BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Properties of numbers

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Sat Dec 08, 2012 5:03 am

Properties of numbers

by saidov.mikhail » Tue Jul 23, 2013 5:52 am
For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?
(1) w = max(20, z) for some integer z.
(2) w = max(10, w)

I'm confused with description of example. Why min (5,2) = 2 ?

thanks for help
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Jul 23, 2013 6:00 am
saidov.mikhail wrote: I'm confused with description of example. Why min (5,2) = 2 ?
We refer to this as a "strange operator" question. For these question types you are introduced to some new kind of symbol. (Aside: remember when you were first introduced to the square root symbol? At first, you didn't know what it meant, and now you do.)

The strange operators here are "max" and "min."
The "max" operation basically says, "take the 2 given values in the brackets and output the greatest one.
So, for example:
max(8, 3) = 8, since 8 is the larger of the two values
max(-3, 4) = 4, since 4 is the larger of the two values
max(-1, 0) = 0, since 0 is the larger of the two values
etc.

The "min" operation says, "take the 2 given values in the brackets and output the smallest one.
So, for example:
min(8, 3) = 3, since 3 is the smaller of the two values
min(-2, 6) = -2, since -2 is the smaller of the two values
min(-5, -7) = -7, since -7 is the smaller of the two values
etc.

I hope that helps.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Jul 23, 2013 6:01 am
saidov.mikhail wrote: For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?

(1) w = max(20, z) for some integer z.
(2) w = max(10, w)
Target question: What is the value of min(10, w)?

Statement 1: w = max(20, z) for some integer z.
Let's take a closer look at max(20, z)
If z < 20, then max(20, z) = 20
If z > 20, then max(20, z) = some value greater than 20
So, max(20, z) must be greater than or equal to 20
Since, w = max(20, z), we can conclude that w is greater than or equal to 20
From this, we can conclude that min(10, w) = 10, since 10 will be the lesser value
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: w = max(10, w)
If w = max(10, w), then w is the larger value.
In other words, w is greater than or equal to 10
If w is greater than or equal to 10, then we can conclude that min(10, w) = 10
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Tue Nov 23, 2010 7:21 am

by prashanthichennupati » Tue Jul 23, 2013 7:04 am
Brent: Can you please explain how statement 2 is sufficient?

Statement 2: w = max(10, w)
If w = max(10, w), then w is the larger value.
In other words, w is greater than or equal to 10
If w is greater ,then we can conclude that min(10, w) = 10
If w is equal, then how can we conclude min(10,w) =10??

Neither in the question stem nor in the statements it is mentioned that min(10,10) or max(10,10) equals 10??

Please clarify.

Best Regards,
Prashanthi Chennupati
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Jul 23, 2013 7:25 am
prashanthichennupati wrote:Brent: Can you please explain how statement 2 is sufficient?

Statement 2: w = max(10, w)
If w = max(10, w), then w is the larger value.
In other words, w is greater than or equal to 10
If w is greater ,then we can conclude that min(10, w) = 10
If w is equal, then how can we conclude min(10,w) =10??

Neither in the question stem nor in the statements it is mentioned that min(10,10) or max(10,10) equals 10??

Please clarify.

Best Regards,
Prashanthi Chennupati
While the question does not explicitly tell us the value of min(10, 10), it does tell us that min(x, y) denotes the minimum value of x and y.
In other words, if we have two values (x and y) then min(x, y) will output the smallest value of the two.
So, what's the minimum (smallest) value of 10 and 10? It's 10 (if it's not 10, what is the smallest value of 10 and 10?)
So, min(10, 10) = 10

Likewise, max(x, y) denotes the maximum (biggest) value of x and y.
So, it must be true that max(10, 10) = 10

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Tue Nov 23, 2010 7:21 am

by prashanthichennupati » Tue Jul 23, 2013 9:15 am
Thanks Brent.
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Tue Jul 23, 2013 2:16 pm
Hi saidov.mikhail,

I've uploaded a video to YouTube that you'll find useful in solving this question:

Click HERE to watch Rich crush this question...

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1