Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 26 Aug 2010
Posts: 70
Location: India

What is the sum of the digits of the positive integer n [#permalink]
Show Tags
04 Nov 2010, 07:24
7
This post received KUDOS
5
This post was BOOKMARKED
Question Stats:
65% (01:35) correct 35% (01:27) wrong based on 536 sessions
HideShow timer Statistics
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 twodigit odd integer.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Spread some happiness..Press Kudos!



Math Expert
Joined: 02 Sep 2009
Posts: 43867

What is the sum of the digits of the positive integer n [#permalink]
Show Tags
04 Nov 2010, 08:20
4
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
samark wrote: 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 twodigit 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 twodigit 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 twodigit number <99 then the sum of its digits must be 9 (18, 27, 36, ..., 90.). Suffiicient. Answer: C.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 11 Nov 2011
Posts: 14

Re: what is the sum.... [#permalink]
Show Tags
26 Nov 2011, 05:09
1
This post received KUDOS
1
This post was BOOKMARKED
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.



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Re: what is the sum.... [#permalink]
Show Tags
26 Nov 2011, 06:27
bobfirth wrote: 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 twodigit 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



Manager
Joined: 08 Sep 2011
Posts: 65
Concentration: Finance, Strategy

Re: what is the sum.... [#permalink]
Show Tags
05 Dec 2011, 10:42
1
This post received KUDOS
+1 C
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.



GMAT Club Verbal Expert
Status: GMAT and GRE tutor
Joined: 13 Aug 2009
Posts: 1448
Location: United States
GMAT 1: 780 Q51 V46 GMAT 2: 800 Q51 V51
GRE 1: 340 Q170 V170

Re: What is the sum of the digits of the positive integer n [#permalink]
Show Tags
23 Nov 2012, 20:24
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 twodigit 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.
_________________
GMAT Club Verbal Expert  GMAT/GRE tutor @ www.gmatninja.com (Now hiring!)  GMAT blog  Food blog  Notoriously bad at PMs
Beginners' guides to GMAT verbal Reading Comprehension  Critical Reasoning  Sentence Correction
YouTube LIVE verbal webinars Series 1: Fundamentals of SC & CR  Series 2: Developing a Winning GMAT Mindset  starts February 14!
SC & CR Questions of the Day (QOTDs), featuring expert explanations All QOTDs  Subscribe via email  RSS
Need an expert reply? Hit the request verbal experts' reply button  and please be specific about your question. Feel free to tag @GMATNinja and @GMATNinjaTwo in your post.
Sentence Correction articles & resources How to go from great (760) to incredible (780) on GMAT SC  That "ing" Word Probably Isn't a Verb  That "ed" Word Might Not Be a Verb, Either  NoBS Guide to GMAT Idioms  "Being" is not the enemy  WTF is "that" doing in my sentence?
Reading Comprehension, Critical Reasoning, and other articles & resources All GMAT Ninja articles on GMAT Club  Using LSAT for GMAT CR & RC 7 reasons why your actual GMAT scores don't match your practice test scores  How to get 4 additional "fake" GMAT Prep tests for $29.99... in any section order



Intern
Joined: 30 Oct 2012
Posts: 18
Location: United States
Concentration: General Management, Entrepreneurship
WE: Science (Transportation)

Re: What is the sum of the digits of the positive integer n [#permalink]
Show Tags
23 Nov 2012, 21:05
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 twodigit 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 ?



GMAT Club Verbal Expert
Status: GMAT and GRE tutor
Joined: 13 Aug 2009
Posts: 1448
Location: United States
GMAT 1: 780 Q51 V46 GMAT 2: 800 Q51 V51
GRE 1: 340 Q170 V170

