Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Sep 2014, 08:09

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

you have 1 minute! If a, b, c and d are four positive

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
CEO
CEO
avatar
Joined: 15 Aug 2003
Posts: 3470
Followers: 60

Kudos [?]: 670 [0], given: 781

you have 1 minute! If a, b, c and d are four positive [#permalink] New post 16 Sep 2003, 23:49
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:14) correct 0% (00:00) wrong based on 0 sessions
you have 1 minute!

If a, b, c and d are four positive real numbers such that
abcd = 1, what is the minimum value of (1 + a) (1 + b) (1 + c) (1 + d).
a) 4
b) 1
c) 16
d) 18

explain your method!

thanks
Senior Manager
Senior Manager
avatar
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
Followers: 1

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

GMAT Tests User
 [#permalink] New post 17 Sep 2003, 22:21
Answer: C (16)
We use the property that:
Arithemetic Mean of two numbers is g.t.e.q Geometric mean.
g.t.e.q = greater than or equal to.

Thus (1+a)/2 >= sqrt(a)
(1+b)/2 >= sqrt(b)
--------
(1+d)/2 >= sqrt(d)

Multiplying above equations (we can mutilply them without chanding sign of inequality because it is given that a,b,c & d are postive real num's)

we get (1 + a) (1 + b) (1 + c) (1 + d)/2^4 >= sqrt (abcd)
Thus minimum is 16.
-Vicks
ps: let me know if u know a faster way to solve this.
Manager
Manager
avatar
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
 [#permalink] New post 17 Sep 2003, 23:51
Vicky wrote:
Answer: C (16)
We use the property that:
Arithemetic Mean of two numbers is g.t.e.q Geometric mean.
g.t.e.q = greater than or equal to.

Thus (1+a)/2 >= sqrt(a)
(1+b)/2 >= sqrt(b)
--------
(1+d)/2 >= sqrt(d)

Multiplying above equations (we can mutilply them without chanding sign of inequality because it is given that a,b,c & d are postive real num's)

we get (1 + a) (1 + b) (1 + c) (1 + d)/2^4 >= sqrt (abcd)
Thus minimum is 16.
-Vicks
ps: let me know if u know a faster way to solve this.


I'm kinda confused as to why you're using Geometric Mean here provided you don't know if these numbers are in sequence or not.
CEO
CEO
avatar
Joined: 15 Aug 2003
Posts: 3470
Followers: 60

Kudos [?]: 670 [0], given: 781

 [#permalink] New post 18 Sep 2003, 00:38
Vicky wrote:
Answer: C (16)
We use the property that:
Arithemetic Mean of two numbers is g.t.e.q Geometric mean.
g.t.e.q = greater than or equal to.

Thus (1+a)/2 >= sqrt(a)
(1+b)/2 >= sqrt(b)
--------
(1+d)/2 >= sqrt(d)

Multiplying above equations (we can mutilply them without chanding sign of inequality because it is given that a,b,c & d are postive real num's)

we get (1 + a) (1 + b) (1 + c) (1 + d)/2^4 >= sqrt (abcd)
Thus minimum is 16.
-Vicks
ps: let me know if u know a faster way to solve this.


Vicky

Unless Akamai or Stolyar have a good idea,yours is really the best analytical approach...very convincing and leaves no room for error.

as for me, I did it this way.

Since the answer choices are integers..i find it very likely that a,b,c,d will be integers

As a check...For example let a=0.5 ,b=2 ,c=2 , d=0.5

a*b*c*d=0.5*2*2*0.5 =1 ...here we have integers and non integers..and we satsify the abcd =1

But (1+a)(1+b)(1+c)(1+d)= 1.5*3*3*1.5 =>> not an integer ...

Another one
3*1/3*2*1/2 =1
but 4*4/3*3*3/2 ==>>not an integer

So lets work with integers first

The answer cannot be 1 as the product is 1 + something ...and the something is positive

4= 1*1*2*2 ..compare with (1+a) (1+b)(1+c)(1+d)

We get a=0 and b =0 ..not possible..as abcd = 1....doesnt satisfy

18= 1*2*3*3 again comparison gives a=0...not possible

16= 2*2*2*2 ...comparison gives a=1,b=1,c=1,d=1...its the only one that holds true.

thanks
praetorian
CEO
CEO
avatar
Joined: 15 Aug 2003
Posts: 3470
Followers: 60

Kudos [?]: 670 [0], given: 781

 [#permalink] New post 18 Sep 2003, 00:43
wonder_gmat wrote:
Vicky wrote:
Answer: C (16)
We use the property that:
Arithemetic Mean of two numbers is g.t.e.q Geometric mean.
g.t.e.q = greater than or equal to.

Thus (1+a)/2 >= sqrt(a)
(1+b)/2 >= sqrt(b)
--------
(1+d)/2 >= sqrt(d)

Multiplying above equations (we can mutilply them without chanding sign of inequality because it is given that a,b,c & d are postive real num's)

we get (1 + a) (1 + b) (1 + c) (1 + d)/2^4 >= sqrt (abcd)
Thus minimum is 16.
-Vicks
ps: let me know if u know a faster way to solve this.


I'm kinda confused as to why you're using Geometric Mean here provided you don't know if these numbers are in sequence or not.


Wonder

I think Geometric Mean and Geometric Progression are two different things.
Senior Manager
Senior Manager
avatar
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
Followers: 1

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

GMAT Tests User
 [#permalink] New post 18 Sep 2003, 00:44
Arithemtic mean (average of two numbers) and Geometric means are properties (or rather expressions) for numbers. Numbers dont necesarily have to be in sequence to use them.
I guess u are confusing them with Arithmetic and geometric progression & for them, YES the numbers should be in sequence.
-Vicks
  [#permalink] 18 Sep 2003, 00:44
    Similar topics Author Replies Last post
Similar
Topics:
The four integers a , b , c , and d are such that a < b kannn 2 14 Jul 2011, 10:06
1 Experts publish their posts in the topic a, b, c and d are four positive real numbers such that abcd= papillon86 3 08 Nov 2009, 12:53
a, b, c, d represent four points from left to right on a bkk145 3 04 Nov 2007, 05:24
If c and d are positive integers, is c even? (1) c2 - 1 is andrehaui 2 29 Mar 2007, 05:14
c^d=(1/c)^(3d-8) what is the value of c^d? a) c=4 b) d= ArvGMAT 2 05 Aug 2006, 19:21
Display posts from previous: Sort by

you have 1 minute! If a, b, c and d are four positive

  Question banks Downloads My Bookmarks Reviews Important topics  


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

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®.