It is currently 18 Nov 2017, 09:20

### 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 June
Open Detailed Calendar

# If x, y, and z are three-digit positive integers and if x =

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Aug 2011
Posts: 78

Kudos [?]: 272 [10], given: 13

If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

18 Sep 2012, 09:10
10
KUDOS
70
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:19) correct 38% (01:36) wrong based on 1572 sessions

### HideShow timer Statistics

If x, y, and z are three-digit 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.

[Reveal] Spoiler:
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??
[Reveal] Spoiler: OA

_________________

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

Last edited by Bunuel on 18 Sep 2012, 09:16, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 272 [10], given: 13

Manager
Joined: 02 Jun 2011
Posts: 116

Kudos [?]: 69 [2], given: 5

Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

18 Sep 2012, 11:04
2
KUDOS
4
This post was
BOOKMARKED
conty911 wrote:
If x, y, and z are three-digit 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.

[Reveal] Spoiler:
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.

Kudos [?]: 69 [2], given: 5

Intern
Joined: 02 Nov 2009
Posts: 42

Kudos [?]: 60 [9], given: 8

Location: India
Concentration: General Management, Technology
GMAT Date: 04-21-2013
GPA: 4
WE: Information Technology (Internet and New Media)
Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

18 Sep 2012, 11:06
9
KUDOS
3
This post was
BOOKMARKED
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

Kudos [?]: 60 [9], given: 8

Intern
Joined: 01 Jun 2012
Posts: 25

Kudos [?]: 7 [0], given: 4

Concentration: Entrepreneurship, Social Entrepreneurship
WE: Information Technology (Consulting)
Re: If x, y, and z are three-digit 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.

Kudos [?]: 7 [0], given: 4

Senior Manager
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 556 [4], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

20 Sep 2012, 00:12
4
KUDOS
8
This post was
BOOKMARKED
x = ABC
y = DEF
z = GHI

DEF
+GHI
_____
ABC

Question: Is D + G = A? This is true if there is no carry-over 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.

_________________

Impossible is nothing to God.

Last edited by mbaiseasy on 15 Jan 2013, 01:23, edited 1 time in total.

Kudos [?]: 556 [4], given: 11

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 250

Kudos [?]: 130 [0], given: 282

Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: If x, y, and z are three-digit 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 succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Kudos [?]: 130 [0], given: 282

Intern
Joined: 13 Apr 2013
Posts: 22

Kudos [?]: 3 [0], given: 3

Re: If x, y, and z are three-digit 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

Kudos [?]: 3 [0], given: 3

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2364 [4], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

13 Apr 2013, 11:27
4
KUDOS
1
This post was
BOOKMARKED
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 three-digit 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 I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2364 [4], given: 219

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132589 [19], given: 12326

Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

21 Aug 2013, 07:45
19
KUDOS
Expert's post
21
This post was
BOOKMARKED
fozzzy wrote:
If x, y, and z are three-digit 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.

Hope it's clear.
_________________

Kudos [?]: 132589 [19], given: 12326

Intern
Joined: 21 Sep 2013
Posts: 9

Kudos [?]: 2 [0], given: 0

Re: If x, y, and z are three-digit 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.

Kudos [?]: 2 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132589 [4], given: 12326

Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

19 Jan 2014, 10:28
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
Abheek wrote:
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.

The tens digit of y is 9 and the tens digit of z is 9 --> 9+9=18 not 8.

Hope it's clear.
_________________

Kudos [?]: 132589 [4], given: 12326

Intern
Joined: 29 Oct 2014
Posts: 23

Kudos [?]: 12 [0], given: 14

Re: If x, y, and z are three-digit 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?

Kudos [?]: 12 [0], given: 14

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132589 [0], given: 12326

Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

16 Dec 2014, 04:23
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?
_________________

Kudos [?]: 132589 [0], given: 12326

Intern
Joined: 29 Oct 2014
Posts: 23

Kudos [?]: 12 [0], given: 14

If x, y, and z are three-digit 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
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!!)

Kudos [?]: 12 [0], given: 14

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132589 [0], given: 12326

Re: If x, y, and z are three-digit 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
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!!)

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.
_________________

Kudos [?]: 132589 [0], given: 12326

Intern
Joined: 29 Oct 2014
Posts: 23

Kudos [?]: 12 [1], given: 14

Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

17 Dec 2014, 14:42
1
KUDOS
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

Kudos [?]: 12 [1], given: 14

Intern
Joined: 06 Dec 2011
Posts: 3

Kudos [?]: 5 [0], given: 6

Re: If x, y, and z are three-digit 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.

Kudos [?]: 5 [0], given: 6

SVP
Joined: 12 Sep 2015
Posts: 1840

Kudos [?]: 2594 [2], given: 362

Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

27 Jul 2016, 08:00
2
KUDOS
Expert's post
Top Contributor
1
This post was
BOOKMARKED
conty911 wrote:
If x, y, and z are three-digit 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 three-digit 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 z
Since 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 z
Case 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 z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

[Reveal] Spoiler:
A

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2594 [2], given: 362

Senior Manager
Joined: 24 Oct 2016
Posts: 318

Kudos [?]: 25 [0], given: 88

Location: India
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: If x, y, and z are three-digit positive integers and if x = [#permalink]

### Show Tags

25 Mar 2017, 05:13
Bunuel wrote:
fozzzy wrote:
If x, y, and z are three-digit 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.

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 .

thanks

Kudos [?]: 25 [0], given: 88

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132589 [0], given: 12326

Re: If x, y, and z are three-digit 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 three-digit 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.

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 .

thanks

Dear nks2611,

Everything highlighted above is general reasoning about the stem and not specifically about the statements...
_________________

Kudos [?]: 132589 [0], given: 12326

Re: If x, y, and z are three-digit positive integers and if x =   [#permalink] 25 Mar 2017, 05:57

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by