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

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heyholetsgo
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If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   Updated on: 22 Apr 2023, 01:23
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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


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

Originally posted by heyholetsgo on 18 Aug 2010, 10:06.
Last edited by Bunuel on 22 Apr 2023, 01:23, edited 3 times in total.
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   18 Aug 2010, 10:18
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If 8x > 4 + 6x, what is the value of the integer x?

First, note that we are given that x is an integer.

Next, simplify the given inequality:

    \(8x>4+6x\);
    \(2x>4\);
    \(x>2\).

(1) \(6-5x>-13\);

    \(19>5x\);

    \(3.8>x\).

Since x is an integer and \(x > 2\), then \(x = 3\). Sufficient.


(2) \(3-2x<-x+4<7.2-2x\)

Consider only the following part:

    \(-x+4<7.2-2x\);

    \(x<3.2\)

Since x is an integer and \(x > 2\), then \(x = 3\). Sufficient.

Answer: D.

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


There is no need to add inequalities in this case. However, 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 the 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: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   19 Aug 2010, 00:55
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: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   19 Aug 2010, 03:15
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: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   19 Aug 2010, 07:24
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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..


The reason for considering only the second part of the second statement is that the first part is not needed to determine the answer. The second part, which states \(-x + 4 < 7.2 - 2x\), provides sufficient information to solve for x: \(x < 3.2\). Since we know that \(x\) is an integer and \(x > 2\), we can conclude that \(x = 3\). This is sufficient to determine the value of x, making the first part of the second statement unnecessary.
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   29 Aug 2013, 08:21
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: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   29 Aug 2013, 09:47
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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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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   29 Aug 2013, 21:15
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: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   30 Aug 2013, 04:34
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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   01 Nov 2016, 06:43
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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...



from the given information
8x-6x > 4
2x > 4
x>2.

1. 19>5x -> 3.8 > x -> since x must be an integer, and since x>2, we know for sure that X is 3. Suficient.

2. 3-2x<-x+4<7.2-2x
add 2x to each side:
3<x+4<7.2
subtract 4
-1<x<3.2
since x>2, must be and integer, and since x<3.2, x must be equal to 3
sufficient.

answer is D.
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   10 Nov 2017, 21:14
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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...


8x>4+6x
therefore, x>2

St. 1: 6-5x>-13
-5x>-19
x<19/5

we know that x>2 and is an integer.

therefore, x=3

St.2: 3-2x<-x+4<7.2-2x
3<x+4<7.2
x=3

Choice D
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   19 Apr 2023, 05:02
Quote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Quote:
Solving The given statement,
2x>4 , x>2




Hi , KarishmaB

I solved Statement 2 using the below method , but couldnt reach an answer.

Step1. Bringing all x in one place

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

Step2. subtracting 4 from all
-1<3x<3.2

Step3. Dividing by 3 in all sides
-1/3 <x<3.2/3

-0.33<x<1.06777

But given in the question that X >2

Hence Statement 2 is INSUFFICIENT

Please guide .
Thanks
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   20 Apr 2023, 04:59
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PriyamRathor wrote:
Quote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x


Quote:
Solving The given statement,
2x>4 , x>2




Hi , KarishmaB

I solved Statement 2 using the below method , but couldnt reach an answer.

Step1. Bringing all x in one place

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

Step2. subtracting 4 from all
-1<3x<3.2

Step3. Dividing by 3 in all sides
-1/3 <x<3.2/3

-0.33<x<1.06777

But given in the question that X >2

Hence Statement 2 is INSUFFICIENT

Please guide .
Thanks


Highlighted is not correct.

a < b < c can be handled in one of two ways:

I. Break into two inequalities and then work on them as usual
a < b and b < c

II. Do the same operation on each inequality
a + 2 < b + 2 < c + 2



So what you can do is add 2x to all three expressions:
\(3 – 2x < -x + 4 < 7.2 – 2x\)
becomes
\(3 – 2x + 2x < -x + 4 + 2x < 7.2 – 2x + 2x\)
which is
\(3 < x + 4 < 7.2\)

Now subtract 4 from all.

\(3-4 < x + 4 - 4 < 7.2 - 4\)
\(-1 < x < 3.2\)
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   21 Apr 2023, 21:12
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.


I think I have a conceptual gap. I started taking two cases x is +ve and x is -ve and (x= 0 is not possible) got everything messed and chose E

Posted from my mobile device
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink] New post   22 Apr 2023, 01:25
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ChanSu wrote:
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.


I think I have a conceptual gap. I started taking two cases x is +ve and x is -ve and (x= 0 is not possible) got everything messed and chose E

Posted from my mobile device


9. Inequalities



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
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Re: If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink]
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