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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # The sum of the digits of [(10^x)^y]-64=279. What is the  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Status: Prevent and prepare. Not repent and repair!! Joined: 13 Feb 2010 Posts: 196 Location: India Concentration: Technology, General Management GPA: 3.75 WE: Sales (Telecommunications) The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] ### Show Tags Updated on: 29 Oct 2012, 00:59 3 24 00:00 Difficulty: 75% (hard) Question Stats: 60% (02:14) correct 40% (02:20) wrong based on 339 sessions ### HideShow timer Statistics The sum of the digits of [(10^x)^y]-64=279. What is the value of xy ? A. 28 B. 29 C. 30 D. 31 E. 32 _________________ I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+ Originally posted by rajathpanta on 28 Oct 2012, 09:18. Last edited by Bunuel on 29 Oct 2012, 00:59, edited 2 times in total. Renamed the topic and edited the question. ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink] ### Show Tags 29 Oct 2012, 00:59 8 11 rajathpanta wrote: The sum of the digits of [(10^x)^y]-64=79. What is the value of xy A. 28 B. 29 C. 30 D. 31 E. 32 The question should read: The sum of the digits of [(10^x)^y]-64=279. What is the value of xy A. 28 B. 29 C. 30 D. 31 E. 32 Also, it should be mentioned that xy is a positive integers. First of all $$(10^x)^y=10^{xy}$$. $$10^{xy}$$ has $$xy+1$$ digits: 1 and $$xy$$ zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros; $$10^{xy}-64$$ will have $$xy$$ digits: $$xy-2$$ 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end; We are told that the sum of all the digits of $$10^{xy}-64$$ is 279 --> $$9(xy-2)+3+6=279$$ --> $$9(xy-2)=270$$ --> $$xy=32$$. Answer: E. Similar questions to practice: the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html 10-25-560-is-divisible-by-all-of-the-following-except-126300.html if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html Hope it's clear. _________________ ##### Most Helpful Community Reply Intern Status: Active Joined: 30 Jun 2012 Posts: 37 Location: India Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] ### Show Tags 29 Oct 2012, 01:26 4 1 As Question is $$(10^x)^y - 64$$ . Let say $$(10^x)^y$$ as Number1 Say Number1 - 64 = Number2 ==> 100 - 64 = 36 [ Number1: No. of zeroes = 2 , Number2: No. of 9's = zero ] and Sum of digits of Number 2 : 9*0 + (3+6) = 1*9 = 9 1000 - 64 = 936 [ Number1: No. of zeroes = 3 , Number2: No. of 9's = 1] and Sum of digits of Number 2 : 9*1 + (3+6) = 9 + 9 = 2*9 = 18 10000 - 64 = 9936 [ Number1: No. of zeroes = 4 , Number2: No. of 9's = 2] and Sum of digits of Number 2 : 9*2 + (3+6) = 18 + 9 = 3*9= 27 100000 - 64 = 99936 [ Number1: No. of zeroes = 5 , Number2: No. of 9's = 3] and Sum of digits of Number 2 : 9*3 + (3+6) = 27 + 9 =4*9= 36 so lets go from right to left for the sum of digits of number2 i.e given as 279 so 279 = 31*9 = 9*30 + (3+6) => Number2: Number of 9's = 30 ==> Number1: Number of zeros = 32 So the Number1 i.e. $$(10^x)^y = 10000.....(32 zeroes)$$ Now, as we now, $$10^1$$ = 10 (1 zero) $$10^2$$ = 100 (2 zeroes) $$10^3$$ = 1000 (3 zeroes) same way, 10000.....