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# The sum of positive integers x and y is 77, what is the

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Intern
Joined: 22 Jan 2012
Posts: 5
The sum of positive integers x and y is 77, what is the  [#permalink]

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29 Jan 2012, 02:34
1
12
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:31) correct 28% (01:31) wrong based on 290 sessions

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Here is the data sufficiency problem from GMATPrep;

The sum of positive integers x and y is 77, what is the value of xy?

(1) x=y+1
(2) x and y have the same tens digit.

I answered the question as A becuase i thought the statement (1) alone was sufficient. GMATPrep on the other hand said that it is a D -each statement alone is sufficient.
Here is my problem, if we do not know the statement (1), how can we decide these numbers? They of course should be with a tens digit of 3, but all those pairs as (30,37), (31,36), (32,35), (33,34) can maintain the sum of 77, with difference results when they are multiplied. It is because i did not think statement 2 is sufficient, can anyone make it clear, if the GMATPrep's answer is correct? Thanks.
Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 220
Location: India
Concentration: General Management, Entrepreneurship
Re: The sum of positive integers x and y is 77..  [#permalink]

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29 Jan 2012, 02:47
2
Hi ,

I got the answer as D
The sum of positive integers x and y is 77, what is the value of xy?

(1) x=y+1
(2) x and y have the same tens digit.

Statement A : X=Y+1 so using eqn X+Y=77
2Y+1=77
Y= 38
X= 39
thus we can find the value of XY
Hence A is sufficient
Statement 2 : Says X & Y have the same 10's digit => X= 10 * A + B & Y = 10 * A + C

For X + Y = 77 & the above constraint we can only opt for a number between 30 - 39 thus the choice of 38 & 39
Hence B is sufficient

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Math Expert
Joined: 02 Sep 2009
Posts: 51229
The sum of positive integers x and y is 77, what is the  [#permalink]

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29 Jan 2012, 02:52
ustureci wrote:
Here is the data sufficiency problem from GMATPrep;

The sum of positive integers x and y is 77, what is the value of xy?

(1) x=y+1
(2) x and y have the same tens digit.

I answered the question as A becuase i thought the statement (1) alone was sufficient. GMATPrep on the other hand said that it is a D -each statement alone is sufficient.
Here is my problem, if we do not know the statement (1), how can we decide these numbers? They of course should be with a tens digit of 3, but all those pairs as (30,37), (31,36), (32,35), (33,34) can maintain the sum of 77, with difference results when they are multiplied. It is because i did not think statement 2 is sufficient, can anyone make it clear, if the GMATPrep's answer is correct? Thanks.

Welcome to GMAT Club. Hope below solution clears your doubts.

The sum of positive integers x and y is 77, what is the value of xy?

Given: x+y=77. Question: xy=?

(1) x=y+1 --> together with x+y=77 we have two distinct linear equations, hence we can solve the for variables and obtain the value of xy. Sufficient.

(2) x and y have the same tens digit --> x and y cannot have the tens digit of 2 or 4 (as 29+29<77 and 40+40>77) --> the units digit is 3 --> now, if x=y then x=y=77/2=38.5 --> as both are integers then x and y are 38 and 39 or vise versa (neither of them can be less than 38 as in this case the sum will be less than 77: 37+39=76). Therefore xy=38*39. Sufficient.

The problem with your solution is that (30,37), (31,36), (32,35), (33,34) add up to 67 not 77.

Hope it's clear.
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Intern
Joined: 22 Jan 2012
Posts: 5
Re: The sum of positive integers x and y is 77, what is the  [#permalink]

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29 Jan 2012, 03:37
sorry for the inconvenience:) it may happen (mistakes in simple math), thanks anyway.
Math Expert
Joined: 02 Sep 2009
Posts: 51229
Re: The sum of positive integers x and y is 77, what is the  [#permalink]

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29 Jan 2012, 03:48
ustureci wrote:
sorry for the inconvenience:) it may happen (mistakes in simple math), thanks anyway.

No need to apologize at all: errare humanum est. We all do similar mistakes from time to time.

You are most welcome to post any question you like.
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Manager
Joined: 19 Apr 2011
Posts: 199
Schools: Booth,NUS,St.Gallon
Re: The sum of positive integers x and y is 77, what is the  [#permalink]

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02 Feb 2012, 02:28
The sum of positive integers x and y is 77, what is the value of xy?

(1) x=y+1
(2) x and y have the same tens digit.

Ans:
consider the first statement x=y+1
By observation x=39 and y=37
xy=39*38
Hence 1 alone is enough .

X and Y have same 10s digit.
tens digits have to be 3 only . Only possibility is
x,y=(38,39).

Both statements alone are sufficient.
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+1 if you like my explanation .Thanks

Intern
Status: Trying to crack GMAT
Joined: 17 May 2012
Posts: 29
Location: India
Concentration: Operations, Technology
GMAT Date: 07-11-2012
GPA: 3.82
WE: Engineering (Computer Software)
Re: The sum of positive integers x and y is 77, what is the  [#permalink]

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30 Jun 2012, 10:58
Is it just me or is it that most questions in GMAT which show A as OK extremely easily(like in this question) will almost always have D as answer....but the second statement will be just a little harder to understand
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Re: The sum of positive integers x and y is 77, what is the  [#permalink]

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10 Oct 2017, 07:56
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Re: The sum of positive integers x and y is 77, what is the &nbs [#permalink] 10 Oct 2017, 07:56
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