GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Nov 2018, 15:56

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
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
8
00:00

Difficulty:

85% (hard)

Question Stats:

61% (02:48) correct 39% (02:49) wrong based on 326 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.

_________________

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.
Math Expert
Joined: 02 Sep 2009
Posts: 50711
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
5
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.

_________________
##### 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: 475
Location: United Kingdom
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: 50711
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.

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: 6529
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 \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 07 May 2017
Posts: 3
Re: What is the value of the three-digit number SSS if SSS is the sum of  [#permalink]

### Show Tags

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.

Hey Bunuel, why are we ruling out $$\sqrt{xz/8}$$=0?
Math Expert
Joined: 02 Sep 2009
Posts: 50711
Re: What is the value of the three-digit number SSS if SSS is the sum of  [#permalink]

### Show Tags

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.

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.
_________________
Intern
Joined: 16 Aug 2018
Posts: 29
Concentration: General Management, Strategy
Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36
Re: What is the value of the three-digit number SSS if SSS is the sum of  [#permalink]

### Show Tags

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 &nbs [#permalink] 27 Aug 2018, 20:39
Display posts from previous: Sort by