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, 19:17

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Question Stats:

71% (03:14) correct

28% (03:50) wrong

based on 2 sessions

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.

[Reveal] Spoiler: OA

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Last edited by Bunuel on 31 Jan 2012, 19:37, edited 1 time in total.

Added the OA

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Re: SSS [#permalink]

31 Jan 2012, 19:36

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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 = 1.75X --> 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.
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Director

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Re: What is the value of the three-digit number SSS if SSS is [#permalink]

02 Feb 2012, 11:13

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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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Re: What is the value of the three-digit number SSS if SSS is [#permalink]

02 Feb 2012, 11:03

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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Re: What is the value of the three-digit number SSS if SSS is [#permalink]

02 Feb 2012, 11:19

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: What is the value of the three-digit number SSS if SSS is [#permalink]

24 May 2013, 04:20

Bumping for review and further discussion.
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Re: What is the value of the three-digit number SSS if SSS is [#permalink] 24 May 2013, 04:20

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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

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