Author 
Message 
TAGS:

Hide Tags

VP
Joined: 04 May 2006
Posts: 1210
Schools: CBS, Kellogg

If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
10 Jun 2008, 22:37
Question Stats:
74% (01:40) correct 26% (01:19) wrong based on 635 sessions
HideShow timer Statistics
If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ? (1) y = 6 (2) z = 3
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15958
Location: United States (CA)

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
25 Dec 2014, 11:37
Hi All, This post is from years ago, but the prompt still serves as an example of how TESTing VALUES can help you to prove the correct answer in many DS questions. We're told that X, Y and Z are POSITIVE INTEGERS. We're asked for the REMAINDER when 100X + 10Y + Z is divided by 7. Fact 1: Y = 6 Since we don't know the values of X or Z, let's TEST VALUES. Technically, we can use ANY positive integers for X and Z, but I'm going to keep things simple... X = 1, Z = 1 (100 + 60 + 1)/7 161/7 = 23r0 so the answer is 0 X = 1, Z = 3 (100 + 60 + 3)/7 163/7 = 23r2 so the answer is 2 Fact 1 is INSUFFICIENT Fact 2: Z = 3 Again, we can use ANY positive integers for X and Y, but let's keep things simple... We can use the second example from Fact 1 here... X = 1, Y = 6, Z = 3 163/7 = 23r2 so the answer is 2 X = 1, Y = 1, Z = 3 (100 + 10 + 3)/7 113/7 = 16r1 so the answer is 1 Fact 2 is INSUFFICIENT Combined, we know Y = 6 Z = 3 X = ANY POSITIVE INTEGER If X = 1 (from our prior work) 163/7 = 23r2 so the answer is 2 If X = 2 (200 + 60 + 3)/7 263/7 = 37r4 so the answer is 4 Combined, INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★




Manager
Joined: 19 Apr 2008
Posts: 226

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
10 Jun 2008, 23:11
I think it should be E you can represent 100X+10Y+Z as a three digit number XYZ now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 remainder is 2 , 263/7 remainder 4 One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution




VP
Joined: 04 May 2006
Posts: 1210
Schools: CBS, Kellogg

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
11 Jun 2008, 00:40
rpmodi wrote: I think it should be E you can represent 100X+10Y+Z as a three digit number XYZ now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 remainder is 2 , 263/7 remainder 4 One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution Thanks rpmodi, smart explaination!and E is OA
_________________



Intern
Joined: 15 Oct 2013
Posts: 1

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
07 Dec 2014, 14:16
sondenso wrote: If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?
(1) y = 6 (2) z = 3 Hi, I set this problem up in a slightly different way. I noticed that it has 1 equation and 4 unknowns, if you include remainder A. Stmt 1 = With that logic, you substitute 6, you still have 3 unknowns and one equation. NS  Eliminate A Stmt 2 = Set up the same equation by substituting 3, you still have 3 unknowns and one equation. NS  Eliminate B If you set up the equation to include y and z (100x +10 (6) + 3)/7 = a) you have one equation and two unknowns Eliminate C. Therefore, the only possible solution is E. Does my logic make sense?



Manager
Joined: 23 May 2014
Posts: 97

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
24 Dec 2014, 20:04
sondenso wrote: If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?
(1) y = 6 (2) z = 3 10y when divided by 7 can leave different remainders. 19*6 = 60 leaves remainder 4 z = 3 leaves remainder 3 but 100x when divided by 7 can leave different remainders. As we don't have concrete value for x, the answer is E



Director
Joined: 26 Oct 2016
Posts: 599
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
28 Jan 2017, 14:31
100x+10y+z a)y=6. if we take x,y as same and keep on changing z, we will get different remainders Thus insufficient. b)z=3. keep x same and z as 6. 10y=10,20,30.... 10 remainder = 3 20 remainder = 6 Insufficient. a&b together) 100x+60+3 = 100x+63. 63 is divisible by 7, thus remainder is based on 100x x=1, 100 remainder=2 x=2, 200 remainder=4 Hence E
_________________
Thanks & Regards, Anaira Mitch



Intern
Joined: 19 Apr 2016
Posts: 10
GMAT 1: 490 Q35 V23 GMAT 2: 540 Q37 V27

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
02 Mar 2017, 06:29
rpmodi wrote: I think it should be E you can represent 100X+10Y+Z as a three digit number XYZ now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 remainder is 2 , 263/7 remainder 4 One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution Hi  Why can we represent 100X+10Y+Z as a three digit number?



