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
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
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Evaluate Statement (1) alone.
- The prime numbers between 15 and 34, not-inclusive, include:
17, 19, 23, 29, 31
- 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.
- Statement (1) alone is NOT SUFFICIENT.
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Evaluate Statement (2) alone.
- 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.
- 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.
- Statement (2) alone is NOT SUFFICIENT.
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Evaluate Statements (1) and (2) together.
- 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
- 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).
- 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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