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GMAT Diagnostic Test Question 43

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GMAT Diagnostic Test Question 43 [#permalink]

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05 Jun 2012, 19:27
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GMAT Diagnostic Test Question 43

Field: Algebra
Difficulty: 700

If 5x=y+7, is (x−y)>0 ?

(1) xy=6
(2) x and y are consecutive integers with the same sign
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Last edited by bb on 29 Sep 2013, 21:07, edited 2 times in total.
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05 Jun 2012, 19:43
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Statement 1: xy=6 is not sufficient to answer the question because solving the equation gives y=3 when x is 2 and y is -10 when x is −3 5 .

5x=y+7

x=y+7 5 ................i

xy=6 ........................ ii

Replacing the value of x on eq ii: y(y+7) 5 =6

y 2 +7y=30

y 2 +10y−3y−30=0

y(y+10)−3(y+10)=0

(y+10)(y−3)=0

y=−10 or 3

If y=−10 , x=−3 5 . In this case, x−y=−3 5 −(−10)=47 5 . Yes.

If y=3 , x=2 . In this case, x−y=2−3=−1 . No.

In each case (x−y)>0 and <0 . Hence statement 1 is not sufficient.

Statement 2: If x and y are consecutive integers, x=2 and y=3 .

When x and y are consecutive integers, either x=y+1 or y=x+1 is possible.

(i) If x=y+1

5x=y+7

5(y+1)=y+7

4y=2

y=1 2 . Then x=3 2 . However this is not possible becase x and y are even not integers. So this option is not valid.

(ii) If y=x+1

5x=y+7

5x=x+1+7

4x=8

x=2

Then, y=3 . This is valid because x and y are consecutive integers.

So (x−y)=2−3=−1 . Hence statement 2 is sufficient.
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06 Jun 2012, 06:23
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If 5x=y+7 , is (x−y)>0 ?

Statement 1: xy=6
=> 5x = (6/x) + 7
=> 5x^2 - 7x - 6 =0
=> (x-2)(5x+3)=0
=> x = 2 or x= -3/5. So the solutions sets are (x,y) = (2,3) and (-3/5,-10). In case 1, x-y<0 and in case 2, x-y>0. Insufficient.

Statement 2: x and y are consecutive integers with the same sign.
Take x=k and y=k+1
=> 5k = (k+1) + 7 => k=2. So one possible solution is x=2,y=3.
Take y=k and x=k+1
=> 5(k+1) = k + 7 => k = 1/2. So no solution possible in integers.
Therefore x-y<0. Sufficient.

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Last edited by GyanOne on 06 Jun 2012, 16:44, edited 1 time in total.
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06 Jun 2012, 09:52
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GyanOne wrote:
=> x = 2 or x= -3/5. So the solutions sets are (x,y) = (2,3) and (-3/5,-10). In both cases, x-y>0. Sufficient.

isn't st-1 insufficient because of the above solution set?
if (x,y) = (2,3), then x-y=2-3 = -1. a 'no'
if (x,y) = (-3/5,-10), then x-y=-3/5+10= 47/5. a 'yes'

so, insufficient.
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]

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19 Feb 2013, 07:00
Bunuel,

x and y are consecutive integers with the same sign

Doesn't the above indicate that y is bigger than x by 1?
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]

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19 Feb 2013, 07:28
Sachin9 wrote:
Bunuel,

x and y are consecutive integers with the same sign

Doesn't the above indicate that y is bigger than x by 1?

No, it dose not. When we are told that x and y are consecutive integers, it doesn't necessarily mean that y=x+1 (y>x), it could be that x=y+1 (x>y).

For example, check the following question: if-m-and-n-are-consecutive-positive-integers-is-m-greater-126287.html#p1031359

Hope it helps.
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]

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19 Feb 2013, 07:55
Bunuel wrote:
Sachin9 wrote:
Bunuel,

x and y are consecutive integers with the same sign

Doesn't the above indicate that y is bigger than x by 1?

No, it dose not. When we are told that x and y are consecutive integers, it doesn't necessarily mean that y=x+1 (y>x), it could be that x=y+1 (x>y).

For example, check the following question: if-m-and-n-are-consecutive-positive-integers-is-m-greater-126287.html#p1031359

Hope it helps.

Bunuel,
I checked The link you gave . There m has to be greater than n.
But here in this question, it is given that x and y are consecutive. Meaning of consecutive from google indicates that y follows x..

con·sec·u·tive
/kənˈsekyətiv/
Following continuously.
In unbroken or logical sequence.
Synonyms
successive - sequential - running - sequent - serial

So y has to be bigger than x right?
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]

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19 Feb 2013, 07:59
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Expert's post
Sachin9 wrote:
Bunuel wrote:
Sachin9 wrote:
Bunuel,

x and y are consecutive integers with the same sign

Doesn't the above indicate that y is bigger than x by 1?

No, it dose not. When we are told that x and y are consecutive integers, it doesn't necessarily mean that y=x+1 (y>x), it could be that x=y+1 (x>y).

For example, check the following question: if-m-and-n-are-consecutive-positive-integers-is-m-greater-126287.html#p1031359

Hope it helps.

Bunuel,
I checked The link you gave . There m has to be greater than n.
But here in this question, it is given that x and y are consecutive. Meaning of consecutive from google indicates that y follows x..

con·sec·u·tive
/kənˈsekyətiv/
Following continuously.
In unbroken or logical sequence.
Synonyms
successive - sequential - running - sequent - serial

So y has to be bigger than x right?

Google is not conducting the test, GMAC does.
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Re: If 5x=y+7, is (x−y)>0 ? [#permalink]

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19 Feb 2013, 08:44
lol
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Re: GMAT Diagnostic Test Question 43 [#permalink]

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18 Dec 2013, 00:35
bb wrote:

GMAT Diagnostic Test Question 43

Field: Algebra
Difficulty: 700

If 5x=y+7, is (x−y)>0 ?

(1) xy=6
(2) x and y are consecutive integers with the same sign

In St.2, answer can be x,y = 2,3 or -2,-3; How is St. 2 sufficient, can someone please explain?
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Re: GMAT Diagnostic Test Question 43 [#permalink]

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18 Dec 2013, 00:49
karankg wrote:
bb wrote:

GMAT Diagnostic Test Question 43

Field: Algebra
Difficulty: 700

If 5x=y+7, is (x−y)>0 ?

(1) xy=6
(2) x and y are consecutive integers with the same sign

In St.2, answer can be x,y = 2,3 or -2,-3; How is St. 2 sufficient, can someone please explain?

There is only one solution for (2): x=2 and y=3. x=-2 and y=-3 does not satisfy 5x=y+7. Check here: gmat-diagnostic-test-question-133991.html#p1093453
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Re: GMAT Diagnostic Test Question 43 [#permalink]

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19 Dec 2013, 03:46
Thank you Bunuel I forget to consider checking the values by placing them in the original equations due to puacity of time. Need to start doing that.
Re: GMAT Diagnostic Test Question 43   [#permalink] 19 Dec 2013, 03:46
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