(32 zeroes) = $$10^32$$ $$(10^x)^y = 10^(xy) = 10^32$$ ==> xy = 32 _________________ Thanks and Regards! P.S. +Kudos Please! in case you like my post. ##### General Discussion Manager Status: Fighting hard Joined: 04 Jul 2011 Posts: 60 GMAT Date: 10-01-2012 Re: The Sum of the digits of(10^x)^y [#permalink] ### Show Tags 28 Oct 2012, 10:13 I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here. _________________ I will rather do nothing than be busy doing nothing - Zen saying Manager Status: Prevent and prepare. Not repent and repair!! Joined: 13 Feb 2010 Posts: 196 Location: India Concentration: Technology, General Management GPA: 3.75 WE: Sales (Telecommunications) Re: The Sum of the digits of(10^x)^y [#permalink] ### Show Tags 28 Oct 2012, 10:22 Pansi wrote: I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here. Well, It is a multiple of 9. How will you arrive at xy with that approach? Try finding patterns. (thats the clue) _________________ I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+ Director Status: Done with formalities.. and back.. Joined: 15 Sep 2012 Posts: 595 Location: India Concentration: Strategy, General Management Schools: Olin - Wash U - Class of 2015 WE: Information Technology (Computer Software) Re: The Sum of the digits of(10^x)^y [#permalink] ### Show Tags 28 Oct 2012, 18:44 1 Pansi wrote: I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here. Well, simple reason is that the question is incorrect. rajathpanta wrote: Well, It is a multiple of 9. How will you arrive at xy with that approach? Try finding patterns. (thats the clue) Question is: 10^xy -64 = N, where sum of digits of N=79 The pattern is like this: 100 -64 = 36 1000 -64 = 936 10000 -64 =9936 or, 1 followed by (n times 0) = (n-2)times 9 followed by 36 Therefore sumof digits on right side is always a multiple of 9 [9s and 6+3 =9] However in question stem RHS is 79, which is not divisible by 9. And therefore you can not arrive at any of the answer choices given. Rajathpanta- on a lighter note - if this too is from Aristotle, I'd suggest please change the source of questions. :D Hope it helps! _________________ Lets Kudos!!! Black Friday Debrief Intern Joined: 04 Aug 2013 Posts: 6 Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink] ### Show Tags 24 Nov 2013, 18:36 Hi Bunuel, Could you please xplain the last bit oft he equations which takes us to a 279? Thanks quote="Bunuel"] rajathpanta wrote: The sum of the digits of [(10^x)^y]-64=79. What is the value of xy A. 28 B. 29 C. 30 D. 31 E. 32 The question should read: The sum of the digits of [(10^x)^y]-64=279. What is the value of xy A. 28 B. 29 C. 30 D. 31 E. 32 Also, it should be mentioned that xy is a positive integers. First of all $$(10^x)^y=10^{xy}$$. $$10^{xy}$$ has $$xy+1$$ digits: 1 and $$xy$$ zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros; $$10^{xy}-64$$ will have $$xy$$ digits: $$xy-2$$ 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end; We are told that the sum of all the digits of $$10^{xy}-64$$ is 279 --> $$9(xy-2)+3+6=279$$ --> $$9(xy-2)=270$$ --> $$xy=32$$. Answer: E. Similar questions to practice: the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html 10-25-560-is-divisible-by-all-of-the-following-except-126300.html if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html Hope it's clear.[/quote] Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: The sum of the digits of [(10^x)^y]-64=79. What is the value [#permalink] ### Show Tags 25 Nov 2013, 01:52 1 Shibs wrote: Hi Bunuel, Could you please xplain the last bit oft he equations which takes us to a 279? Thanks quote="Bunuel"] rajathpanta wrote: The sum of the digits of [(10^x)^y]-64=79. What is the value of xy A. 28 B. 29 C. 30 D. 31 E. 32 The question should read: The sum of the digits of [(10^x)^y]-64=279. What is the value of xy A. 28 B. 29 C. 30 D. 31 E. 32 Also, it should be mentioned that xy is a positive integers. First of all $$(10^x)^y=10^{xy}$$. $$10^{xy}$$ has $$xy+1$$ digits: 1 and $$xy$$ zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros; $$10^{xy}-64$$ will have $$xy$$ digits: $$xy-2$$ 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end; We are told that the sum of all the digits of $$10^{xy}-64$$ is 279 --> $$9(xy-2)+3+6=279$$ --> $$9(xy-2)=270$$ --> $$xy=32$$. Answer: E. Similar questions to practice: the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html 10-25-560-is-divisible-by-all-of-the-following-except-126300.html if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html Hope it's clear. $$10^{xy}-64$$ will have $$xy$$ digits: $$xy-2$$ 9's and 36 in the and. Threfore the sum of the digits is $$9(xy-2)+3+6=279$$. Hope it's clear. _________________ Manager Status: Student Joined: 26 Aug 2013 Posts: 190 Location: France Concentration: Finance, General Management Schools: EMLYON FT'16 GMAT 1: 650 Q47 V32 GPA: 3.44 Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] ### Show Tags 08 Jan 2014, 03:19 1 Hi, this is my process (edited to be the most efficient possible): $$1000-64= 936$$. Whatever XY is you finish with $$36 ==> 3+6=9$$ Therefore, $$279-9=270$$ and $$270/9=30$$ Now you add the last two digits (3 and 6) Answer is $$30+2=32$$ Hope it helps _________________ Think outside the box CEO Joined: 20 Mar 2014 Posts: 2633 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] ### Show Tags 30 Jan 2016, 06:00 1 rajathpanta wrote: The sum of the digits of [(10^x)^y]-64=279. What is the value of xy ? A. 28 B. 29 C. 30 D. 31 E. 32 Sum of the digits of (10^x)^y - 64 = 279. We know that (X^a)^b = X^(ab) Thus, the given form becomes = 10^(xy) - 64. Now start with xy=2, 10^2 - 64 = 36, sum of the digits = 6+3=9 (realize that the sum of digits is 9*(xy-1)) xy=3 ---> 1000-64=936 = 18 (realize that the sum of digits is 9*(xy-1)) xy=4 ---> 10000-64=9936 = 27 (realize that the sum of digits is 9*(xy-1)) xy=5 ---> 100000-64 = 99936 (realize that the sum of digits is 9*(xy-1))... etc so this is your pattern. The sum of the digits = 9*(xy-1) Now sum of the digits given = 279. Thus, based on the pattern above, the sum of the digits must be ---> 9*(xy-1) = 279 ---> xy = 32. E is thus the correct answer. Hope this helps. Board of Directors Joined: 17 Jul 2014 Posts: 2618 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] ### Show Tags 24 Feb 2016, 17:32 gosh..the structure of the question is hideous... i solved it this way.. the sum is 279. the last 2 digits must be 3 and 6, or 9. so the rest will be a bunch of 9's. how many 9's? 30. now, 30 of nines + 36 -> 32 digits +1 since we need to round up - 33 in total, we thus must have 10^32. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13095 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The sum of the digits of [(10^x)^y]-64=279. What is the [#permalink] ### Show Tags 27 Mar 2018, 10:43 Hi All, This question has some awkward wording to it, but here's its intent: the number 10^(xy) - 64 has digits that add up to 279. So, we need to figure out what THAT number is. Here's what you need to "see" to solve this problem: IF xy = 3, then 1,000 - 64 = 936 and the sum of digits = 18 = (2)(9) If xy = 4, then 10,000 - 64 = 9,936 and the sum of digits = 27 = (3)(9) If xy = 5, then 100,000 - 64 = 99,936 and the sum of digits = 36 = (4)(9) Notice the pattern? The sum of digits is increasing by 9 every time. So, how many times does 9 divide into 279? 31 times As a reminder of the pattern: xy = 3 --> (2)(9) xy = 4 --> (3)(9) xy = 5 --> (4)(9) So, (31)(9) --> xy = 32 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The sum of the digits of [(10^x)^y]-64=279. What is the &nbs [#permalink] 27 Mar 2018, 10:43
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