Practice GMAT Data Sufficiency Question

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How many prime numbers are there between the integers 7 and X, not-inclusive?

15 < X < 34
X is a multiple of 11 whose sum of digits is between 1 and 7

A)	Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)	Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)	BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)	EACH statement ALONE is sufficient.
E)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: E

In evaluating this problem, it is important to keep in mind the list of possible prime numbers:
7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53
Evaluate Statement (1) alone.
1. The prime numbers between 15 and 34, not-inclusive, include:
  17, 19, 23, 29, 31
2. Since there is no definitive information about the value of X, we do not know how many prime numbers exist between 7 and X.
  If X = 17, there would be 2 prime numbers between 7 and X (i.e., 11 and 13).
  If X = 18, there would be 3 prime numbers between 7 and X (i.e., 11, 13, and 17).
  If X = 21, there would be 4 prime numbers between 7 and X (i.e., 11, 13, 17, and 19).
  There is not enough information to definitively answer the question.
3. Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
1. List the multiples of 11 and their sums (stopping when the sum is no longer less than 7).
  x = 11; sum of digits is 1+1 = 2
  x = 22; sum of digits is 2+2 = 4
  x = 33; sum of digits is 3+3 = 6
  x = 44; sum of digits is 4+4 = 8, which is too high so x cannot be greater than 33.
2. Since X can be 11, 22, or 33, there are different possible answers to the question of how many prime numbers are there between the integers 7 and X:
  If X = 11, there would be 0 prime numbers between 7 and X.
  If X = 22, there would be 4 prime numbers between 7 and X (i.e., 11, 13, 17, and 19).
  There is not enough information to definitively answer the question.
3. Statement (2) alone is NOT SUFFICIENT.
Evaluate Statements (1) and (2) together.
1. Putting Statements (1) and (2) together, X must meet the following conditions:
  (1) 15 < X < 34
  (2) X = 11, 22, 33
  This means that possible values for X include:
  X = 22 or 33
2. The two possible values for X give different answers to the original question:
  If X = 22, there would be 4 prime numbers between 7 and X (i.e., 11, 13, 17, and 19).
  If X = 33, there would be 7 prime numbers between 7 and X (i.e., 11, 13, 17, 19, 23, 29, and 31).
3. Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT, Statement (2) alone is NOT SUFFICIENT, and Statements (1) and (2), even when taken together, are NOT SUFFICIENT, answer E is correct.

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