It is currently 12 Dec 2017, 21:39

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the value of |a + b|?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42575

Kudos [?]: 135411 [1], given: 12692

What is the value of |a + b|? [#permalink]

### Show Tags

08 Jun 2015, 06:40
1
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:11) correct 25% (01:14) wrong based on 308 sessions

### HideShow timer Statistics

What is the value of |a + b|?

(1) (a + b + c + d) (a + b – c – d) = 16
(2) c + d = 3

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135411 [1], given: 12692

SVP
Joined: 08 Jul 2010
Posts: 1857

Kudos [?]: 2400 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: What is the value of |a + b|? [#permalink]

### Show Tags

08 Jun 2015, 06:52
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
What is the value of |a + b|?

(1) (a + b + c + d) (a + b – c – d) = 16
(2) c + d = 3

Kudos for a correct solution.

Statement 1: (a + b + c + d) (a + b – c – d) = 16

i.e. [(a + b) + (c + d)] [(a + b) – (c + d)] = 16

i.e. $$(a + b)^2 – (c + d)^2 = 16$$

No information about (c+d) hence we can't infer the value of (a+b)

Hence, NOT SUFFICIENT

Statement 2: c + d = 3

No information about (a+b) hence we can't infer the value of (a+b)

Hence, NOT SUFFICIENT

Combining the two statements:

i.e. $$(a + b)^2 – (c + d)^2 = 16$$ AND c + d = 3

i.e. $$(a + b)^2 – (3)^2 = 16$$

i.e. $$(a + b)^2 = 16+9$$
i.e. $$(a + b)^2 = 25$$

i.e. $$(a + b) = +5$$

But anyways, |a + b| = 5

Hence, SUFFICIENT

[Reveal] Spoiler:
C

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2400 [0], given: 51

Retired Moderator
Joined: 06 Jul 2014
Posts: 1271

Kudos [?]: 2423 [0], given: 178

Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Re: What is the value of |a + b|? [#permalink]

### Show Tags

08 Jun 2015, 07:00
Bunuel wrote:
What is the value of |a + b|?

(1) (a + b + c + d) (a + b – c – d) = 16
(2) c + d = 3

Kudos for a correct solution.

1) Insufficient because there is a lot of variants possible
2) Insufficient because we know nothing about a and b

1+2) if c + d = 3 than -c-d = -3
so we can rewrite first statement as
$$(a+b+3)(a+b-3)=16$$
$$(a+b)^2-9=16$$
$$(a+b)^2=25$$
$$|a+b|=5$$
Sufficient
_________________

Kudos [?]: 2423 [0], given: 178

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10379

Kudos [?]: 3683 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: What is the value of |a + b|? [#permalink]

### Show Tags

09 Jun 2015, 18:06
Hi All,

This is a layered, scary-"looking" DS question, but if you organize the given information in a certain way, you can take advantage of the built-in patterns and get to the correct answer without too much trouble (you will need to take a bunch of notes though and TESTing VALUES will help).

We're asked for the value of |A+B|.

Fact 1: (A + B + C + D) (A + B – C – D) = 16

The equation we have here is certainly complicated, but there are some patterns in it worth noting:
1) (A+B) exists in both parentheses
2) (C+D) exists in the both parentheses (in the 1st, it's added; in the 2nd, it's subtracted)
3) The product is +16, so the parentheses are either BOTH positive OR BOTH negative.

IF...
A = 4
B=C=D=0
(4+0+0+0)(4+0+0+0) = 16
The answer to the question is |4+0| = 4

For the second TEST, I'm going to actually consider the information in Fact 2....what IF... C+D = 3....how would that impact the equation in Fact 1.....

