• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

if each term in the sum a1 + a2 + ... is either 7 or 77

This topic has 9 expert replies and 9 member replies
Goto page
  • 1,
  • 2
Next

GMAT/MBA Expert

if each term in the sum a1 + a2 + ... is either 7 or 77

Post
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

  • +1 Upvote Post
  • Quote
  • Flag
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
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
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 Default Avatar
Joined
17 Apr 2008
Posted:
144 messages
Upvotes:
8
Target GMAT Score:
800
Post
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

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1507 members
Upvotes:
2256
GMAT Score:
800
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
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 Default Avatar
Joined
17 Feb 2008
Posted:
106 messages
Upvotes:
3
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
Master | Next Rank: 500 Posts Default Avatar
Joined
17 Apr 2008
Posted:
144 messages
Upvotes:
8
Target GMAT Score:
800
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag
Master | Next Rank: 500 Posts Default Avatar
Joined
13 Jan 2008
Posted:
320 messages
Upvotes:
10
Post
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!

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1507 members
Upvotes:
2256
GMAT Score:
800
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
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 Default Avatar
Joined
17 Apr 2008
Posted:
144 messages
Upvotes:
8
Target GMAT Score:
800
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
30 Mar 2011
Posted:
19 messages
Upvotes:
1
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag
Senior | Next Rank: 100 Posts
Joined
01 Jun 2012
Posted:
89 messages
Followed by:
2 members
Upvotes:
6
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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 Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
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 Default Avatar
Joined
05 Feb 2015
Posted:
13 messages
Upvotes:
1
Post
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!

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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 Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
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 Default Avatar
Joined
12 Sep 2012
Posted:
2635 messages
Followed by:
117 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 32 first replies
5 GMATGuruNY 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

159 posts
2 image description Max@Math Revolution

Math Revolution

92 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

60 posts
4 image description Ian Stewart

GMATiX Teacher

50 posts
5 image description GMATGuruNY

The Princeton Review Teacher

37 posts
See More Top Beat The GMAT Experts