Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Statement 1: Tells us number of element is even. So it can 22+23 (2 even) = 45 or 1+ 2 + 3+ ...+ 9 (9 odd)= 45 or 5+6+7+...+10 (6 even) = 45, So insufficient.

Statement 2: Tells us total number of terms is less than 9. In all the cases considered above n is less than 9. So this statement alone is also insufficient.

Combining them together is not going to give any results as we are using same set of example for both the statements.

The formula n(n+1)/2 is only valid if you have series starting from 1. So it will be valid for 1+2+3+...+9 But it will not be valid for 4+5+6+7 or for that matter any series that does not start with 1.

sum=45. So, construct all sequences: n is odd. For odd n we can say that ((n+1)/2)th number is median and equal sum/n. In our case, 45 is divisible by odd n only if n is {3,5,9,15,45} (odd factors of 45) n=3: 45/3=15. 14,15,16 n=5: 45/5=9. 7,8,9,10,11 n=9: 45/5=5. 1,2,3,4,5,6,7,8,9 n=15,45: sequences will be include negative numbers that contradicts the problem.

n is even. For even n we can say that sum/n is median and has to be equidistant between (n/2)th and (n/2+1)th numbers. In other words, sum has to be decimal number like xxx,5

In our case, 45 is divisible by even n and result xxx.5 only if n is {2,6,10,18,30,90} n=2: 45/2=22.5. 22,(22.5),23 n=6: 45/6=7.5. 5,6,7,(7.5),8,9,10 n=10,18,30,90: sequences will be include negative numbers that contradicts the problem.

The sum of arthimetic progression (here with diff = 1) needs is

S = n(a1 + aN)/2 OR S = N [2*a1 + (N-1)d] /2

Thus if you know sum, you still have 2 unknowns,

(1) & (2) individually or together do not give any definite value of N,

So E.

But how can you use your approach for slightly modified problem: "The sum of n consecutive positive integers is 47. What is the value of n?" _________________

Maybe I've understood incorrectly, Alpha_plus_gamma's approach in based on S = N [2*a1 + (N-1)d] /2 formula and he chose E because too many unknowns. So, if we substitute 45 for 47 his approach is insensitive to this substitution, isn't it? _________________

Maybe I've understood incorrectly, Alpha_plus_gamma's approach in based on S = N [2*a1 + (N-1)d] /2 formula and he chose E because too many unknowns. So, if we substitute 45 for 47 his approach is insensitive to this substitution, isn't it?

- I wouldn't say E is chosen bcoz of too many unknowns; rather given the two infos in original questions i.e 1) n is even and 2) n<9, the formula nicely gives E. - You are right; substitute 45 for 47 is insensitive to the substitution. - On a side note even the method you gave for counting 5s in 4500! question is an offshoot of this method.

When dealing with the sum of evenly spaced integers (also known as arithmetic progression or sequence), just remember the simple, universal formula: Sum = Average* (# of values). [* represents the multiplication sign.] The space is 1 here. Applied to this problem, Sum = n*(a1+aN)/2. a1 and aN are the first term and the last term of the sequence respectively, (a1+ aN)/2 being the average, but also the median or the midpoint. They all coincide when dealing with an arithmetic progression. n is of course the number of terms. So, it follows that n(a1 + aN)/2 = 45 and (a1 + aN) = 90/n. Since a1 + a2 is an integer, so must be 90/n. It then boils down to finding the positive factors of 90. Let's find the prime factorization of 90. 90 = 9*10 = 3*3*2*5 = 3^2 * 2 * 5. We can easily list all the positive factors of 90; there are 12 of them. I actually have a formula to find them fast but that's another topic. 1/Since n is even, let's focus on the even values of n; they are 2, 6, 10, 18, 30, and 90. But if n = 10 then the median of the sequence will be (a1 + a2)/2 = 45/10 = 4.5 and some of the terms will be negative (NOT Allowed). Any n > 10 will have to be rejected for the same reason. Therefore n must be 2 or 6: UNSUFF. 2/ n < 9 includes more than one n (2, 3, 5, 6): UNSUFF. Together, we are still stuck with 2 and 6. Note that when n = 2, the average is 45/2 = 22.5; then a1 = 22 and aN = a2 = 23. 22+23 = 45 When n = 6, then a1 = 5; a2 = 6; a3 =7; a4 = 8, a5 = 9, a6 = 10. 5+6+7 +8+9+10 = 45. Regards,

Quote:

How you perceive people and things will set the pace of your journey and dictate your reality!

_________________

Dakar Azu is The GMAT Doctor. Dakar is an experienced GMAT teacher who can be reached at http://700gmatclub.com. He prepares aspiring business students thoroughly to get them well over the GMAT 700-score hurdle through his online GMAT courses.

Last edited by TheGMATDoctor on 13 Jul 2010, 13:10, edited 2 times in total.

Maybe I've understood incorrectly, Alpha_plus_gamma's approach in based on S = N [2*a1 + (N-1)d] /2 formula and he chose E because too many unknowns. So, if we substitute 45 for 47 his approach is insensitive to this substitution, isn't it?

- I wouldn't say E is chosen bcoz of too many unknowns; rather given the two infos in original questions i.e 1) n is even and 2) n<9, the formula nicely gives E. - You are right; substitute 45 for 47 is insensitive to the substitution. - On a side note even the method you gave for counting 5s in 4500! question is an offshoot of this method.

I too meant >> given the two infos in original questions i.e 1) n is even and 2) n<9, the formula nicely gives E.

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...