IF...
A = 4
B = 1
C+D = 3
(4+1+3)(4+1-3) = (8)(2) = 16
The answer to the question is |4+1| = 5
Fact 1 is INSUFFICIENT

Fact 2: C+D = 3

This tells us NOTHING about A or B.
Fact 2 is INSUFFICIENT

Combined, we know....
(A + B + C + D) (A + B – C – D) = 16
C+D = 3

Substituting in, we have...
(A+B+3)(A+B-3) = 16

There aren't that many ways to end up with a product of 16 under these circumstances. From our prior TESTs, we know that A+B = 5 is one possibility....

To find the other possibility, I'm going to refer to (A+B) as X....now the given equation is...
(X+3)(X-3) = 16

FOILing this out gives us...
X^2 - 9 = 16
X^2 = 25
X = 5 or -5

Thus the only OTHER possibility is if A+B = -5.
|5| = 5
|-5| = 5
The answer to the question is ALWAYS 5.
Combined, SUFFICIENT

[Reveal] Spoiler:
C

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3683 [0], given: 173

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1347

Kudos [?]: 2042 [4], given: 6

What is the value of |a + b|? [#permalink]

### Show Tags

09 Jun 2015, 18:20
4
KUDOS
Expert's post
Whenever we see a or b, we always see "a+b", and whenever we see c or d, we see "c+d" (or "-c-d" which is just -(c+d) ). So we can make everything look a lot simpler if we just let k = a+b and m = c+d and rephrase the entire question:

What is |k| ?

1. (k + m)(k - m) = 16
2. m = 3

Then each statement is clearly insufficient alone, and using both statements, noticing the factors on the left side of S1 are in the difference of squares pattern, we find k^2 - 9 = 16, so k^2 = 25 and |k| = 5, so the answer is C.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 2042 [4], given: 6

Current Student
Joined: 29 Mar 2015
Posts: 44

Kudos [?]: 12 [0], given: 9

Location: United States
Re: What is the value of |a + b|? [#permalink]

### Show Tags

10 Jun 2015, 02:02
Bunuel wrote:
What is the value of |a + b|?

(1) (a + b + c + d) (a + b – c – d) = 16
(2) c + d = 3

Kudos for a correct solution.

1. $$(a + b + c + d) (a + b – c – d) = 16$$ --> $$(a + b + c + d) (a + b - (c + d)) = 16$$. Not sufficient since c+d could be 0, meaning |a+b| is 4. If c+d is 1, we have $$(a + b + 1) (a + b - (1)) = 16$$ --> $$(a + b)^2 - 1 = 16$$ --> $$(a + b)^2= 17$$ so not sufficient.
2. Nothing about a or b so not sufficient.

Together: $$(a + b + 3) (a + b - 3) = 16$$ --> $$(a + b)^2 - 9 = 16$$ --> $$(a + b)^2= 25$$ so sufficient, the answer is C.

Kudos [?]: 12 [0], given: 9

Manager
Joined: 01 Jan 2015
Posts: 56

Kudos [?]: 3 [0], given: 7

Re: What is the value of |a + b|? [#permalink]

### Show Tags

14 Jun 2015, 03:26
ST-1
(A+B+C+D)(A+B-C-D)=16
Now we can see the above expression can be written as (A+B)+(C+D) X (A+B)-(C+D) = (A+B)^2 - (C+D)^2
So we got to this expression but cannot solve it further, hence NS

ST-2
C+D=3
NS

Combining ST1 AND ST2 we get
(A+B)^2 - 9 =16
(A+B)^2 = 25
(A+B) = +/-5
|A+B|=5

Kudos [?]: 3 [0], given: 7

Math Expert
Joined: 02 Sep 2009
Posts: 42575

Kudos [?]: 135411 [0], given: 12692

Re: What is the value of |a + b|? [#permalink]

### Show Tags

15 Jun 2015, 05:12
Bunuel wrote:
What is the value of |a + b|?

(1) (a + b + c + d) (a + b – c – d) = 16
(2) c + d = 3

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

We are asked for the absolute value of a + b, so we will try to manipulate the statements to isolate that combination of variables, a + b. We will start with the easier statement, which in this case is Statement (2).

(2) INSUFFICIENT: This gives us information about c and d, and the relationship between them, but no information about a or b.

