May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th. Jun 01 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jun 02 07:00 AM PDT  09:00 AM PDT Get personalized insights and an accurate assessment of your current quant score to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55274

If a = b, and c = d, is a = c?
[#permalink]
Show Tags
23 Feb 2016, 02:54
Question Stats:
76% (01:06) correct 24% (01:12) wrong based on 189 sessions
HideShow timer Statistics
If a = b, and c = d, is a = c? (1) b = d (2) b = d Kudos for correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Math Expert
Joined: 02 Aug 2009
Posts: 7686

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
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
Status: Persevere
Joined: 09 Jan 2016
Posts: 118
Location: Hong Kong
GPA: 3.52

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
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
Joined: 16 Aug 2015
Posts: 7372
GPA: 3.82

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
23 Feb 2016, 18:57
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 spareThe oneandonly 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 Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Senior Manager
Joined: 24 Nov 2015
Posts: 497
Location: United States (LA)

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
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
Joined: 04 Sep 2016
Posts: 1342
Location: India
WE: Engineering (Other)

If a = b, and c = d, is a = c?
[#permalink]
Show Tags
19 Nov 2017, 04:46
chetan2u Bunuel VeritasPrepKarishma niks18I 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
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
19 Nov 2017, 23:49
adkikani wrote: chetan2u Bunuel VeritasPrepKarishma niks18I 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 adkikanimod 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
Joined: 04 Sep 2016
Posts: 1342
Location: India
WE: Engineering (Other)

If a = b, and c = d, is a = c?
[#permalink]
Show Tags
20 Nov 2017, 00:02
Hi niks18Quote: 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
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
20 Nov 2017, 01:19
adkikani wrote: Hi niks18Quote: 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 adkikaniAs I mentioned mod is always positive, because it represents the distance from the 0point 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
Joined: 04 Sep 2016
Posts: 1342
Location: India
WE: Engineering (Other)

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
20 Nov 2017, 06:42
niks18Crystal clear now. +1 Kudos
_________________
It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!!



SVP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1675
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Real Estate)

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
09 Mar 2018, 00:46
niks18 wrote: adkikani wrote: chetan2u Bunuel VeritasPrepKarishma niks18I 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 adkikanimod 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 nonnegative rather than always positive. Please clarify. QZ
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Retired Moderator
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
09 Mar 2018, 11:56
QZ wrote: niks18 wrote: adkikani wrote: chetan2u Bunuel VeritasPrepKarishma niks18I 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 adkikanimod 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 nonnegative rather than always positive. Please clarify. QZ Hi QZYou 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
Joined: 17 May 2018
Posts: 137
Location: India

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
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
Joined: 22 Jun 2018
Posts: 28
Location: India
GPA: 3.82

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
15 May 2019, 22:14
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
Joined: 18 Aug 2017
Posts: 3535
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: If a = b, and c = d, is a = c?
[#permalink]
Show Tags
16 May 2019, 01:20
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.




Re: If a = b, and c = d, is a = c?
[#permalink]
16 May 2019, 01:20






