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• ### $450 Tuition Credit & Official CAT Packs FREE February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT practice February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST Instead of wasting 3 months solving 5,000+ random GMAT questions, focus on just the 1,500 you need. # What is the value of the three-digit number SSS if SSS is the sum of  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Senior Manager Status: Finally Done. Admitted in Kellogg for 2015 intake Joined: 25 Jun 2011 Posts: 468 Location: United Kingdom Concentration: International Business, Strategy GMAT 1: 730 Q49 V45 GPA: 2.9 WE: Information Technology (Consulting) What is the value of the three-digit number SSS if SSS is the sum of [#permalink] ### Show Tags Updated on: 15 Dec 2017, 23:44 5 10 00:00 Difficulty: 85% (hard) Question Stats: 60% (02:49) correct 40% (02:51) wrong based on 335 sessions ### HideShow timer Statistics What is the value of the three-digit number SSS if SSS is the sum of the three-digit numbers ABC and XYZ, where each letter represents a distinct digit from 0 to 9, inclusive? (1) S = 1.75 X (2) S^2 = 49zx/8 I don't have an OA but for me the answer is D. This is how I got it. Again please check my approach and let me know if anything is not right. Statement 1 S = 1.75 x ==> 175 x/100 ==>7x/4. x has to be a multiple of 4 for S to be an integer. So x can ONLY be 4. X cannot be 8 or any other multiple of 4 because if we take x = 8 then S =14 which is a 2 digit number. So S = 7. Therefore SSS is 777. Sufficient. Statement 2 $$S^2$$ = 49zx/8 ==> S = 7 $$\sqrt{zx/8}]$$. Now since S is an integer, 7 $$\sqrt{zx/8}$$ must be an integer as well. Also, 7 $$\sqrt{zx/8}$$must also be less than 10. and this can only happen when $$\sqrt{zx/8}$$ = 1. Therefore, S = 7(1) = 7 and SSS will become 777. Sufficient. Therefore D is my answer. _________________ Best Regards, E. MGMAT 1 --> 530 MGMAT 2--> 640 MGMAT 3 ---> 610 GMAT ==> 730 Originally posted by enigma123 on 31 Jan 2012, 18:17. Last edited by Bunuel on 15 Dec 2017, 23:44, edited 2 times in total. Added the OA ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 52905 Re: What is the value of the three-digit number SSS if SSS is the sum of [#permalink] ### Show Tags 31 Jan 2012, 18:36 6 2 What is the value of the three-digit number SSS if SSS is the sum of the three-digit numbers ABC and XYZ, where each letter represents a distinct digit from 0 to 9, inclusive? (1) S = 1.75X --> as S and X are digits, then X must be 4 and S must be 7: 7=1.75*4 --> SSS=777. Sufficient. (2) S^2= 49zx/8 --> $$S=7*\sqrt{\frac{zx}{8}}$$ --> again as S is a digit then $$\sqrt{\frac{zx}{8}}$$ must be 1 --> S=7 --> SSS=777. Sufficient. Answer: D. _________________ ##### General Discussion Intern Joined: 25 Aug 2010 Posts: 17 Re: What is the value of the three-digit number SSS if SSS is the sum of [#permalink] ### Show Tags 02 Feb 2012, 10:03 hi bunuel, unable to understand ur explanation. how are u arriving at values 4 and 7? and option B _________________ regards eshwar Senior Manager Status: Finally Done. Admitted in Kellogg for 2015 intake Joined: 25 Jun 2011 Posts: 468 Location: United Kingdom Concentration: International Business, Strategy GMAT 1: 730 Q49 V45 GPA: 2.9 WE: Information Technology (Consulting) Re: What is the value of the three-digit number SSS if SSS is the sum of [#permalink] ### Show Tags 02 Feb 2012, 10:13 2 Hi pappueshwar I thought to reply on behalf of Bunuel, but Bunuel can always correct me if he thinks I am wrong. Statement 1 S=1.75 x and question says S is an integer and each letter represents a distinct digit So if we take x = 4 then S = 1.75 *4 then S = 7. Only 4 can give us S as an integer and therefore x has to be 4. Considering statement 2 S^2= 49zx/8 S = 7 * square root of 49zx/8. Again for S to be an integer square root of 49zx/8 has to be 1 as no other value fits the bill. I hope I answered your question. I f I haven't then please free to let me know and I will explain it again. _________________ Best Regards, E. MGMAT 1 --> 530 MGMAT 2--> 640 MGMAT 3 ---> 610 GMAT ==> 730 Math Expert Joined: 02 Sep 2009 Posts: 52905 Re: What is the value of the three-digit number SSS if SSS is the sum of [#permalink] ### Show Tags 02 Feb 2012, 10:19 2 pappueshwar wrote: hi bunuel, unable to understand ur explanation. how are u arriving at values 4 and 7? and option B (1) $$S=1.75*X=\frac{7}{4}*X$$. Notice that X and S are single digits, hence $$\frac{7}{4}*X$$ must equal to a single digit which is only possible for X=4 --> $$\frac{7}{4}*4=7=S$$, for other values of X, $$\frac{7}{4}*X$$ is either more than 9, so not a single digit or/and not an integer at all. (There is though one more case for X=0 --> S=0, but stems says that each letter represents a distinct digit, so this option is also out.) The same logic applies to (2). Hope it's clear. _________________ Intern Joined: 23 Jul 2013 Posts: 19 Re: What is the value of the three-digit number SSS if SSS is the sum of [#permalink] ### Show Tags 11 Sep 2013, 23:58 Bunuel wrote: What is the value of the three-digit number SSS if SSS is the sum of the three-digit numbers ABC and XYZ, where each letter represents a distinct digit from 0 to 9, inclusive? (1) S = 1.75X --> as S and X are digits, then X must be 4 and S must be 7: 7=1.75*4 --> SSS=777. Sufficient. (2) S^2= 49zx/8 --> $$S=7*\sqrt{\frac{zx}{8}}$$ --> again as S is a digit then $$\sqrt{\frac{zx}{8}}$$ must be 1 --> S=7 --> SSS=777. Sufficient. Answer: D. very nicely explained Bunuel.. I was totally tricked... started thinking too much on this.. it was simple and answer was in question only. Thanks Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of the three-digit number SSS if SSS is the sum of [#permalink] ### Show Tags 22 Nov 2015, 01:20 Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. What is the value of the three-digit number SSS if SSS is the sum of the three-digit numbers ABC and XYZ, where each letter represents a distinct digit from 0 to 9, inclusive? 1) S = 1.75 X 2) S^2 = 49zx/8 There are 6 variables (x,y,z,a,b,c), but only 2 equations are given by the 2 conditions, so there is high chance (E) will be the answer. Looking at the conditions together, From condition 1, S=175x/100=7x/4, S and x are all integers, and x=4, S=7. From condition 2, S^2=49zx/8, z=sqrt (49zx/8)=7sqrt(zx/8)=7 (because S is 1-digit integer) Condition 1 = condition 2, and the answer becomes (D). For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: What is the value of the three-digit number SSS if SSS is the sum of  [#permalink]

