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:

What is the sum of the digits of the positive integer n where n < 99?

1) n is divisible by the square of the prime number y.

2) y4 is a two-digit odd integer.

What is the sum of the digits of the positive integer n where n < 99?

(1) n is divisible by the square of the prime number y --> clearly insufficient, as no info about y.

2) y^4 is a two-digit odd integer --> also insufficient, as no info about n, but from this statement we know that if y is an integer then y=3 (y must be odd in order y^4 to be odd and it cannot be less than 3 or more than 3 since 1^4 and 5^4 are not two digit numbers).

(1)+(2) Since from (1) y=integer then from (2) y=3, so n is divisible by 3^2=9. Number to be divisible by 9 sum of its digits must be multiple of 9, as n is two-digit number <99 then the sum of its digits must be 9 (18, 27, 36, ..., 90.). Suffiicient.

1. INSUFFICIENT e.g. take y = 2, if n = 6, 6 x 2^2 = 24, sum of digits is 6 if n = 3, 3 x 2^2 = 12, sum of digits is 3

2. INSUFFICIENT e.g. y = 3 then y^4 = 81 (a 2 digit odd number) if y = 5^1/2 then y^4=25 (a 2 digit odd number)

1. & 2. SUFFICIENT y = 3 (the only prime number with an odd two digit result when raised to the 4th power) therefore n is a multiple of 9, and the sum of the digits of all multiples of 9 is 9.

1. & 2. SUFFICIENT y = 3 (the only prime number with an odd two digit result when raised to the 4th power) therefore n is a multiple of 9, and the sum of the digits of all multiples of 9 is 9.

The sum of the digits of all multiples of 9 is divisible by 9. It is not generally equal to 9. For example, 99 is divisible by 9, and the sum of its digits is 18.

That turns out not to affect the solution here, however, since we are only concerned with two-digit numbers less than 99, and the sum of the digits of every multiple of nine between 18 and 90 inclusive is always 9.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Stmt 1 tells you that y is a small prime integer because the square has to be lower than 99 and has to have a multiple lower than 99. This leaves us 3 and 5 but we. So insuff

stmt 2 tells us that y is 3 or less but is insuff by itself because the stem of the question does not say anything about y

together y = 3 and stmt 1 tells us that it is divisible by 9 and for something to be divisible by 9 the digits add up to 9.

Re: What is the sum of the digits of the positive integer n [#permalink]

Show Tags

23 Nov 2012, 22:57

1

This post received KUDOS

OK, so if we're going with your version...

Quote:

What is the sum of the digits of the positive integer n where n<99 ?

1) n is divisible by the square of y.

2) y*y*y*y (y raised to the power 4) is equal to a two digit positive odd integer.

Statement 1: We don't even know that y is an integer, so the square of y could be anything... which means that n could be anything, too. (The square of y could, for example, be 1.) -- incredibly insufficient

Statement 2: We don't know that y is an integer, so y^4 could be any two-digit positive odd integer... and that gives us 45 possible values for y^4, most of which are not integers. And the statement says absolutely nothing about n. -- still incredibly insufficient

Together: y^4 could be any two-digit odd integer, which means that we have tons of possible values for y^2, including 5, 7, and 9. N could then be any multiple of 5, 7, or 9. -- still not sufficient

So in the version without the phrase "prime number" in statement 1, the answer would definitely be E.
_________________

Helping students kick the GMAT in the nuts since 2002... http://www.gmatninja.com.

Re: What is the sum of the digits of the positive integer n [#permalink]

Show Tags

23 Nov 2012, 21:24

I think your conclusion is correct, harsh6239, though I'm pretty sure that this is an MGMAT question, and I found a slightly different version of it elsewhere:

What is the sum of the digits of the positive integer n where n < 99?

(1) n is divisible by the square of the prime number y. (2) y^4 is a two-digit odd integer.

So if we go with the version that specifies that y is prime, then...

Statement 1: y could be any number of primes, which means that n must be divisible by 4, 9, 25, or 49. And that really doesn't narrow things down very much. -- not sufficient

Statement 2: tells us absolutely nothing about n. -- not sufficient

Together: since we know that y is prime, then y^4 could be 16 or 81... except that y^4 has to be odd. So y^4 must be 81. And if n < 99, then n must also be 81.

The answer is C, and you were completely correct.
_________________

Helping students kick the GMAT in the nuts since 2002... http://www.gmatninja.com.

Re: What is the sum of the digits of the positive integer n [#permalink]

Show Tags

23 Nov 2012, 22:05

GMATNinja wrote:

I think your conclusion is correct, harsh6239, though I'm pretty sure that this is an MGMAT question, and I found a slightly different version of it elsewhere:

What is the sum of the digits of the positive integer n where n < 99?

(1) n is divisible by the square of the prime number y. (2) y^4 is a two-digit odd integer.

So if we go with the version that specifies that y is prime, then...

Statement 1: y could be any number of primes, which means that n must be divisible by 4, 9, 25, or 49. And that really doesn't narrow things down very much. -- not sufficient

Statement 2: tells us absolutely nothing about n. -- not sufficient

Together: since we know that y is prime, then y^4 could be 16 or 81... except that y^4 has to be odd. So y^4 must be 81. And if n < 99, then n must also be 81.

The answer is C, and you were completely correct.

Thank you sir for your reply. The slightly different version of question which you have given here states that y is a prime and hence an integer. My confusion in the original question which I had posted is that if we see statement 2 then y^4 is equal to a two digit odd integer and so y need not be an integer always. so going back to statement 1 then y^2 may be a fraction and not necessarily 9. In this case answer will be E. How to confirm this one mathematically ?

Stmt 1 tells you that y is a small prime integer because the square has to be lower than 99 and has to have a multiple lower than 99. This leaves us 3 and 5 but we. So insuff

stmt 2 tells us that y is 3 or less but is insuff by itself because the stem of the question does not say anything about y

together y = 3 and stmt 1 tells us that it is divisible by 9 and for something to be divisible by 9 the digits add up to 9.

I think your conclusion to (1) is incomplete. y could also = 7, because (7^2)*2 = 98, which is < 99.

Re: What is the sum of the digits of the positive integer n [#permalink]

Show Tags

31 Jan 2015, 04:57

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: What is the sum of the digits of the positive integer n [#permalink]

Show Tags

10 Oct 2016, 18:47

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

There is without a doubt a stereotype for recent MBA grads – folks who are ambitious, smart, hard-working, but oftentimes lack experience or domain knowledge. Looking around and at...