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Is |a-c| + |a| = |c|?

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Is |a-c| + |a| = |c|?  [#permalink]

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New post 14 Feb 2019, 03:24
5
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (02:28) correct 66% (02:12) wrong based on 98 sessions

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Is |a-c| + |a| = |c|?

(1) ab > bc
(2) ab < 0

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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 14 Feb 2019, 05:43
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|a-c| + |a| = |c|
|a-c| = |c| - |a|
to satisfy "|a-c| = |c| - |a|", there are 3 options:
1. a = c
2. a = 0
3. |c| > |a| (c>a in magnitude) but have similar signs.

statement 1: ab > bc
eliminates option 1 and 2, but leaves us with option 3 which can't be known as the sign of b is unknown.

statement 2: ab < 0
gives no information except that a and b \(\neq{0}\) and that a and b has different signs.

by combining statement 1 and 2: (see the testing table)
0>ab>bc while a and b have different signs, so a and c must have similar signs
so if b>0, then both a and b are negative and c>a in magnitude (|c| > |a|)
so if b<0, then both a and b are positive and c>a in magnitude (|c| > |a|)
these criteria satisfies the tested equation

so C
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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 14 Feb 2019, 07:48
Ans (C). Both statements together are sufficient to answer the question.
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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 14 Mar 2019, 13:46
In my opinion,
Such type of question (mentioned in main question) ask u a simple thing I.e. the two variables are in same directions or not.

For example
(I)
{|x|+|y|} is either EQUAL or GREATER than {|x+y|}.
When the two numbers (x & y) are in SAME DIRECTION (both positive or both negatives or both zero), both expressions [(|x|+|y|) & |x+y|] are EQUAL.

When the two numbers (x & y) are in OPPSITE DIRECTION (one positive and another one negative), |x|+|y| is GREATER than |x+y|.

(ii)
{|x|-|y|} is either EQUAL or LESS than {|x-y|}.
When the two numbers (x & y) are in SAME DIRECTION (both positive or both negatives or both zero) & x has greater ABSOLUTE value, both expressions [(|x|-|y|) & |x-y|] are EQUAL.

When the two numbers (x & y) are in OPPSITE DIRECTION (one positive and another one negative), |x|-|y| is LESS than |x-y|.

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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 14 Mar 2019, 14:28
2
In this question,
|a-c| + |a| = |c|?
or |a-c| = |c| - |a|?
or |c-a| = |c| - |a|?
That is (ii) situation of my previous post.

Thus, the question is asking : IS a & c in same direction & is the absolute value of a is greater than that of C?

statement 1 & 2 don’t guarantee anything about same direction of a&c.
Only combination of of c says the both requirement (same direction & absolute value of c).
So I would go for C.

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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 14 Mar 2019, 14:43
1
Number picking (I think better approach).

Statement 1: Insufficient
Case 1: a=1, b=-2 & c=3 (yes to main question)
Case 2: a=-1, b=2, &c=-3 (yes to main question)
Case 3: a=1,b=2 & c=-3 (no to main question)

Statement 2: insufficient. Coz no info about c.

Combined:
Case 3 from statement 1 is out coz statement 2 says ab is negative.
So remaining case 1&2 say YES to main question.

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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 14 Mar 2019, 15:02
1
1
Absolute value concept.

Absolute always says about distance.
|a| or |a-0| is the distance between 0 and a.

|a-c| is same thing as |c-a| which means the distance between a and c.

|c| is the distance between 0 and c.

Thus the question says
Is the sum of (I) DISTANCE between (0&a) & (ii) DISTANCE between (a&c) is EQUAL to DISTANCE between (0 &c)?

This is only possible if
I) a&c are on the same side of zero and
(ii) a is closer to zero and c is distant from zero.
[this is possible in positive and negative sides, as shown in attached photo.]

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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 20 Mar 2019, 08:16
is this problem from gmatprep? show me the screen, pls
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Re: Is |a-c| + |a| = |c|?  [#permalink]

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New post 22 Mar 2019, 20:51
to have /a-c/+/a/=/c/
we have /a-c/=/c/-/a/
c and a must be the same sign

from both condition
b(a-c)>0
ab<0

case 1
b<0 and a<c
b<0 then a>0, this mean c also >0
this is good
case 2
b>0 and a>c
b>0 the a<0 , the mean c also < 0
this is good

answer C.
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Re: Is |a-c| + |a| = |c|?   [#permalink] 22 Mar 2019, 20:51
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