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08 Nov 2017, 23:50
Bunuel wrote:
What is the value of the three-digit number SSS if SSS is the sum of the three-digit numbers ABC and XYZ, where each letter represents a distinct digit from 0 to 9, inclusive?

(1) S = 1.75X --> as S and X are digits, then X must be 4 and S must be 7: 7=1.75*4 --> SSS=777. Sufficient.

(2) S^2= 49zx/8 --> $$S=7*\sqrt{\frac{zx}{8}}$$ --> again as S is a digit then $$\sqrt{\frac{zx}{8}}$$ must be 1 --> S=7 --> SSS=777. Sufficient.

Answer: D.

Hey Bunuel, why are we ruling out $$\sqrt{xz/8}$$=0?
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Re: What is the value of the three-digit number SSS if SSS is the sum of  [#permalink]

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09 Nov 2017, 00:53
1
richabala26 wrote:
Bunuel wrote:
What is the value of the three-digit number SSS if SSS is the sum of the three-digit numbers ABC and XYZ, where each letter represents a distinct digit from 0 to 9, inclusive?

(1) S = 1.75X --> as S and X are digits, then X must be 4 and S must be 7: 7=1.75*4 --> SSS=777. Sufficient.

(2) S^2= 49zx/8 --> $$S=7*\sqrt{\frac{zx}{8}}$$ --> again as S is a digit then $$\sqrt{\frac{zx}{8}}$$ must be 1 --> S=7 --> SSS=777. Sufficient.

Answer: D.

Hey Bunuel, why are we ruling out $$\sqrt{xz/8}$$=0?

This would imply that S = 0. In this case SSS = 000, which is not a three-digit number but a single digit number 0.
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Re: What is the value of the three-digit number SSS if SSS is the sum of  [#permalink]

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27 Aug 2018, 20:39
alternative approach for statement 2:
S^2= 49zx/8
we can see S has 7 as its prime factor. out of SSS, only 777 can be evenly divided by 7. so SSS has to be 777
Re: What is the value of the three-digit number SSS if SSS is the sum of   [#permalink] 27 Aug 2018, 20:39
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