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.