Re: What is the sum of the digits of the positive integer n [#permalink]
Show Tags
23 Nov 2012, 21:57
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 twodigit 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 twodigit 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.
_________________
GMAT Club Verbal Expert  GMAT/GRE tutor @ www.gmatninja.com (Now hiring!)  GMAT blog  Food blog  Notoriously bad at PMs
Beginners' guides to GMAT verbal Reading Comprehension  Critical Reasoning  Sentence Correction
YouTube LIVE verbal webinars Series 1: Fundamentals of SC & CR  Series 2: Developing a Winning GMAT Mindset  starts February 14!
SC & CR Questions of the Day (QOTDs), featuring expert explanations All QOTDs  Subscribe via email  RSS
Need an expert reply? Hit the request verbal experts' reply button  and please be specific about your question. Feel free to tag @GMATNinja and @GMATNinjaTwo in your post.
Sentence Correction articles & resources How to go from great (760) to incredible (780) on GMAT SC  That "ing" Word Probably Isn't a Verb  That "ed" Word Might Not Be a Verb, Either  NoBS Guide to GMAT Idioms  "Being" is not the enemy  WTF is "that" doing in my sentence?
Reading Comprehension, Critical Reasoning, and other articles & resources All GMAT Ninja articles on GMAT Club  Using LSAT for GMAT CR & RC 7 reasons why your actual GMAT scores don't match your practice test scores  How to get 4 additional "fake" GMAT Prep tests for $29.99... in any section order



Intern
Joined: 21 Oct 2012
Posts: 13

Re: What is the sum of the digits of the positive integer n [#permalink]
Show Tags
24 Nov 2012, 06:28
3
This post received KUDOS
samark wrote: 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 twodigit odd integer. Statement 1 : Square of prime number less than 99 leaves us with 3,5,7,9 (Not sufficient) Statement 2 : y^4 is a two digit odd integer (Not sufficient) But when we combine both the we are left only with y=3 and the n is divisible by 9, so we get a unique answer which also 9 Answer : C



Senior Manager
Joined: 10 Mar 2013
Posts: 261
GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39

Re: what is the sum.... [#permalink]
Show Tags
03 Jan 2014, 21:50
Bowtie wrote: +1 C
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.



Retired Moderator
Joined: 12 Aug 2015
Posts: 2424
GRE 1: 323 Q169 V154

Re: What is the sum of the digits of the positive integer n [#permalink]
Show Tags
11 Dec 2016, 10:33
Fun Property of first ten multiples 9 > 09 18 27 36 45 54 63 72 81 90
The units digit is increasing by 1 and units digit is decreasing by 1=> Sum of digits remain the same =9
From 1 and 2 => y must be 3 Hence x must be a multiple of 9 between 0 and 99 Hence sum of its digits must be 9
Hence C
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)



Manager
Joined: 13 Apr 2010
Posts: 88

Re: What is the sum of the digits of the positive integer n [#permalink]
Show Tags
18 Jan 2017, 05:42
Nahid078 wrote: 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^4 is a twodigit positive odd integer. From Statement 1, n is divisible by square of y . y can be 1 , 4 , 9, 16 ... Clearly Insufficient . From Statement 2 , Y^4 is a two digit positive odd integer y^4 = 81 => y = 3 No information on n . So, statement is Insufficient . Combine , we know that sum of digits of n is equal to 9 . Answer is C .



Manager
Joined: 03 May 2014
Posts: 166
Location: India
WE: Sales (Mutual Funds and Brokerage)

Re: What is the sum of the digits of the positive integer n [#permalink]
Show Tags
04 Aug 2017, 01:34
n<99 or n can be any of the following no 98, 97......1
Statement 1 n is divisible by the square of the prime number y
Prime nos 2, 3, 5, 7, 11.....
Square of prime 4, 9, 25, 49, 121 n can be divisible by any of the above prime nos till 7since n<99
Statement2y⁴ is a twodigit odd integer what is yNo information hence statement is not sufficient
Statement 1 and 2. y is primey² divides n and y⁴ is a 2 digit odd no.
Test the nos 2is even 33²=9 and 3⁴=81=odd. Hence the no is divisible by 9 and any no is divisible by 9 if its sum must be divisible by 9. since n<99 the n is a 2 digit no whose sum=9(18, 27, 36, 72, 81)




Re: What is the sum of the digits of the positive integer n
[#permalink]
04 Aug 2017, 01:34






