GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 07 Dec 2019, 10:11

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Status: wake up with a purpose
Joined: 24 Feb 2017
Posts: 151
Concentration: Accounting, Entrepreneurship
Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

14 Feb 2019, 03:24
2
1
26
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:36) correct 57% (02:14) wrong based on 310 sessions

### HideShow timer Statistics

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

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

Posted from my mobile device

_________________
If people are NOT laughing at your GOALS, your goals are SMALL.
Director
Status: Manager
Joined: 27 Oct 2018
Posts: 746
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

Updated on: 12 Jun 2019, 15:17
8
|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 c are negative and c>a in magnitude (|c| > |a|)
so if b<0, then both a and c are positive and c>a in magnitude (|c| > |a|)
these criteria satisfies the tested equation

so C
Attachments

Untitled.png [ 16.41 KiB | Viewed 3131 times ]

Originally posted by MahmoudFawzy on 14 Feb 2019, 05:43.
Last edited by MahmoudFawzy on 12 Jun 2019, 15:17, edited 1 time in total.
##### General Discussion
Intern
Joined: 24 Jan 2019
Posts: 18
Location: India
GMAT 1: 690 Q50 V36
GPA: 3.94
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

14 Feb 2019, 07:48
Ans (C). Both statements together are sufficient to answer the question.
Manager
Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

14 Mar 2019, 13:46
4
2
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|.

Posted from my mobile device
Manager
Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

14 Mar 2019, 14:28
2
1
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.

Posted from my mobile device
Manager
Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

14 Mar 2019, 14:43
3
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.

Posted from my mobile device
Manager
Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

14 Mar 2019, 15:02
5
1
Absolute value concept.

|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.]

Posted from my mobile device
Attachments

image.jpg [ 1.07 MiB | Viewed 2675 times ]

Director
Joined: 29 Jun 2017
Posts: 927
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

20 Mar 2019, 08:16
is this problem from gmatprep? show me the screen, pls
Director
Joined: 29 Jun 2017
Posts: 927
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

22 Mar 2019, 20:51
1
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

Manager
Joined: 28 May 2018
Posts: 150
Location: India
Schools: ISB '21 (A)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

12 Jun 2019, 10:55
1
Mahmoudfawzy83 wrote:
|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

Small correction here.
so if b>0, then both a and c are negative and c>a in magnitude (|c| > |a|)
so if b<0, then both a and c are positive and c>a in magnitude (|c| > |a|)
Manager
Joined: 27 Nov 2015
Posts: 120
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

15 Jun 2019, 09:27
i do not understand this question at all.. can we get some expert reply on this please?
Intern
Joined: 31 Mar 2019
Posts: 5
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

26 Jun 2019, 17:02
Bunuel

what is the correct answer to this question?

Manager
Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

26 Jun 2019, 22:23
Giro2345 wrote:
Bunuel

what is the correct answer to this question?

Posted from my mobile device
VP
Joined: 14 Feb 2017
Posts: 1314
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 650 Q48 V31
GMAT 6: 600 Q38 V35
GPA: 3
WE: Management Consulting (Consulting)
Re: Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

02 Jul 2019, 01:25
This question follows the rules of the general form:
|x-y|=|x| - |y|
if:
a. y = 0; or
b. x and y have the same sign, and x>y

So reorganising the stem.
is |a-c| + |a| =|c|

is |a-c| =|c| - |a|
reshuffle by multiply by -1

is -|a-c| = |a| - |c|

For this to be true c must equal 0 or a and c must have the same sign and a must be greater than c
(1) ab > bc
++ >+(-) a and c could have different signs; or--> No
++>++ a and c could have the same signs; or -->Yes
++>+(0) c could be equal to zero -->Yes

Insufficient

(2) ab<0
could be +- or -+
either way we knowing about c
Insufficient

Combined (1+2)
ab<0
therefore
ab > bc
(-) > bc

Possible cases:
ab > bc
(-)+> +(-) a and c are both negative, but a must be greater than c to satisfy the constraint
+(-)>(-)+ a and c are both positive, but a must be greater than c to satisfy the constraint

In either case, a must be greater than c and must have the same sign as c, therefore combined statements are sufficient.

We can test numbers to validate the theory.
-|a-c| = |a| - |c|

condition 1: a and c are both negative and a > c
-|-2-(-3)| = |-2|-|-3|
-|1| = 2-3
-1 = -1

condition 2: a and c are both positive and a > c
-|3-2|=|3|-|2|
-|1| = |3|-|2|
-1 = 1 is not possible, therefore a and c must both be negative

Bunuel, sorry to pester but is my working out correct?
SVP
Joined: 03 Jun 2019
Posts: 1876
Location: India
Is |a-c| + |a| = |c|?  [#permalink]

### Show Tags

24 Sep 2019, 09:18
RashedVai wrote:
Is |a-c| + |a| = |c|?

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

Posted from my mobile device

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

(1) ab > bc
ab - bc > 0
b (a-c) > 0
If b>0; a-c>0; a>c
If b<0; a-c<0; a<c
NOT SUFFICIENT

(2) ab < 0
If b>0; a<0
If b<0; a>0
No information provided for c
NOT SUFFICIENT

(1) + (2)
(1) ab > bc
ab - bc > 0
b (a-c) > 0
If b>0; a-c>0; a>c
If b<0; a-c<0; a<c
(2) ab < 0
If b>0; a<0
If b<0; a>0
If b>0; a-c>0; a>c; c<a<0; |c-a| = |c| - |a|
c------a-----------0
If b<0; a-c<0; a<c; c>a>0; |c-a| = |c| - |a|
0-------a------------c
SUFFICIENT

IMO C
Is |a-c| + |a| = |c|?   [#permalink] 24 Sep 2019, 09:18
Display posts from previous: Sort by