Author 
Message 
TAGS:

Hide Tags

SVP
Joined: 04 May 2006
Posts: 1736
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% (01:10) correct 26% (00:51) wrong based on 614 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.
_________________
GMAT Club Premium Membership  big benefits and savings




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12432
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************




Senior Manager
Joined: 19 Apr 2008
Posts: 303

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




SVP
Joined: 04 May 2006
Posts: 1736
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
_________________
GMAT Club Premium Membership  big benefits and savings



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: 101

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: 649
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: 49303

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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 18 Jan 2017
Posts: 31

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: 3515
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
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 29 Oct 2016
Posts: 27

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: 382
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 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.




If x, y, and z are positive integers, what is the remainder when 100x &nbs
[#permalink]
27 Aug 2018, 08:19






