If w + z = 28, what is the value of wz : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 Feb 2017, 01:34

### 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

# If w + z = 28, what is the value of wz

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

### Hide Tags

Intern
Joined: 14 Jul 2012
Posts: 8
Concentration: Marketing, Entrepreneurship
WE: Sales (Other)
Followers: 0

Kudos [?]: 20 [0], given: 4

If w + z = 28, what is the value of wz [#permalink]

### Show Tags

22 Mar 2013, 09:14
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:48) correct 19% (00:39) wrong based on 271 sessions

### HideShow timer Statistics

If w + z = 28, what is the value of wz

(1) w and z are positive integers
(2) w and z are consecutive odd integers
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Mar 2013, 12:19, edited 1 time in total.
Edited the question.
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313
Followers: 110

Kudos [?]: 271 [1] , given: 66

Re: if w + Z = 28, what is the value of wz [#permalink]

### Show Tags

22 Mar 2013, 10:21
1
KUDOS
Expert's post
GMAThirst wrote:
if w + Z = 28, what is the value of wz

1. w and z are positive integers
2. w and z are consecutive odd integers

Hi GMAThirst, let's examine these statements one at a time:

1. w and z are positive integers.
We know that both must be positive, so this eliminates 30 and -2, but it could be 1 and 27, 2 and 26, 3 and 25, etc. All of which have different products (1x27=27, 2x26=52, etc) A is insufficient on its own

2. w and z are consecutive odd integers
This would have to be 13 and 15. No other positive consecutive odd integers would add up to 28. Statement A makes us wonder about negative numbers, what about -13 and -15? Well they would add up to -28, which isn't the same as +28, so they're out as possibilities. What about other negative consecutive odd integers? Nothing is ever going to give you anything other than a negative number, so no negative numbers could work here. Statement 2 is thus sufficient on its own, with no need to bring in statement #1. (w*z must be either 13*15 or 15*13, either way giving the answer of 195 by commutativity)

Hope this helps!
-Ron
_________________
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1123
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 184

Kudos [?]: 2000 [0], given: 219

Re: if w + Z = 28, what is the value of wz [#permalink]

### Show Tags

22 Mar 2013, 10:21
1. w and z are positive integers; thay can be any number < 27 as long as w+z=28

$$w=1, z=27$$

$$wz=27$$

$$w=2 ,z=26$$

$$wz=52$$

$$....$$

Not sufficient

2. w and z are consecutive odd integers; so they can be only 15 and 13

$$w=13, z =15$$

$$wz=195$$

$$z=13 ,w =15$$

$$wz=195$$

Sufficient

B
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Intern
Joined: 14 Jul 2012
Posts: 8
Concentration: Marketing, Entrepreneurship
WE: Sales (Other)
Followers: 0

Kudos [?]: 20 [0], given: 4

Re: if w + Z = 28, what is the value of wz [#permalink]

### Show Tags

22 Mar 2013, 10:47
Thanks VeritasPrepRon
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313
Followers: 110

Kudos [?]: 271 [5] , given: 66

Re: if w + Z = 28, what is the value of wz [#permalink]

### Show Tags

22 Mar 2013, 11:13
5
KUDOS
Expert's post
No problemo!

Just to clarify one thing. Two consecutive odd numbers adding up to 28 must be 13 and 15, but if the numbers get unwieldy, such as w+z = 280, just divide the sum by 2 and then take the numbers on either side. In other words, the two numbers need to average out to that, so it would be 139 and 141 in this example. Obviously, since this is the GMAT, the numbers will lead you to an even integer so you can take the odd ones on either side.

This is the same principle for dividing by 3 or any other number, you just need to divide by the number of terms. Ex: w + x + z = 279. What are the 3 consecutive odd integers that form w, x and z: 279 /3 = 93. The three odd numbers would be 91, 93 and 95, so that they average out to 93.

Hope this helps on questions like this when the numbers aren't so easy to spot!
-Ron
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37151
Followers: 7275

Kudos [?]: 96830 [0], given: 10800

If w + z = 28, what is the value of wz [#permalink]

### Show Tags

22 Mar 2013, 12:23
If w + z = 28, what is the value of wz

(1) w and z are positive integers. Infinitely many values are possible for w and z, for example: ..., (0, 28), (1, 27), ... Not sufficient.

(2) w and z are consecutive odd integers. So, we have that 28 is the sum of two consecutive odd integers: x+(x+2)=28 (where x is an odd integer) --> x=13. So, either w=13 and z=15 OR w=15 and z=13. In any case, wz=13*15. Sufficient.

_________________
Manager
Joined: 12 Jan 2013
Posts: 244
Followers: 4

Kudos [?]: 71 [0], given: 47

Re: If w + z = 28, what is the value of wz [#permalink]

### Show Tags

18 Jul 2013, 23:47
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?
Math Expert
Joined: 02 Sep 2009
Posts: 37151
Followers: 7275

Kudos [?]: 96830 [0], given: 10800

Re: If w + z = 28, what is the value of wz [#permalink]

### Show Tags

19 Jul 2013, 00:02
Expert's post
1
This post was
BOOKMARKED
aeglorre wrote:
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?

No. |28|=28, so w + z = |28| is the same as w + z = 28.

Guess, you meant: |w + z| = 28. Now, if the question were: "|w + z| = 28, what is the value of wz?", the correct answer would still be B. From |w + z| = 28 and w and z are consecutive odd integers, it follows that the integers can be 13 and 15 OR -13 and -15. In any case wz = 195.

