
Data Sufficiency  Quant/Math  CAT 2013
Question 4 the day:
October , 2003
The question for the day is from the topic of Data Sufficiency.
Choose 1 if the question can be answered by one of the statements alone and not by the other.
Choose 2 if the question can be answered by using either statement alone.
Choose 3 if the question can be answered by using both the statements together, but cannot be
answered by using either statement alone.
Choose 4 if the question cannot be answered even by using both statements together.
Is X a prime number, given that X is a positive integer?
A. X^4 > 3000
B. X^4 < 10,000
Correct Answer  (3)
Solution:
From statement A we know that X^{4} is greater than 3000. There are infinite values for X possible for which X^{4} is greater than 3000
From statement B we know that X^{4} is less than 10,000. This one is a lot better. There are only 9 integer values that satisfy this condition. But this still does not give us a unique answer.
Combining the two statements, we know that 2000 < X^{4} < 10000. The following values of X satisfy this condition > 8 and 9. Both 8 and 9 are not prime. Hence, the question can be answered conclusively using the two statements. Hence answer choice (3)



