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Intern  Joined: 08 Jun 2014
Posts: 12
If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 59% (02:15) correct 41% (02:13) wrong based on 179 sessions

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If 8x > 3x + 4x, what is the value of the integer x?

(1) 6 – 4x > –2
(2) 3 – 2x ≤ 4 – x ≤ 5 – 2x

I have an explanation for this problem which goes against the general explanation. Please explain me why I am wrong.

Here
8x> 3x+4x
8x>7x is the condition given in the question
so
if x<0 8x<7x
and if x>0 8x>7x So there is an ambiguity with the condition mentioned in the question. We cant right away decide that 8x>7x => 8x-7x>0 => x>0

Lets come to the options now

#1 6-4x >-2
=> x<2 and this condition does not help to solve the ambiguity in the Question stem as x can be -ve or +ve . so insufficient.

#2 3 – 2x ≤ 4 – x ≤ 5 – 2x
=> -1≤ x≤ 1 which also says that x can be +ve or -ve . So cant resolve the ambiguity in the question stem. Not sufficient

I would choose the 5th option for this data sufficiency question as the statements are not sufficient individually or collectively.

But the right answer is individually both the conditions are sufficient i.e D

What is wrong with my explanation????

need help ASAP as i feel i'm kinda ambiguous with regards to inequality data sufficiency problems. Thank you.

Originally posted by sasha40612 on 03 Sep 2014, 21:45.
Last edited by Bunuel on 04 Sep 2014, 04:35, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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sasha40612 wrote:
If 8x > 3x + 4x, what is the value of the integer x?
(1) 6 – 4x > –2
(2) 3 – 2x ≤ 4 – x ≤ 5 – 2x

I have an explanation for this problem which goes against the general explanation. Please explain me why I am wrong.

Here
8x> 3x+4x
8x>7x is the condition given in the question
so
if x<0 8x<7x
and if x>0 8x>7x So there is an ambiguity with the condition mentioned in the question. We cant right away decide that 8x>7x => 8x-7x>0 => x>0

Not correct. You are given that 8x is greater than 3x + 4x.
What does this mean "If x is positive, what is the value of x+2?" - It means that x is given to be positive and keeping that in mind, you need to find the value of x+2.

Similarly, here you are given that 8x > 3x + 4x and you have to find x. Since you are given that 8x > 7x, you cannot consider that 8x < 7x.
We can right away say that x > 0.
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Intern  Joined: 08 Jun 2014
Posts: 12
Re: If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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Ok I get it. I'm the one who is making these problems complex. So if in the above question 8x>7x means x>0.

Lets say instead of 8x>7x if the condition is x not equal to zero with the same conditions, then both the conditions are not sufficient individually or collectively right?
Intern  Joined: 16 May 2013
Posts: 20
Re: If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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2
Hi Sasha,

As per the condition in the question statement,We get x > 0

Now from first condition we get..
6 -4x > -2
8>4x
x<2
now it is said that x is an integer which is greater than 0 and less than 2. So it has to be 1 . Therefore,x=1 .Statement 1 alone is sufficient.

Now from the Second condition, we get

3-2x ≤ 4-x ≤ 5-2x
solving this we get..

-1≤ x ≤ 1
Now we already know that x>0 so from the above equation and keeping in mind that x is greater than 0 ,We get..
0<x≤1
Thus,getting an integral solution x=1.Therefore,Statement 2 alone is sufficient.
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Re: If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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1
sasha40612 wrote:
If 8x > 3x + 4x, what is the value of the integer x?
(1) 6 – 4x > –2
(2) 3 – 2x ≤ 4 – x ≤ 5 – 2x

I have an explanation for this problem which goes against the general explanation. Please explain me why I am wrong.

Here
8x> 3x+4x
8x>7x is the condition given in the question
so
if x<0 8x<7x
and if x>0 8x>7x So there is an ambiguity with the condition mentioned in the question. We cant right away decide that 8x>7x => 8x-7x>0 => x>0

Lets come to the options now

#1 6-4x >-2
=> x<2 and this condition does not help to solve the ambiguity in the Question stem as x can be -ve or +ve . so insufficient.

