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If 8x > 4 + 6x, what is the value of the integer x? (1) 6

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If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post 18 Aug 2010, 09:06
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If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...
[Reveal] Spoiler: OA
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Re: Inequality [#permalink] New post 18 Aug 2010, 09:18
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heyholetsgo wrote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...


Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.

So no need to add inequality in this case. But if you are interested:

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

Hope it helps.
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Re: Inequality [#permalink] New post 18 Aug 2010, 23:55
Bunuel wrote:
heyholetsgo wrote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...


Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.

So no need to add inequality in this case. But if you are interested:

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

Hope it helps.


Hi,

can you explain stmt B please, why is that only the second part is considered?
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Re: Inequality [#permalink] New post 19 Aug 2010, 02:15
Hi Bunuel,
why have to taken only the second equation in Statement B not the first one? Plz explain briefly.

Thanks..
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Re: Inequality [#permalink] New post 19 Aug 2010, 06:24
Expert's post
ramana wrote:
Bunuel wrote:
Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.


Hi,

can you explain stmt B please, why is that only the second part is considered?

mission2009 wrote:
Hi Bunuel,
why have to taken only the second equation in Statement B not the first one? Plz explain briefly.

Thanks..


Because to reach the answer we don't need the first part at all. The part which says \(-x+4<7.2-2x\) is enough to give necessary info: \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.
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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

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Re: Inequality [#permalink] New post 19 Aug 2010, 22:44
Bunuel wrote:
heyholetsgo wrote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...


Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(18>5x\) --> \(\frac{18}{5}=3.6>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.

So no need to add inequality in this case. But if you are interested:

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

Hope it helps.


Slightly off on statement 1, however the answer doesn't change.

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.
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Re: Inequality [#permalink] New post 27 Sep 2011, 11:24
Bunuel wrote:
heyholetsgo wrote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...


Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.

So no need to add inequality in this case. But if you are interested:

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

Hope it helps.


One small doubt...
As said X>2 and x>3.8 how can we say x=3 even it is integer.The 2nd one say X.3.8 so y can't we take x=4????
Thanks to help
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Re: Inequality [#permalink] New post 27 Sep 2011, 19:37
8x>4+6x
=>2x>4
=> x>2
x=?

1. Sufficient

6-5x>-13
-5x>-19 => x<19/5 => x<3.2 => x ={..........-1,0,1,2,3} as x is an integer

as x>2 and x<3.2=> x can only be 3


2. Sufficient

3-2x < - x+4 <7.2-2x

3-2x<-x+4 => -1 < x
-x+4 < 7.2-2x => x<3.2

=> -1<x<3.2 , but we know x>2 = 2<x<3.2 then x can only be 3 as it has to be an integer.

Answer is D.
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Re: Inequality [#permalink] New post 28 Sep 2011, 09:33
heyholetsgo wrote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...


Given equation can be simplified to
8x > 4 + 6x => x < 2
Given x is an integer

1) 6 – 5x > -13 => x < 3.2
and since x > 2
It means x = 3
Sufficient

2) -x + 4 < 7.2 – 2x => x < 3.2
3 – 2x < -x + 4 => x > -1
And we know x > 2 and x is an integer
So x can be only 3
Sufficient.

So D is the answer.
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Re: Inequality [#permalink] New post 29 Aug 2013, 07:21
Bunuel wrote:
ramana wrote:
Bunuel wrote:
Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.


Hi,

can you explain stmt B please, why is that only the second part is considered?

mission2009 wrote:
Hi Bunuel,
why have to taken only the second equation in Statement B not the first one? Plz explain briefly.

Thanks..


Because to reach the answer we don't need the first part at all. The part which says \(-x+4<7.2-2x\) is enough to give necessary info: \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Hi Bunuel,

but if we consider the first part of the statement B we don't get the answer, right? if we have been given the equation with both the parts then we should be considering both the parts, right??? please explain...
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Re: Inequality [#permalink] New post 29 Aug 2013, 08:47
Expert's post
Reetabrata Ghosh wrote:
Bunuel wrote:
ramana wrote:
Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.

Hi,

can you explain stmt B please, why is that only the second part is considered?

mission2009 wrote:
Hi Bunuel,
why have to taken only the second equation in Statement B not the first one? Plz explain briefly.

Thanks..


Because to reach the answer we don't need the first part at all. The part which says \(-x+4<7.2-2x\) is enough to give necessary info: \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Hi Bunuel,

but if we consider the first part of the statement B we don't get the answer, right? if we have been given the equation with both the parts then we should be considering both the parts, right??? please explain...


Yes, if (2) were just \(3-2x<-x+4\) --> \(x>-1\), then it wouldn't be sufficient. As for your other question: can you please elaborate what you mean? Thank you.
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COLLECTION OF QUESTIONS:
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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.


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Re: Inequality [#permalink] New post 29 Aug 2013, 12:40
Bunuel wrote:
ramana wrote:
Bunuel wrote:
Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.


Hi,

can you explain stmt B please, why is that only the second part is considered?

mission2009 wrote:
Hi Bunuel,
why have to taken only the second equation in Statement B not the first one? Plz explain briefly.

Thanks..


Because to reach the answer we don't need the first part at all. The part which says \(-x+4<7.2-2x\) is enough to give necessary info: \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.



So, Does it mean that in the questions where more than one IE are given such as in option B, we dont need to look at the first part?
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Re: Inequality [#permalink] New post 29 Aug 2013, 12:43
Expert's post
swati007 wrote:
Bunuel wrote:
ramana wrote:
Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)

(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.

Answer: D.

Hi,

can you explain stmt B please, why is that only the second part is considered?

mission2009 wrote:
Hi Bunuel,
why have to taken only the second equation in Statement B not the first one? Plz explain briefly.

Thanks..


Because to reach the answer we don't need the first part at all. The part which says \(-x+4<7.2-2x\) is enough to give necessary info: \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.



So, Does it mean that in the questions where more than one IE are given such as in option B, we dont need to look at the first part?


Of course not! It was only for that particular question.
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Re: Inequality [#permalink] New post 29 Aug 2013, 20:15
Hi Bunuel,

but if we consider the first part of the statement B we don't get the answer, right? if we have been given the equation with both the parts then we should be considering both the parts, right??? please explain...[/quote]

Yes, if (2) were just \(3-2x<-x+4\) --> \(x>-1\), then it wouldn't be sufficient. As for your other question: can you please elaborate what you mean? Thank you.[/quote]

Hi Bunuel,

what I meant to say that in the statement B there are two equations and both gives us different answers for X, but you have taken the 2nd part only and discarded the first part..why is that..if both the parts are given then should not we take both the parts into consideration?? and if we take both the parts into consideration we do not get the desired result..hope I am able to explain myself....
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Re: Inequality [#permalink] New post 30 Aug 2013, 03:34
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Reetabrata Ghosh wrote:

what I meant to say that in the statement B there are two equations and both gives us different answers for X, but you have taken the 2nd part only and discarded the first part..why is that..if both the parts are given then should not we take both the parts into consideration?? and if we take both the parts into consideration we do not get the desired result..hope I am able to explain myself....


I did not discard anything. The point is that the first part does not give us any relevant info.

If we use both we'd have the same!

\(3-2x < -x + 4 < 7.2 - 2x\) --> \(-1<x<3.2\). We know that \(x>2\), so we have \(2<x<3.2\).

Hope it's clear now.
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post 25 Aug 2015, 03:42
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6   [#permalink] 25 Aug 2015, 03:42
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