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# If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the

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Kudos [?]: 1159 [0], given: 5501

If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the [#permalink]  13 Apr 2018, 06:13
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Question Stats:

87% (00:30) correct 12% (01:19) wrong based on 8 sessions
If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true?

A. ab < 0

B. ab > 0

C. a - b > 0

D. a + b < 0

E. a + b > 0
[Reveal] Spoiler: OA

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Kudos [?]: 546 [0], given: 88

Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the [#permalink]  16 Apr 2018, 20:58
Let $$a = -1$$
Let $$b = -2$$

Then $$|a| + |b| = 1 + 2 =3$$
and, $$|a + b| = |-3|= 3$$

Similarly,
Let $$a = 1$$
Let $$b = 2$$

Then, $$|a| + |b| = 1 + 2 =3$$
and, $$|a + b| = |3|= 3$$

Therefore either $$a,b$$ can be $$-1,-2$$ or $$1,2$$

The correct option should satisfy both the condition for $$(a,b)$$
only option b does that since $$a*b$$ is always$$+$$ve since we are multiplying $$2$$ $$+$$ve numbers or 2 $$-$$ve numbers which will always be $$+$$ve.
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the   [#permalink] 16 Apr 2018, 20:58
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