Hope it's clear.
_________________
Manager
Joined: 12 Jan 2013
Posts: 244
Followers: 4

Kudos [?]: 71 [0], given: 47

Re: If w + z = 28, what is the value of wz [#permalink]

### Show Tags

19 Jul 2013, 00:08
Bunuel wrote:
aeglorre wrote:
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?

No. |28|=28, so w + z = |28| is the same as w + z = 28.

Guess, you meant: |w + z| = 28. Now, if the question were: "|w + z| = 28, what is the value of wz?", the correct answer would still be B. From |w + z| = 28 and w and z are consecutive odd integers, it follows that the integers can be 13 and 15 OR -13 and -15. In any case wz = 195.

Hope it's clear.

It is very clear - in my assumption I completely missed that what they asked was not for me to know what w and z in theirselves are, but what the PRODUCT of the two is. Since the PRODUCT of the two is the same irrespective of if both are positive or negative, B is sufficent.

Thanks a lot, there are severe flaws in my understanding, intuition and knowledge of concept but you're helping me a great deal.
Manager
Joined: 13 Oct 2013
Posts: 137
Concentration: Strategy, Entrepreneurship
Followers: 2

Kudos [?]: 38 [0], given: 125

Re: if w + Z = 28, what is the value of wz [#permalink]

### Show Tags

30 Nov 2013, 17:51
VeritasPrepRon wrote:
GMAThirst wrote:
if w + Z = 28, what is the value of wz

1. w and z are positive integers
2. w and z are consecutive odd integers

Hi GMAThirst, let's examine these statements one at a time:

1. w and z are positive integers.
We know that both must be positive, so this eliminates 30 and -2, but it could be 1 and 27, 2 and 26, 3 and 25, etc. All of which have different products (1x27=27, 2x26=52, etc) A is insufficient on its own

2. w and z are consecutive odd integers
This would have to be 13 and 15. No other positive consecutive odd integers would add up to 28. Statement A makes us wonder about negative numbers, what about -13 and -15? Well they would add up to -28, which isn't the same as +28, so they're out as possibilities. What about other negative consecutive odd integers? Nothing is ever going to give you anything other than a negative number, so no negative numbers could work here. Statement 2 is thus sufficient on its own, with no need to bring in statement #1. (w*z must be either 13*15 or 15*13, either way giving the answer of 195 by commutativity)

Hope this helps!
-Ron

But statement 2 does not say anything about positive or negative odd integers.So why we are considering positive consecutive odd integers here.In that way are we not taking statement 1 into consideration and which leads to answer C?
_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way

Math Expert
Joined: 02 Sep 2009
Posts: 37151
Followers: 7275

Kudos [?]: 96830 [0], given: 10800

Re: if w + Z = 28, what is the value of wz [#permalink]

### Show Tags

01 Dec 2013, 06:17
sunita123 wrote:
VeritasPrepRon wrote:
GMAThirst wrote:
if w + Z = 28, what is the value of wz

1. w and z are positive integers
2. w and z are consecutive odd integers

Hi GMAThirst, let's examine these statements one at a time:

1. w and z are positive integers.
We know that both must be positive, so this eliminates 30 and -2, but it could be 1 and 27, 2 and 26, 3 and 25, etc. All of which have different products (1x27=27, 2x26=52, etc) A is insufficient on its own

2. w and z are consecutive odd integers
This would have to be 13 and 15. No other positive consecutive odd integers would add up to 28. Statement A makes us wonder about negative numbers, what about -13 and -15? Well they would add up to -28, which isn't the same as +28, so they're out as possibilities. What about other negative consecutive odd integers? Nothing is ever going to give you anything other than a negative number, so no negative numbers could work here. Statement 2 is thus sufficient on its own, with no need to bring in statement #1. (w*z must be either 13*15 or 15*13, either way giving the answer of 195 by commutativity)

Hope this helps!
-Ron

But statement 2 does not say anything about positive or negative odd integers.So why we are considering positive consecutive odd integers here.In that way are we not taking statement 1 into consideration and which leads to answer C?

Please check here: if-w-z-28-what-is-the-value-of-wz-149627.html#p1201241 You can see there that we can find w and z even not knowing their signs.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13995
Followers: 592

Kudos [?]: 168 [0], given: 0

Re: If w + z = 28, what is the value of wz [#permalink]

### Show Tags

01 Apr 2016, 23:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If w + z = 28, what is the value of wz   [#permalink] 01 Apr 2016, 23:55
Similar topics Replies Last post
Similar
Topics:
What is the value of x + y ? (1) xy+ wz + xz+ wy= 8 (2) y + z = 4 1 23 Nov 2016, 02:05
1 What is the value of x + y ? (1) xy+ wz + xz+ wy= 8 (2) y + z = 4 1 23 Nov 2016, 02:05
2 If w ≠ x, w ≠ z, and x ≠ y, is (x-y)^3(w - z)^3/(w-z)^2(x-y)(w-x)^2 ? 4 13 Dec 2015, 04:52
6 If w+ z = 28, what is the value of wz? 7 13 Jan 2014, 00:58
4 If w and z are positive is w/z < 1 ? 9 25 Jul 2010, 23:58
Display posts from previous: Sort by

# If w + z = 28, what is the value of wz

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.