of 5.
(2) The median of the list is an integer.
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Given:
1. List A = {a1, a2, a3, a4, a5, a6, a7, a8, a9, a10}
1. consists of all integers,
2. where a10 > a9> a8…> a2> a1
To Find:  Is a6 – a5 > 5?
Step 4: Analyse Statement 2 independently
The median of the list is an integer.
• Median =?
• List contains 10 elements
• a5 & a6 are integers at the centre of the list (in ascending order)
• Median of the list = a5+a62
•  = m, where m is an integer
• Rearranging, we get a5+ a6 = 2m = even
• If sum of a6 & a5 is even, then
• Difference of a6 & a5 is also even
• No information about values of the terms , so cannot tell if (a6 – a5) > 5
• Hence, statement 2 is insufficient to answer the question.
Step 5: Analyse Both Statements Together (if needed)
• From statement 1, a6 – a5 = {5, 10, 15}
• From statement 2, a6 – a5 = even
• Combining the two,
• a6 – a5 = even multiples of 5 = {10, 20, 30…}
• a6 – a5 > 5
• So, we can answer the question.
• Hence statement 1 and statement 2 together are sufficient to arrive at a definite answer.
Step 3: Analyse Statement 1 independently
The difference between any two integers in list A is a multiple of 5.
• Difference between any two terms of A can be = {5,10,15…}
• a6 – a5 = {5, 10, 15…}
• Since the difference can also = 5, we cannot be certain that a6 – a5 > 5.
• Hence, Statement 1 is insufficient to answer the question.

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