#2 3 – 2x ≤ 4 – x ≤ 5 – 2x
=> -1≤ x≤ 1 which also says that x can be +ve or -ve . So cant resolve the ambiguity in the question stem. Not sufficient

I would choose the 5th option for this data sufficiency question as the statements are not sufficient individually or collectively.

But the right answer is individually both the conditions are sufficient i.e D

What is wrong with my explanation????

need help ASAP as i feel i'm kinda ambiguous with regards to inequality data sufficiency problems. Thank you.

let me try to explain.

If 8x > 3x + 4x, this implies 8x -7x > 0 => x > 0, so x is +ve

lets assume, question is asking what is the value of integer x.

st # 1 => 6-4x>-2, this can be simplified to, -4x > -8

removed -ve sign, we have

4x < 8, now since 8 is > 4x, that means x can't be 2, in that case it will be equal and x has to be greater then 0, so value is 1. Sufficient.

St# 2 , 3 – 2x ≤ 4 – x ≤ 5 – 2x

add +2x , we have => 3 ≤ 4 + x ≤ 5

subtract -4, we have ==> -1≤x≤1,

now it shows x can be -1,0 or 1. question says integer x, so 0 is not considered, it also says x > 0, so -ve is also gone.

we have the answer as x=1, Sufficient.
Intern  Joined: 21 Apr 2014
Posts: 39
Re: If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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sasha40612 wrote:
If 8x > 3x + 4x, what is the value of the integer x?

(1) 6 – 4x > –2
(2) 3 – 2x ≤ 4 – x ≤ 5 – 2x

I have an explanation for this problem which goes against the general explanation. Please explain me why I am wrong.

Here
8x> 3x+4x
8x>7x is the condition given in the question
so
if x<0 8x<7x
and if x>0 8x>7x So there is an ambiguity with the condition mentioned in the question. We cant right away decide that 8x>7x => 8x-7x>0 => x>0

Lets come to the options now

#1 6-4x >-2
=> x<2 and this condition does not help to solve the ambiguity in the Question stem as x can be -ve or +ve . so insufficient.

#2 3 – 2x ≤ 4 – x ≤ 5 – 2x
=> -1≤ x≤ 1 which also says that x can be +ve or -ve . So cant resolve the ambiguity in the question stem. Not sufficient

I would choose the 5th option for this data sufficiency question as the statements are not sufficient individually or collectively.

But the right answer is individually both the conditions are sufficient i.e D

What is wrong with my explanation????

need help ASAP as i feel i'm kinda ambiguous with regards to inequality data sufficiency problems. Thank you.

The key thing to note with this problem is that x is an integer. That means it can't be 1.4 or 1.7, etc. (1) tells us that x<2 and we already know that x>0, so we then know that x has to equal one, because it is the only integer in between those numbers.

(2) tells us that -1≤ x≤ 1 and since we know that x>0, the only integer available is 1, making each one sufficient
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Re: If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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1
Given
From the question stem, we can infer several things:
- Constraint: x is an integer.
- Since 8x > 7x, then x is positive.
- The question asks about a definite value of x, but both the question stem and the statements are inequalities. Mmmmh interesting...

Statement 1
Solve the inequality to get x < 2. Since the question stem has already told us that x is a positive integer, then the only possible answer is x = 1.

Statement 2
Solve the compound inequality. First adding to ALL 3 PARTS +2x and then -4. You´ll get -1 ≤ x ≤ 1. Since the question stem has already told us that x is a positive integer, then the only possible answer is x = 1.

OA = D

Takeaways
- Translate the question stem and statements
- Pay attention to constraints. If you had missed that x is an integer, you would have yield to a different, yet incorrect answer. Be careful with this.
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Re: If 8x > 3x + 4x, what is the value of the integer x?  [#permalink]

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_________________ Re: If 8x > 3x + 4x, what is the value of the integer x?   [#permalink] 12 Jan 2018, 18:22
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