Guide 4 Chap 10 page 169

[kpkanupriyakhmi]

Q 8 :-
Between 5 and 10 on a number line, exclusive,.....
Q9 same page:-
Suppose that |b-a|=2. Which of the following......

[n00bpron00bpron00b]

Q8)

https://www.manhattanprep.com/gre/forum ... fe397e0a33


Q9)

|b-a| = 2 ; which of the following must be true :

Simplifying the given condition -

b-a = 2
a = b -2 and

b-a = -2
a = b + 2

Each answer choice should satisfy both the equations -
a = b-2
a = b+2

1st) a must be positive if b is positive

consider b=1
a = 1-2
a = -1 (does not satisfy)

a=1+2
a=3 (does satisfy) ; the question states must be true (the value should hold true for both conditions)

So 1st option is not valid.

2nd) a must be negative if b is negative

consider b=-1
a=-1-2
a=-3 (satisfies)

a=-1+2
a=1 (does not satisfy)

Same reason as we saw in the 1st option - this case is invalid

3) b>0 if a>2
consider the minimum value for "a"
a>2 ; let a=2.1

a = b-2
2.1=b-2
b=4.1 (satisfies)

a = b+2
2.1=b+2
b=0.1 (satisfies)

Both conditions hold true

So ans is only (C)

[tommywallach]

Hey Kp,

Just a reminder. Please only post ONE question at a time in each thread.

Great explanation from Noob. Another, perhaps simpler way to think of this, is that the real MEANING of abs(b-a) = 2 is simply: "a and b are two units apart."

This means that of course they could both be positive, or both negative, or one of each (-1 and 1). Also, the third statement should be obvious, because if a is greater than 2, then whether we go two units UP or two units DOWN, we'll still be positive for b.

Hope that makes sense!

-t