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

It is currently 25 May 2019, 22:12

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If a = b, and c = d, is |a| = |c|?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55274
If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 23 Feb 2016, 02:54
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (01:06) correct 24% (01:12) wrong based on 189 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7686
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 23 Feb 2016, 09:59
Bunuel wrote:
If a = b, and c = d, is |a| = |c|?

(1) |b| = |d|
(2) b = -d


Kudos for correct solution.


Hi,
Since it is dealing with modulus, lets see what info we get from the Q..

Quote:
If a = b, and c = d, is |a| = |c|?

|a|=|c| means that irreespective of sign of b and d, the answer will be YES, if b and d have SAME NUMERIC VALUE..
lets see the choices..
(1) |b| = |d|
same numeric value..
suff

(2) b = -d
same numeric value..
suff
D

_________________
Current Student
avatar
B
Status: Persevere
Joined: 09 Jan 2016
Posts: 118
Location: Hong Kong
GMAT 1: 750 Q50 V41
GPA: 3.52
Reviews Badge
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 23 Feb 2016, 10:11
Bunuel wrote:
If a = b, and c = d, is |a| = |c|?

(1) |b| = |d|
(2) b = -d


Kudos for correct solution.


Statement 1:
|b| = |d|
This implies that either b = d or b = -d [Though, we will also get -b = -d and -b = d, we can ignore them as they are equivalent to b = d and b = -d]
First consider, b = d
replacing b = a and d = c, we get a = c.
Hence, |a| = |c|
Now, consider, b = -d
Again, replacing b = a and d = c, we get a = -c
Hence, |a| = |c|
Therefore, in either case we are able to answer the question is |a| = |c| = 0? with a definitive 'yes'.
Hence, statement 1 is sufficient. Options B, C and E are ruled out.

Statement 2:
b = -d
Again, replacing b = a and d = c, we get a = -c
Hence, |a| = |c|
Therefore, we are able to answer the question is |a| = |c| = 0? with a definitive 'yes'.
Hence, statement 2 is also sufficient. Option A is also ruled out.

The correct answer, therefore, is D
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 23 Feb 2016, 18:57
2
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a = b, and c = d, is |a| = |c|?

(1) |b| = |d|
(2) b = -d


When you modify the original condition and the question, they become |a|=|c|?--> |b|=|d|?--> b=-d or d?, which makes 1)=2). Also, each of them is yes, which is sufficient.
Therefore, the answer is D.


 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Senior Manager
Senior Manager
User avatar
G
Joined: 24 Nov 2015
Posts: 497
Location: United States (LA)
Reviews Badge
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 10 May 2016, 14:20
From the question it is clear that we have to check if numerical values of a and c are equal (signs will not matter)
Statement 1 says |b| = |d| . It clearly shows that |a| = |c| as a = b and c = d so sufficient
Statement 2 says b = -d. It clearly tells that numerical value of b and d is same which in turn says |a| = |c| so sufficient
Correct answer - D
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1342
Location: India
WE: Engineering (Other)
CAT Tests
If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 19 Nov 2017, 04:46
chetan2u Bunuel VeritasPrepKarishma niks18

I am really confused about opening modulus in both sides of equality
in spite of going through chetan2u signature

I could get away by simply substituting a and c for b and d resp to establish suff for St 1
but St 2 was confusing.

Can you please add your two cents?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 19 Nov 2017, 23:49
2
adkikani wrote:
chetan2u Bunuel VeritasPrepKarishma niks18

I am really confused about opening modulus in both sides of equality
in spite of going through chetan2u signature

I could get away by simply substituting a and c for b and d resp to establish suff for St 1
but St 2 was confusing.

Can you please add your two cents?


Hi adkikani

mod is always positive, so if \(x<0\) i.e negative then \(|x| =-x\)

for eg. if \(x=-3\) then \(|-3|=-(-3)=3\)

so for Statement 2: \(b=-d\) is simply \(|b|=|-d|\), apply mod on both sides

which in turn is \(|b|=|d|\), now substitute the value of \(b\) & \(d\) to get \(|a|=|c|\)

Alternatively, we are asked is \(|a|=|c|\), square both sides to remove mod. so the question becomes Is \(a^2=c^2\)?

Statement 2: \(b=-d\), substitute the value of \(b\) & \(d\) to get \(a=-c\). Now square both sides to get \(a^2=c^2\). Sufficient
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1342
Location: India
WE: Engineering (Other)
CAT Tests
If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 20 Nov 2017, 00:02
Hi niks18

Quote:
mod is always positive, so if \(x<0\) i.e negative then \(|x| =-x\)

for eg. if \(x=-3\) then \(|-3|=-(-3)=3\)


how did you use above knowledge to infer below :

Quote:
\(|b|=|-d|\), apply mod on both sides

which in turn is \(|b|=|d|\),


To be more specific, \(|b|=|d|\), note that we do not know whether b or d is less than zero
but all we know is that b and d have opposite signs. Let me know if I missed anything.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 20 Nov 2017, 01:19
1
adkikani wrote:
Hi niks18

Quote:
mod is always positive, so if \(x<0\) i.e negative then \(|x| =-x\)

for eg. if \(x=-3\) then \(|-3|=-(-3)=3\)


how did you use above knowledge to infer below :

Quote:
\(|b|=|-d|\), apply mod on both sides

which in turn is \(|b|=|d|\),


To be more specific, \(|b|=|d|\), note that we do not know whether b or d is less than zero
but all we know is that b and d have opposite signs. Let me know if I missed anything.


