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What is the value of the three-digit number SSS if SSS is

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What is the value of the three-digit number SSS if SSS is [#permalink]  31 Jan 2012, 18:17
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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.

[Reveal] Spoiler: OA

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MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Last edited by Bunuel on 31 Jan 2012, 18:37, edited 1 time in total.
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Re: SSS [#permalink]  31 Jan 2012, 18:36
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Expert's post
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.

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Re: What is the value of the three-digit number SSS if SSS is [#permalink]  02 Feb 2012, 10:03
hi bunuel,

unable to understand ur explanation. how are u arriving at values 4 and 7? and option B
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eshwar

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Status: Finally Done. Admitted in Kellogg for 2015 intake
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WE: Information Technology (Consulting)
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Re: What is the value of the three-digit number SSS if SSS is [#permalink]  02 Feb 2012, 10:13
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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.
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Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

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Posts: 29217
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Kudos [?]: 50427 [1] , given: 7546

Re: What is the value of the three-digit number SSS if SSS is [#permalink]  02 Feb 2012, 10:19
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Expert's post
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.
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Re: SSS [#permalink]  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.

very nicely explained Bunuel.. I was totally tricked... started thinking too much on this.. it was simple and answer was in question only.

Thanks
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Re: What is the value of the three-digit number SSS if SSS is [#permalink]  06 Oct 2014, 23:29
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