Math Expert
Joined: 02 Sep 2009
Posts: 60580

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
02 Mar 2017, 06:36
mhill5446 wrote: rpmodi wrote: I think it should be E you can represent 100X+10Y+Z as a three digit number XYZ now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 remainder is 2 , 263/7 remainder 4 One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution Hi  Why can we represent 100X+10Y+Z as a three digit number? This is a way of writing an xdigit number. For example, any twodigit integer can be represented as 10a+b (where a and b are single digit integers), for example 37=3*10+7, 88=8*10+8, etc. Any threedigit integer can be represented as 100a+10b+c (where a, b and c are single digit integers), for example 371=3*100+7*10+1, ... Hope it's clear.
_________________



Intern
Joined: 18 Jan 2017
Posts: 23

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
02 Mar 2017, 06:43
E... since we have no idea of what x is Sent from my GTI9060I using GMAT Club Forum mobile app



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9092
Location: United States (CA)

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
06 Mar 2017, 18:08
sondenso wrote: If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?
(1) y = 6 (2) z = 3 We need to determine the remainder of (100x + 10y + z)/7. If we can determine the remainder of 100x/7, 10y/7, and z/7, then we can determine the remainder of (100x + 10y + z)/7. Statement One Alone:y = 6 Using the information in statement one, we have: (100x + 60 + z)/7 Although we know the remainder of 60/7 is 4 (note: 60/7 = 8 + 4/7), we still cannot determine the remainder of 100x/7 or z/7. Statement one alone is not sufficient to answer the question. Statement Two Alone:z = 3 Using the information in statement two, we have: (100x + 10y + 3)/7 Although we know the remainder of 3/7 is 3, we still cannot determine the remainder of 10y/7 or 100x/7. Statement two alone is not sufficient to answer the question. Statements One and Two Together:Using the information from statements one and two, we have: (100x + 60 + 3)/7 = (100x + 63)/7 Although we know the remainder of 63/7 is 0, we still cannot determine the remainder of 100x/7. Different values of x might yield different remainders. For example, if x = 1, then the remainder of 100/7 is 2, since 100/7 = 14 + 2/7. However, if x = 2, then the remainder of 200/7 is 4, since 200/7 = 28 + 4/7. Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 29 Oct 2016
Posts: 23

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
08 May 2017, 19:01
I had guessed E because we are given only two of three variables with the two statements. I didn't consider testing values and/or reasoning it out  moreso guessed it straight away because we are still missing one variable within the equation (similar to hsingh2008's post above)  is this a valid approach or no?



Senior Manager
Joined: 29 Dec 2017
Posts: 369
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)

If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
27 Aug 2018, 08:19
The number XYZ is devided by 7 if 2*ZXY can be devided by 7. In this case we have got only Z and Y but not X. So the answer is E. Another way to silve is to take 163 and 263 and compare remainders  they are different.



Senior Manager
Joined: 10 Apr 2018
Posts: 266
Location: United States (NC)

If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
Updated on: 04 Apr 2019, 08:38
Bunuel wrote: mhill5446 wrote: rpmodi wrote: I think it should be E you can represent 100X+10Y+Z as a three digit number XYZ now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 remainder is 2 , 263/7 remainder 4 One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution Hi  Why can we represent 100X+10Y+Z as a three digit number? This is a way of writing an xdigit number. For example, any twodigit integer can be represented as 10a+b (where a and b are single digit integers), for example 37=3*10+7, 88=8*10+8, etc. Any threedigit integer can be represented as 100a+10b+c (where a, b and c are single digit integers), for example 371=3*100+7*10+1, ... Hope it's clear. Bunuel, Hi i wanted to understand how did we come to know that its a three digit number ? But we are told that that X,Y,Z are positive integers. Had we be given that they are digits we can express 100X+10Y+Z as three digit positive integer. Here is what i mean if X= 2 Y=6 Z=3 then the number would be 263 But if X = 20 Y=6 and Z 3 then the number would be 2063. So with certainty how can we say that its a three digit positive number, while we only know that X,Y,Z are positive integers. But i had a different approach for this question n= 100X+10Y+Z n= 98X+2X+7Y+3Y+Z \(\frac{n}{7}\)= \(\frac{98X+2X+7Y+3Y+Z}{7}\) so remainder will be \(\frac{2X+3Y+Z}{7}\) So to answer the question we need to know all the three variable X,Y,Z
_________________
Probus
~You Just Can't beat the person who never gives up~ Babe Ruth
Originally posted by Probus on 15 Mar 2019, 08:09.
Last edited by Probus on 04 Apr 2019, 08:38, edited 2 times in total.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15958
Location: United States (CA)

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
15 Mar 2019, 15:16
Hi Probus, You're correct  there is nothing in the prompt that states that the final number must be a 3digit number. By thinking in those terms however, the work becomes a lot easier  and you can quickly prove that Fact 1 and Fact 2 are each INSUFFICIENT (as well as prove that combining both Facts still leads to an INSUFFICIENT answer). GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 22 Nov 2019
Posts: 24
Location: China
GPA: 4

Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
Show Tags
15 Dec 2019, 19:15
hsingh2088 wrote: sondenso wrote: If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?
(1) y = 6 (2) z = 3 Hi, I set this problem up in a slightly different way. I noticed that it has 1 equation and 4 unknowns, if you include remainder A. Stmt 1 = With that logic, you substitute 6, you still have 3 unknowns and one equation. NS  Eliminate A Stmt 2 = Set up the same equation by substituting 3, you still have 3 unknowns and one equation. NS  Eliminate B If you set up the equation to include y and z (100x +10 (6) + 3)/7 = a) you have one equation and two unknowns Eliminate C. Therefore, the only possible solution is E. Does my logic make sense? I would love to be able to validate this approach too, as it seems like the fastest solution to me? Thanks




Re: If x, y, and z are positive integers, what is the remainder when 100x
[#permalink]
15 Dec 2019, 19:15






