Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 23 Aug 2011
Posts: 76

If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
Updated on: 18 Sep 2012, 09:16
Question Stats:
61% (01:18) correct 39% (01:38) wrong based on 2109 sessions
HideShow timer Statistics
If x, y, and z are threedigit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? (1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z. Is it safe to conclude that the place value of an integer number (represented as a sum of different integers), depends upon only the preceding place value of integers being summed up?
for eg: x=1000a+100b+10c+1d y=1000e+100f+10g+1h z=1000l+100m+10n+1p if z=x+y then
is l only dependent upon value of b and f or some other parameters also??
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Whatever one does in life is a repetition of what one has done several times in one's life! If my post was worth it, then i deserve kudos
Originally posted by conty911 on 18 Sep 2012, 09:10.
Last edited by Bunuel on 18 Sep 2012, 09:16, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
21 Aug 2013, 07:45
fozzzy wrote: If x, y, and z are threedigit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?
(1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z.
Is there an alternative approach for this problem? The question basically asks whether there is a carry over 1 from the tens place to the hundreds place. Consider the following examples: (i) 123 234357 Here when we add the tens digits 2 and 3 there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) is equal to the sum of the hundreds digits of y (1) and z (2). (ii) 153 147300 Here when we add the tens digits 5 and 4 and carry over 1 from the units place, we get 10, so we have carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) does NOT equal to the sum of the hundreds digits of y (1) and z (1). The first statement implies that there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x is equal to the sum of the hundreds digits of y and z. Sufficient. The second statement does not provide us with sufficient information about carry over 1 from the tens place to the hundreds place. Answer: A. 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




Senior Manager
Joined: 13 Aug 2012
Posts: 441
Concentration: Marketing, Finance
GPA: 3.23

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
Updated on: 15 Jan 2013, 01:23
x = ABC y = DEF z = GHI DEF +GHI _____ ABC Question: Is D + G = A? This is true if there is no carryover from the tens digits' sum. 1. E + H = B, This means there is no carry over to hundreds position. SUFFICIENT. 2. C + F = I, This means there is no carry over to tens position BUT we do not know if there will be a carry over during the sum of tens. INSUFFICIENT. Answer: A
_________________
Impossible is nothing to God.
Originally posted by mbaiseasy on 20 Sep 2012, 00:12.
Last edited by mbaiseasy on 15 Jan 2013, 01:23, edited 1 time in total.




Manager
Joined: 02 Jun 2011
Posts: 99

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
18 Sep 2012, 11:04
conty911 wrote: If x, y, and z are threedigit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? (1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z. Is it safe to conclude that the place value of an integer number (represented as a sum of different integers), depends upon only the preceding place value of integers being summed up?
for eg: x=1000a+100b+10c+1d y=1000e+100f+10g+1h z=1000l+100m+10n+1p if z=x+y then
is l only dependent upon value of b and f or some other parameters also?? Question is demanding 100 digit of Y + 100 digit of Z is equal to 100 digit of X, means there will not be any carryover from the sum of tens digit of Y and Z. therefore from Option 1, sum of tens digit of Y and Z equal to of X means there will not be any carryforward from here to 100 digit of Y and Z. therefore option 1 is sufficient to answer. Option 2 unit digit sum is equal, will not give any indication whether tens digit will not carryforward any to hundered. therefore this is not sufficient. ANswer "A"



Intern
Joined: 02 Nov 2009
Posts: 41
Location: India
Concentration: General Management, Technology
GMAT Date: 04212013
GPA: 4
WE: Information Technology (Internet and New Media)

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
18 Sep 2012, 11:06
Let x= a b c y = d e f z= g h i x= y+z 1 > b= e+h which in turn implies c=f+i and so a=d+g (and this implies there is no carry forward in the addition of units and tens place digit of the two numbers) 2> c=f+i which does not tell us if b= e+h(as there could be a carry forward bcos of this addition to the hundred place) and so the answer is A
_________________
KPV



Intern
Joined: 01 Jun 2012
Posts: 24
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Information Technology (Consulting)

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
18 Sep 2012, 21:13
The concern here is the sum of the tenth digit might have a carryover, so the sum of the hundredth digit on Y & Z might not be equal to X's hundredth digit. So A is the right answer.



Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 219
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
23 Feb 2013, 03:18
Let the 3 digit numbers be, x=ABC y=DEF z=GHI Now, its given that DEF + GHI _____ ABC _____ Statement 1 says that E+H=B. Substitute any digit for E and H, you will find that D+G must be equal to A. Sufficient Statement2.......says F+I=C. E and H can be anything and in turn D and G can be anything. Not sufficient.
_________________
I've failed over and over and over again in my life and that is why I succeedMichael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+



Intern
Joined: 13 Apr 2013
Posts: 21

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
13 Apr 2013, 11:23
abhishekkpv wrote: Let x= a b c y = d e f z= g h i
x= y+z
1 > b= e+h which in turn implies c=f+i and so a=d+g (and this implies there is no carry forward in the addition of units and tens place digit of the two numbers)
2> c=f+i which does not tell us if b= e+h(as there could be a carry forward bcos of this addition to the hundred place)
and so the answer is A my confusion is the following regarding (1). maybe i am not reading the question right, but assume the following: y: 6 4 3 z: 4 4 2 x: 1 0 8 5 so, the tens digit of x is equal to the sum of the tens digit of y + z. however, the hundreds digit, 6 + 4 = 1 0. The hundreds digit of x would be 0. can someone please explain? thank you



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1096
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
13 Apr 2013, 11:27
mokura wrote: my confusion is the following regarding (1). maybe i am not reading the question right, but assume the following: y: 6 4 3 z: 4 4 2 x: 1 0 8 5 so, the tens digit of x is equal to the sum of the tens digit of y + z. however, the hundreds digit, 6 + 4 = 1 0. The hundreds digit of x would be 0. can someone please explain? thank you Your problem is very simple : "x, y, and z are threedigit positive integers". x cannot be 1085, it must be \(\leq{999}\) P.S: welcome to GmatClub!
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Intern
Joined: 21 Sep 2013
Posts: 8

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
19 Jan 2014, 10:16
For Statement I my problem pertains to the fact that the ten's digit of x will be expressed as ten's digit of y + ten's digit of z. But if y=190 ,z=190 then x =380 the 1 does carry over from the ten's digit. Although the ten's digit of x is the sum of ten's digit of y and z.
Please Elaborate



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
19 Jan 2014, 10:28



Intern
Joined: 29 Oct 2014
Posts: 24

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
15 Dec 2014, 16:57
Hi Guys,
I thought statement #1 can't be correct alone because (I thought) we must know that BOTH the unit & the tens digits do not carry over:
i.e.
153 147 300
vs
152 147 299
Don't we need to know that both to confirm that the hundreds digit is a 3 rather than 2?



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
16 Dec 2014, 04:23



Intern
Joined: 29 Oct 2014
Posts: 24

If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
17 Dec 2014, 05:35
Bunuel wrote: ColdSushi wrote: Hi Guys,
I thought statement #1 can't be correct alone because (I thought) we must know that BOTH the unit & the tens digits do not carry over:
i.e.
153 147 300
vs
152 147 299
Don't we need to know that both to confirm that the hundreds digit is a 3 rather than 2? But in your second example there IS a carry over 1 from the tens place to the hundreds place. No? Ok let me clarify my question: 153 147300 In this case the hundreds digit became 3 because the unit total 10 > carries 1 to the tens digit > tens digit adds to 10, so carries 1 to the hundreds digit. The hundreds digit thus = 3 vs 152 147299 In this case the hundreds digit remains 2 because the unit total didn't exceed 9 > nothing carries over to the tens digit (i.e. tens digit remains 9), The hundreds digit thus = remains 2 So don't we need to know the unit digit AND the tens digit to confirm whether the hundreds digit will remain 2 or pushed to 3? (I'm not sure why I'm just not getting it!!)



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
17 Dec 2014, 06:14
ColdSushi wrote: Bunuel wrote: ColdSushi wrote: Hi Guys,
I thought statement #1 can't be correct alone because (I thought) we must know that BOTH the unit & the tens digits do not carry over:
i.e.
153 147 300
vs
152 147 299
Don't we need to know that both to confirm that the hundreds digit is a 3 rather than 2? But in your second example there IS a carry over 1 from the tens place to the hundreds place. No? Ok let me clarify my question: 153 147300 In this case the hundreds digit became 3 because the unit total 10 > carries 1 to the tens digit > tens digit adds to 10, so carries 1 to the hundreds digit. The hundreds digit thus = 3 vs 152 147299 In this case the hundreds digit remains 2 because the unit total didn't exceed 9 > nothing carries over to the tens digit (i.e. tens digit remains 9), The hundreds digit thus = remains 2 So don't we need to know the unit digit AND the tens digit to confirm whether the hundreds digit will remain 2 or pushed to 3? (I'm not sure why I'm just not getting it!!) Your first example does NOT satisfy the first statement: the tens digit of x is equal to the sum of the tens digits of y and z. So, it'as not valid. Sorry, cannot explanation any better.
_________________
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: 29 Oct 2014
Posts: 24

