Is |a| = |b| ? (1) a + b = 0 (2) a - b = 2

Question

Is |a| = |b| ?

(1) a + b = 0
(2) a - b = 2

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gmatophobia · Answer

Question  : Is the distance of a from 0 = the distance of b from 0 ?

Statement 1

a + b = 0

a = -b

This means, a and b lie on the opposite side of number line. The distance between a and 0 is same as the distance between b and 0.

Hence the statement is sufficient.

We can eliminate B, C and E.

Statement 2

a - b = 2

a = b + 2

This means that a lies 2 units to the right on a number line.

-------- b -------- 0 -------- a ---------

If the distance between 0 and b = 1 unit and the distance between 0 and a = 1, a will still lie 2 units right of b and the distance between a and 0 is same as the distance between b and 0.

However, if the arrangement is as shown

-------- 0 -------- b -------- a ---------

The distance between a and 0 is not same as the distance between b and 0.

The statement is not sufficient

Option A

Maria240895chile · Answer

why is not D?

if a-b=2 it means they differ by 2
if a =4 b=2
if a=6 b=4

so |a| = |b| will never be equal.

so should be sufficient.

please someone explain it to me

AntonEfimov · Answer

Square |a| = |b| and get a^2=b^2

This breaks down to (a-b)(a+b) = 0

a=b or a=-b

Then look at the statements:
1) If a+b=0, then a=-b. Definitely is sufficient to tell whether |a| = |b|

2) If a-b=2, then a=b+2. Substitute to a=b - insolvable. Then substitute to a=-b. We get b=1. We don't know whether b=1 or some other number. Theoretically if b=1, then |a| = |b| is true, but we don't know if b=1, therefore it is insufficient

Is |a| = |b| ? (1) a + b = 0 (2) a - b = 2

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