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

Question

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.

Bunuel · Accepted Answer

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.

enigma123 · Answer

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.

pappueshwar · Answer

hi bunuel,

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

Bunuel · Answer

(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.

ishdeep18 · Answer

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

Thanks

MathRevolution · Answer

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.

gmatpreprb26 · Answer

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

Bunuel · Answer

This would imply that S = 0. In this case SSS = 000, which is not a three-digit number but a single digit number 0.

shmba · Answer

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

osama750 · Answer

How did you directly conclude that  S^2 = 49zx/8 -->  S=7*\sqrt{\frac{zx}{8}} ? My understanding is that 49zx is a 4 digit number. Not sure if I have the conceptual clarity. Please help.

Bunuel · Answer

49zx is not a four-digit number, it's 49*z*x. If it were, it would have been specifically mentioned. So, we get  S=7*\sqrt{\frac{zx}{8}}  from S^2= 49zx/8 by simply taking the square root from it.

peaarrr · Answer

How about the case where sqrt(49zx/8) here = 1/7? So that would give the S value as 1 and SSS = 111.

Bunuel · Answer

\sqrt{\frac{zx}{8}}=\frac{1}{7} ;

\frac{zx}{8}=\frac{1}{49} ;

zx=\frac{8}{49} .

The above does not have solutions for  digits  z and x.

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

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