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
17 Dec 2014, 14:42
Ok let me clarify my question:
153 147 300
In this case the hundreds digit became 3 because the unit total 10 > carries 1 to the tens digit > tens digit adds to 10, so carries 1 to the hundreds digit. The hundreds digit thus = 3
vs
152 147 299
In this case the hundreds digit remains 2 because the unit total didn't exceed 9 > nothing carries over to the tens digit (i.e. tens digit remains 9), The hundreds digit thus = remains 2
So don't we need to know the unit digit AND the tens digit to confirm whether the hundreds digit will remain 2 or pushed to 3?
(I'm not sure why I'm just not getting it!!)[/quote]
Your first example does NOT satisfy the first statement: the tens digit of x is equal to the sum of the tens digits of y and z. So, it'as not valid. Sorry, cannot explanation any better.[/quote]
OMG  yes, got it!! :S



Intern
Joined: 06 Dec 2011
Posts: 3

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
25 Aug 2015, 23:28
If the 10's digit of x is equal to the sum of the 10's digit of Y and Z, then it implies that there was no carry over from the units digits. Thus statement 2 does not provide any additional information.
In other words, if there IS a carry over from the unit's digits, the 10's digit of x will not equal to the sum of the tens digits of y and z.



CEO
Joined: 12 Sep 2015
Posts: 2707
Location: Canada

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
27 Jul 2016, 08:00
conty911 wrote: If x, y, and z are threedigit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?
(1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z.
Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are threedigit integers Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313. Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308 Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.This rules out scenarios 2 and 3 (plus we already ruled out scenario 1). So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and zSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The units digit of x is equal to the sum of the units digits of y and z.This rules out scenario 3, but not scenario 2. Consider these two conflicting cases: Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and zCase b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and zSince we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer = Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com



Senior Manager
Joined: 24 Oct 2016
Posts: 293
Location: India
Concentration: Finance, International Business
GPA: 3.96
WE: Human Resources (Retail Banking)

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
25 Mar 2017, 05:13
Bunuel wrote: fozzzy wrote: If x, y, and z are threedigit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?
(1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z.
Is there an alternative approach for this problem? The question basically asks whether there is a carry over 1 from the tens place to the hundreds place. Consider the following examples: (i) 123 234357 Here when we add the tens digits 2 and 3 there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) is equal to the sum of the hundreds digits of y (1) and z (2). (ii) 153 147300 Here when we add the tens digits 5 and 4 and carry over 1 from the units place, we get 10, so we have carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) does NOT equal to the sum of the hundreds digits of y (1) and z (1). The first statement implies that there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x is equal to the sum of the hundreds digits of y and z. Sufficient. The second statement does not provide us with sufficient information about carry over 1 from the tens place to the hundreds place. Answer: A. Hope it's clear. hi bunuel although i have understood your method but in statement 2nd you have written (ii) 153 147 300 so you are violating the 2nd statement,not sure , see The units digit of x is equal to the sum of the units digits of y and z., but 3+7=10 but the unit digit is 0 of X , so i think we can not use this example , the condition itself not satisfied in the example . although i can be wrong but what i understood i this . please clarify thanks



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: If x, y, and z are threedigit positive integers and if x =
[#permalink]
Show Tags
25 Mar 2017, 05:57
nks2611 wrote: Bunuel wrote: fozzzy wrote: If x, y, and z are threedigit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?
(1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z.
Is there an alternative approach for this problem? The question basically asks whether there is a carry over 1 from the tens place to the hundreds place.
Consider the following examples: (i) 123 234 357
Here when we add the tens digits 2 and 3 there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) is equal to the sum of the hundreds digits of y (1) and z (2).
(ii) 153 147 300
Here when we add the tens digits 5 and 4 and carry over 1 from the units place, we get 10, so we have carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) does NOT equal to the sum of the hundreds digits of y (1) and z (1).The first statement implies that there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x is equal to the sum of the hundreds digits of y and z. Sufficient. The second statement does not provide us with sufficient information about carry over 1 from the tens place to the hundreds place. Answer: A. Hope it's clear. hi bunuel although i have understood your method but in statement 2nd you have written (ii) 153 147 300 so you are violating the 2nd statement,not sure , see The units digit of x is equal to the sum of the units digits of y and z., but 3+7=10 but the unit digit is 0 of X , so i think we can not use this example , the condition itself not satisfied in the example . although i can be wrong but what i understood i this . please clarify thanks Dear nks2611, Everything highlighted above is general reasoning about the stem and not specifically about the statements...
_________________
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




Re: If x, y, and z are threedigit positive integers and if x = &nbs
[#permalink]
25 Mar 2017, 05:57



Go to page
1 2
Next
[ 26 posts ]



