bakfed
Harvey teaches a certain number of biology students in 2 classes, K and L. He can divide the students in class K into 7 groups of n students each. He can divide the students in class L into 6 groups of p students each with 1 student left over. How many students are in class L ?
(1) n = p
(2) There are 5 more students in class K than in class L.
AntonioGalindoStatement two, by itself, is not sufficient.
Could I come up with a more elegant solution on a question like this? Sure, but my approach is typically to take a quick shot at seeing whether brute force is going to be manageable. In this case, it is, so why bother with anything else? There are no style points on the GMAT, only right/wrong.
Possible values for the number of students in K:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, ...
Possible values for the number of students in L:
7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, ...
(Notice that the first terms of the lists are equal, the second terms differ by 1, the third terms differ by 2, the fourth terms differ by 3, the fifth terms differ by 4, etc.)
Looking at statement 1 alone:
This just tells us that we need to pick the same numbered term from each list. We could have K=7 and L=7, K=14 and L=13, K=21 and L=19, K=28 and L=25, etc. Do we have enough information to say how many students are in L? No. BCE.
Looking at statement 2 alone:
We are looking for opportunities to select a number from the K list that is 5 more than some number from the L list. We could have K=42 and L=37, K=84 and L=79, etc. Do we have enough information to say how many students are in L? No. CE.
Looking at both statements together:
As we keep going to the right in both lists, the difference between them keeps increasing. There is only one spot where the same numbered terms are going to be separated by 5: K=42 and L=37. Do we have enough information to say how many students are in L? Yes. C.
Answer choice C.