Quant: Data Sufficiency: Questions/Discussion

[Matt P]

(Just attempting to keep things organized)

From Sulman:

If x is positive, is x > 4?

(1) (4  x)^2 < 1

(2) (x  4)^2 < 1

- Sulman, I'm not sure if it's just my computer, but I can't see anything in the two equations between the 4 and the x. I'll assume it's a minus sign, but correct me if I'm wrong:

Here is my approach; hopefully someone else can confirm or refute.

Rigorous Method:

(1): (4-x)^2 < 1 means that |4-x| < 1. 

If x < 4, (4-x) will be positive. Thus (4-x) < 1 reduces to x > 3. In this case, 3 < x < 4.

If x > 4, (4-x) will be negative. Thus (x-4) < 1 reduces to x < 5. In this case, 4 < x < 5.

We have a case in which x > 4 is true, and a case in which x > 4 is false. 

Statement 1 is therefore insufficient.

(2): (x-4)^2 < 1 means that |x-4| < 1. This will be analyzed like the last case:

If x < 4, (x-4) will be negative. Thus (4-x) < 1 reduces to x > 3. In this case, 3 < x < 4.

If x > 4, (x-4) will be positive. Thus (x-4) < 1 reduces to x < 5. In this case, 4 < x < 5.

Again, we have cases that demonstrate both truth and falsehood of the question stem.

Statement (2) is thus insufficient.

(1) + (2) together: looking at the two equations, we can see that they don't provide any extra information than either one alone. Still insufficient.

The answer is thus (E).

Simple Method:

We want to know if x > 4:

Imagine a number line:  <-------------------------(4)--------------------------->

Statement 1 simply tells us the maximum distance between x and 4 is 1.         <------------------------(3)///////////(4)////////////(5)----------------->

The shaded region represents the possible value for x.

Statement 2 tells us the exact same thing. 

So, clearly we cannot determine whether or not x > 4.

(E).

[Sulman Raja]

My bad. I copied and pasted it from a document that didn't transfer correctly.  Yes it is a negative sign so your efforts didn't go to waste!. Here's the question restated correctly for clarification. 

If x is positive, is x > 4?

(1) (4 - x)^2 < 1

(2) (x - 4)^2 < 1

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[Matt P]

Hey Guys,

Nice 700 level Data Sufficiency question today from BeatTheGMAT, if you haven't checked it out.

If n is a positive integer and r is the remainder when n^2-1 is divided by 8, what is the value of r? 
1)n is odd 
2)n is not divisible by 8

[Vaibhav Sinha]

Clearly A is sufficient here. 

Expression n^2-1 can be expanded as (n-1)(n+1). 

When N is odd here, we basically have consecutive even integers multiplied. And since we have 3 2's in the product (except for the case when n=1 in which case the final number is 0 which is again divisible by 8), the final product will always be divisible by 8; hence the value of R=0 in each case.

Statement B: R in this case is not constant. Hence this statement is not sufficient.

Thanks,

Vaibhav.