Hi adkikani

As I mentioned mod is always positive, because it represents the distance from the 0-point in the number line and distance cannot be negative.
so irrespective of the value of b or d; |-d|=|d|

let b=2 then b=-d will result in d=-2

So |2|=2 and |-2|=-(-2)=2=|2| so we have |b|=|-d| =>|b|=|d|
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1342
Location: India
WE: Engineering (Other)
CAT Tests
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 20 Nov 2017, 06:42
niks18

Crystal clear now. +1 Kudos :-)
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
SVP
SVP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1675
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Reviews Badge
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 09 Mar 2018, 00:46
niks18 wrote:
adkikani wrote:
chetan2u Bunuel VeritasPrepKarishma niks18

I am really confused about opening modulus in both sides of equality
in spite of going through chetan2u signature

I could get away by simply substituting a and c for b and d resp to establish suff for St 1
but St 2 was confusing.

Can you please add your two cents?


Hi adkikani

mod is always positive, so if \(x<0\) i.e negative then \(|x| =-x\)

for eg. if \(x=-3\) then \(|-3|=-(-3)=3\)

so for Statement 2: \(b=-d\) is simply \(|b|=|-d|\), apply mod on both sides

which in turn is \(|b|=|d|\), now substitute the value of \(b\) & \(d\) to get \(|a|=|c|\)

Alternatively, we are asked is \(|a|=|c|\), square both sides to remove mod. so the question becomes Is \(a^2=c^2\)?

Statement 2: \(b=-d\), substitute the value of \(b\) & \(d\) to get \(a=-c\). Now square both sides to get \(a^2=c^2\). Sufficient


Hey niks18,

Red part marked above is inconsistent as to my understanding absolute values are always non-negative rather than always positive.

Please clarify.

QZ
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 09 Mar 2018, 11:56
QZ wrote:
niks18 wrote:
adkikani wrote:
chetan2u Bunuel VeritasPrepKarishma niks18

I am really confused about opening modulus in both sides of equality
in spite of going through chetan2u signature

I could get away by simply substituting a and c for b and d resp to establish suff for St 1
but St 2 was confusing.

Can you please add your two cents?


Hi adkikani

mod is always positive, so if \(x<0\) i.e negative then \(|x| =-x\)

for eg. if \(x=-3\) then \(|-3|=-(-3)=3\)

so for Statement 2: \(b=-d\) is simply \(|b|=|-d|\), apply mod on both sides

which in turn is \(|b|=|d|\), now substitute the value of \(b\) & \(d\) to get \(|a|=|c|\)

Alternatively, we are asked is \(|a|=|c|\), square both sides to remove mod. so the question becomes Is \(a^2=c^2\)?

Statement 2: \(b=-d\), substitute the value of \(b\) & \(d\) to get \(a=-c\). Now square both sides to get \(a^2=c^2\). Sufficient


Hey niks18,

Red part marked above is inconsistent as to my understanding absolute values are always non-negative rather than always positive.

Please clarify.

QZ


Hi QZ

You are right that mod is "Always Non negative" i.e. either positive or 0. I think either I missed mentioning 0 or I might had wrote that statement in the context of the question. Anyways thanks for highlighting.
Manager
Manager
avatar
S
Joined: 17 May 2018
Posts: 137
Location: India
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 15 May 2019, 21:43
From statement 1 we get that even if b and d are of opposite signs the absolute value of a would be equal to the absolute value of c. Sufficient.
From statement 1 we get that b and d are of opposite signs, the absolute value of a would be equal to the absolute value of c even then. Sufficient.
IMO D

Posted from my mobile device
Intern
Intern
avatar
S
Joined: 22 Jun 2018
Posts: 28
Location: India
GMAT 1: 670 Q49 V34
GRE 1: Q170 V160
GPA: 3.82
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 15 May 2019, 22:14
1
As we our taking absolute values, this seems obvious that irrespective of positive or negative numbers, we will get sufficient statements.

=> |b| = |d|

sufficient.

=> b = -d

Sufficient. D

We can also plug numbers.
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3535
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If a = b, and c = d, is |a| = |c|?  [#permalink]

Show Tags

New post 16 May 2019, 01:20
1
Bunuel wrote:
If a = b, and c = d, is |a| = |c|?

(1) |b| = |d|
(2) b = -d


Kudos for correct solution.



#1
|b| = |d|
irrespective of b & d sign ; value of a & c will be equal since they are in modulus
sufficient
#2
b=-d
again same logic as #1; sufficient
IMO D
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
GMAT Club Bot
Re: If a = b, and c = d, is |a| = |c|?   [#permalink] 16 May 2019, 01:20
Display posts from previous: Sort by

If a = b, and c = d, is |a| = |c|?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.