Data Sufficiency Question: Multiples and Integers
If q is a multiple of n, and n is a positive integer, is 360/q an integer?
(1) n < 7
(2) q < 16
Here we are asked to determine if 360 is evenly divisible by some number q. Make sure to note that, as n is a positive integer and q is a multiple of n, q must be a positive integer.
Statement 1 tells us that n must be less than 7. If n is 2, q can be any positive even number. Thus, q can be 12, in which case the answer to the question is ‘yes,’ OR q can be 14, in which case the answer to the question is ‘no.’ Sometimes yes, and sometimes no is insufficient in yes/no questions, therefore, statement 1 is not sufficient.
Statement 2 tells us that q must be less than 16. Just as was the case in statement 1, q can be 12, providing an answer of ‘yes,’ or q can be 14, providing an answer of ‘no.’ Again we have sometimes yes, sometimes no, which is NOT sufficient.
Looking at the statements together, we can immediately see that q could STILL equal 12 or 14 when both statements are true. Thus, together the statements are still not sufficient for the same reasons as they were insufficient alone, and your final answer choice is E or choice 5—there is not enough information here to answer the question.