hpgmat wrote:if each term in the sum a1+a2+....+an is either 7 or 77 and the sum equalls 350 , which of the following could be n?
38
39
40
41
42
I can think of a couple of approaches here: either backsolving plus reasoning OR pure reasoning.
Approach 1--Backsolving + Reasoning:
Reasoning part: We know there are a certain number of 7s and 77s that sum to 350. The question is asking for the number of 7s and 77s (whatever their ratio). If they were all 7s, you would have...50 7s (because 50*7=350). Because the answer choices run from 38-42, we know we have a lot of 7s, and that they can`t all be 7s.
Backsolving part: Start with answer choice C because it is clearly the easiest one to evaluate. 40*7=280. But, remember, they can`t all be 7s (because we would need 50 7s then). So if 39 of these 40 were 7s, we would have...one less 7 or 280-7=273. The other one would be 77 and 350-273 just happens to equal 77. Therefore, we have 39 7s and one 77. Done.
Approach 2--Pure Reasoning (and this is the approach I, personally, would have employed):
If 7 multiplied by a number equals another number whose units digits is zero, then the number being multiplied by 7 must be a multiple of 10. In other words, if 7*x= a number ending in zero, then x is a multiple of ten. Both 7 and 77 have 7 as their units digits. For a certain number of them to sum to 350, the number of them must be a multiple of ten. There is only one multiple of ten in the answer choices...choice C
I think a pure algebraic approach such as the one papgust adopted while technically correct is far more time-consuming than either of the approaches I outlined above (especially the second approach). Remember, GMAT wants to reward critical reasoning. It's not just about getting to the correct answer but also about how fast you get to the correct answer. Therefore, when reviewing, make sure you also review the questions you answered correctly and ask yourself "is there a quicker way I could have gotten to the correct answer? Could I have employed some reasoning or commonsense? Could I have used the answer choices or picked numbers?" Etc.
Kaplan Teacher in Toronto
