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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## if each term in the sum a1 + a2 + ... is either 7 or 77 tagged by: ##### This topic has 9 expert replies and 9 member replies Goto page • 1, • 2 ### GMAT/MBA Expert ## if each term in the sum a1 + a2 + ... is either 7 or 77 courtesy of user 'karenmeow' if each term in sum a1+a2+...+an is either 7 or 77, and the sum equals 350, which can be n? choices: 38, 39, 40, 41, 42 _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions à Ron en français Voit esittää kysymyksiä Ron:lle myös suomeksi -- Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1507 members Upvotes: 2256 GMAT Score: 800 well, first, think about the qualitative aspects of the sequence: if the sequence consisted entirely of 7's, then there would be fifty terms in the sequence. these answer choices are reasonably close to fifty, so it stands to reason that by far the majority of the terms will be 7's. therefore, try as few 77's as possible. try only one 77: remaining terms = 350 - 77 = 273 this would be 273 / 7 = 39 sevens so ... you'd have one '77' and thirty-nine '7's this works! answer = c -- notice that if you're adept at noticing patterns in DIGITS, you can also notice the following: both 7 and 77 end with '7', so a look at the units digit of the sum will give telltale information about the number of terms. specifically, the final sum, 350, ends with a zero. this means that, in the units column, you've added together a bunch of 7's and gotten a number ending in 0. the only way this can happen is if the number of 7's is a multiple of ten: there could be 10, 20, ... "7"s to be added together. the only such number in the answer choices is 40, so that must be the correct answer. _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions à Ron en français Voit esittää kysymyksiä Ron:lle myös suomeksi -- Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Master | Next Rank: 500 Posts Joined 17 Apr 2008 Posted: 144 messages Upvotes: 8 Target GMAT Score: 800 Hi Ron, I solved it this way:- Lets say there are x number of 7's and y number of 77's so 7x+77y=350 i.e. x+11y=50 Normally I take the highest and lowest values when substituting values.In this case, x will be 39 and y is 1. x+y is n which will be 40. Let me know if this is correct. _________________ You cannot discover new oceans unless you have the courage to loose sight of the shore. Last edited by Sunny22uk on Tue Jul 15, 2008 9:25 am; edited 1 time in total ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1507 members Upvotes: 2256 GMAT Score: 800 Sunny22uk wrote: Hi Ron, I solved it this way:- Lets say there are x number of 7's and y number of 77's so 7x+77y=750 i.e. x+11y=50 Normally I take the highest and lowest values when substituting values.In this case, x will be 39 and y is 1. x+y is n which will be 40. Let me know if this is correct. if you're going to go to the trouble of writing equations, then you may as well write a pair of simultaneous equations, so that you can just solve them the way you'd solve any other system. you can indeed write x + 11y = 50, as above. and then your second equation comes from the fact that there are forty numbers in the sequence: x + y = 40 so: x + 11y = 50 x + y = 40 subtract gives 10y = 10 y = 1 there you go. whatever works! _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions à Ron en français Voit esittää kysymyksiä Ron:lle myös suomeksi -- Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Master | Next Rank: 500 Posts Joined 17 Feb 2008 Posted: 106 messages Upvotes: 3 Sunny22uk wrote: Hi Ron, I solved it this way:- Lets say there are x number of 7's and y number of 77's so 7x+77y=750 i.e. x+11y=50 Normally I take the highest and lowest values when substituting values.In this case, x will be 39 and y is 1. x+y is n which will be 40. Let me know if this is correct. Hi sunny, where from u got 750? the qustion states the sum is 350 Master | Next Rank: 500 Posts Joined 17 Apr 2008 Posted: 144 messages Upvotes: 8 Target GMAT Score: 800 Sorry about the typo, it should be 350, it doesnot affect the end result. _________________ You cannot discover new oceans unless you have the courage to loose sight of the shore. Master | Next Rank: 500 Posts Joined 13 Jan 2008 Posted: 320 messages Upvotes: 10 Here, we are assuming that X+Y = 40 terms and backsolving. The criteria for choosing I assume if when we get integer values for X and Y by backsolving. Can there be a scenario where couple of answer choices can solve this criteria when we are backsolving? If so, how to narrow it down. Appreciate your reponse. lunarpower wrote: Sunny22uk wrote: Hi Ron, I solved it this way:- Lets say there are x number of 7's and y number of 77's so 7x+77y=750 i.e. x+11y=50 Normally I take the highest and lowest values when substituting values.In this case, x will be 39 and y is 1. x+y is n which will be 40. Let me know if this is correct. if you're going to go to the trouble of writing equations, then you may as well write a pair of simultaneous equations, so that you can just solve them the way you'd solve any other system. you can indeed write x + 11y = 50, as above. and then your second equation comes from the fact that there are forty numbers in the sequence: x + y = 40 so: x + 11y = 50 x + y = 40 subtract gives 10y = 10 y = 1 there you go. whatever works! ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1507 members Upvotes: 2256 GMAT Score: 800 ildude02 wrote: Can there be a scenario where couple of answer choices can solve this criteria when we are backsolving? well, sure there can, but not on a problem whose setup is like this one. the setup of this problem is basically two simultaneous linear equations in two variables, so it's guaranteed to have one unique solution (unless the equations are multiples of each other, which they aren't). you might get something where the problem asks you to maximize some quantity with some other equation given as a condition. for instance, you might be given that x + 11y = 50 and then asked to maximize the value of, say, -2x + 3y. in that case, it's sufficient just to find the extremes of x + 11y = 50 - namely, (50, 0) and (0, 50/11), or (50, 0) and (6, 4) if you're restricted to integers - and then just plug them into the expression you're trying to maximize. _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions à Ron en français Voit esittää kysymyksiä Ron:lle myös suomeksi -- Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Master | Next Rank: 500 Posts Joined 17 Apr 2008 Posted: 144 messages Upvotes: 8 Target GMAT Score: 800 I think the "pattern recognition" can be really helpful where drawing equations can be a tedious and time consuming task, To Ron-Thanks for illustrating the approach here. _________________ You cannot discover new oceans unless you have the courage to loose sight of the shore. Junior | Next Rank: 30 Posts Joined 30 Mar 2011 Posted: 19 messages Upvotes: 1 Sum of x times 7 and y times 77 gives a number whose unit can be 4, 1, 8, 5, 2, 9, 6, 3, 0. The unit will be 0 only if x+y = 10 (which is n the same as n). So to get 350, n must be a multiple of 10, hence the only acceptable solution is 40. Answer C) Please correct me if the above reasoning is wrong. Senior | Next Rank: 100 Posts Joined 01 Jun 2012 Posted: 89 messages Followed by: 2 members Upvotes: 6 I did the following way. 350 = 7+77+7+77+........ 350 = 7(1+11+1+11+....) 7*50 = 7(1+11+1+11+....) So (1+11+1+11+....) must be equal to 50. Since the question asks which of the following, we can say that one 11 and thirty nine 1's will give a sum of 50. Hence the number of terms is 1+39 which is 40. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13035 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 sidceg wrote: I did the following way. 350 = 7+77+7+77+........ 350 = 7(1+11+1+11+....) 7*50 = 7(1+11+1+11+....) So (1+11+1+11+....) must be equal to 50. Since the question asks which of the following, we can say that one 11 and thirty nine 1's will give a sum of 50. Hence the number of terms is 1+39 which is 40. Clever approach! This tells us that the number of terms must be divisible by 10, and only answer choice C works. Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! Junior | Next Rank: 30 Posts Joined 05 Feb 2015 Posted: 13 messages Upvotes: 1 Hi, I struggled with this question and am looking for other similar questions (preferably from the Official Guide or OG Quant) to practice. Can anyone recommend similar problems to this one? Thank you! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13035 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 Quote: If each term in sum a1+a2+ ... +an is either 7 or 77 and the sum equals 350, which of the following could be equal to n? A)37 B)39 C)40 D)41 E)42 Another possible approach it to look for a pattern: Since both 7 and 77 have 7 as their units digit, we know that if we take any two terms, their sum will have a units digit of 4 (e.g., 7 + 7 = 14, 7 + 77 = 84, 77 + 77 = 154) Similarly, if we take any three terms, their sum will have a units digit of 1. (e.g., 7 + 7 + 7 = 21, 7 + 7 + 77 = 91, etc.) Now let's look for a pattern. The sum of any 1 term will have units digit 7 The sum of any 2 terms will have units digit 4 The sum of any 3 terms will have units digit 1 The sum of any 4 terms will have units digit 8 The sum of any 5 terms will have units digit 5 The sum of any 6 terms will have units digit 2 The sum of any 7 terms will have units digit 9 The sum of any 8 terms will have units digit 6 The sum of any 9 terms will have units digit 3 The sum of any 10 terms will have units digit 0 The sum of any 11 terms will have units digit 7 (at this point, the pattern repeats) From this, we can conclude that the sum of any 20 terms will have units digit 0 And the sum of any 30 terms will have units digit 0, and so on. We are told the sum of the terms is 350 (units digit 0), so the number of terms must be 10 or 20 or 30 or . . . Since C is a multiple of 10, this must be the correct answer. Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Most of these explanations seem overly complex. We know that 350 = 7 * 50, so we must have fifty 7s in some fashion. Every time we replace 7s with a 77, we turn ELEVEN terms into ONE: in other words, we subtract 10 total terms. So we could have 50 terms (all 7s), 40 terms (39 7s and one 77), 30 terms (28 7s and two 77s), etc. The only choice given here that works is C, so we're done. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? 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