(1) INSUFFICIENT: We can manipulate the equation to group (a + b) and (c + d) terms:
(a + b + c + d) (a + b – c – d) = 16
[(a + b) + (c + d)][(a + b) – (c + d)] = 16

Note that this is of the form (x + y)(x – y), where x = (a + b) and y = (c + d). We recognize this as the “difference of two squares” special product, (x + y)(x – y) = x^2 – y^2. Thus, we may transform this expression:
[(a + b) + (c + d)][(a + b) – (c + d)] = 16
(a + b)^2 – (c + d)^2 = 16
(a + b)^2 = 16 + (c + d)^2

We don't know the value of c + d, so we cannot determine the value of (a + b)^2.

(1) AND (2) SUFFICIENT: From statement (2), we know that (a + b)^2 = 16 + (c + d)^2. From statement (1) we know that c + d = 3. Substituting for c + d:
(a + b)^2 = 16 + (c + d)^2
(a + b)^2 = 16 + 3^2
(a + b)^2 = 16 + 9
(a + b)^2 = 25
(a + b) = 5 or –5
|a + b| = 5

_________________

Kudos [?]: 135411 [0], given: 12692

Manager
Joined: 10 Dec 2011
Posts: 100

Kudos [?]: 37 [0], given: 82

Location: India
Concentration: Finance, Economics
GMAT Date: 09-28-2012
WE: Accounting (Manufacturing)
Re: What is the value of |a + b|? [#permalink]

### Show Tags

11 Nov 2017, 07:36
Good question.
replacing c+d by 3 in both the brackets solves this.
I. (a+b+c+d) (a+b-(c+d)) = 16
let a+b=x.
II. c+d = 3
(x + 3) ((x-3) = 16. therefore, x = 5 = (a+b)
suffient both. C

Kudos [?]: 37 [0], given: 82

Manager
Joined: 10 Dec 2011
Posts: 100

Kudos [?]: 37 [0], given: 82

Location: India
Concentration: Finance, Economics
GMAT Date: 09-28-2012
WE: Accounting (Manufacturing)
Re: What is the value of |a + b|? [#permalink]

### Show Tags

11 Nov 2017, 07:41
Good question.
replacing c+d by 3 in both the brackets solves this.
I. (a+b+c+d) (a+b-(c+d)) = 16
let a+b=x.
II. c+d = 3
(x + 3) ((x-3) = 16. therefore, x = 5 = (a+b)
suffient both. C

Kudos [?]: 37 [0], given: 82

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4461

Kudos [?]: 3141 [0], given: 0

GPA: 3.82
What is the value of |a + b|? [#permalink]

### Show Tags

13 Nov 2017, 23:40
Bunuel wrote:
What is the value of |a + b|?

(1) (a + b + c + d) (a + b – c – d) = 16
(2) c + d = 3

Kudos for a correct solution.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables ( a and b ) and 0 equations, C is most likely to be the answer.
Thus, we need to consider both conditions together first.

$$(a+b+c+d) (a+b–c–d) = 16$$
$${(a+b)+(c+d)}{(a+b)–(c+d)} = 16$$
$$(a+b)^2 - (c+d)^2 = 16$$
$$(a+b)^2 = 25$$ since $$c + d = 3$$
$$|a+b| = 5$$

They are sufficient.

By CMT(Common Mistake Type)4, we need to check A or B and consider each condition only.

Condition 1)
$$(a+b+c+d) (a+b–c–d) = 16$$
$${(a+b)+(c+d)}{(a+b)–(c+d)} = 16$$
$$(a+b)^2 - (c+d)^2 = 16$$
This is not sufficient, since we don't know $$c+d$$.

Condition 2)
We don't have anything about $$a$$ and $$b$$.
This is not sufficient either.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E).
_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 3141 [0], given: 0

What is the value of |a + b|?   [#permalink] 13 Nov 2017, 23:40
Display posts from previous: Sort by