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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

a,b,c and d are four +ve real nubers 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

what is the best way to solve such question where in we need to calculate the min or max values?

Think there is no catch in this question. As the numbers are positive and their product is 1: either 2,3, or all 4 numbers are reciprocals and rest is 1 OR all numbers are equal to 1.

Minimum value will be when a=b=c=d=1, hence (1+a)(1+b)(1+c)(1+d)=16. (You can try reciprocals to see that the product will be greater)

Re: a, b, c and d are four positive real numbers such that abcd= [#permalink]

Show Tags

14 Jul 2014, 13:06

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.
_________________

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

As Bunuel said, abcd = 1 implies that either the numbers are equal to 1 or there are pairs of reciprocals e.g. (1, 1, 1, 1) or (1, 1, 2, 1/2) or (3, 1/3, 4, 1/4) etc.

If a and b are 1 and 1, (1+a)(1+b) = (1+1)(1+1) = 4

If a and b are 2 and 1/2, (1+a)(1+b) = (1+2)(1+1/2) = 9/2 = 4.5

If a and b are 3 and 1/3, (1+a)(1+b) = (1+3)(1+1/3) = 16/3 = 5.3

As you keep taking higher reciprocals, the value of (1+a)(1+b) keeps increasing.

So taking reciprocals is a bad idea and all numbers must be 1 giving us the minimum value of 16.

Anyway, in any minimum-maximum question, it is a good idea to check on equality. Often, the point of equality is a transition point.
_________________

Re: a, b, c and d are four positive real numbers such that abcd= [#permalink]

Show Tags

22 Oct 2014, 00:20

Hello All, My first reply on this site. Another approach can be - For constant sum, product is minimum when terms are equal. 1+1/a = 1+1/b implies a=b=c=d. gives a hint that all can be 1.

Re: a, b, c and d are four positive real numbers such that abcd= [#permalink]

Show Tags

28 Dec 2015, 09:14

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: a, b, c and d are four positive real numbers such that abcd= [#permalink]

Show Tags

24 Mar 2016, 03:18

papillon86 wrote:

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

In terms of quality of the problem, isn't different names for the variables implies ( implicitly mean ) that the variables is different ? What is the probability that such problem can actually appears in the actual test ? In other words, does creators of the GMAT exam when naming of the different variables with different names assumes ( by default ) that the variables can be equals to each other on special circumstances ( like the problem above ) ?
_________________

I’m not afraid of the man who knows 10,000 kicks and has practiced them once. I am afraid of the man who knows one kick & has practiced it 10,000 times! - Bruce Lee

Please, press the +1 KUDOS button , if you find this post helpful

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

In terms of quality of the problem, isn't different names for the variables implies ( implicitly mean ) that the variables is different ? What is the probability that such problem can actually appears in the actual test ? In other words, does creators of the GMAT exam when naming of the different variables with different names assumes ( by default ) that the variables can be equals to each other on special circumstances ( like the problem above ) ?

Unless it is explicitly stated otherwise, different variables CAN represent the same number.
_________________

Re: a, b, c and d are four positive real numbers such that abcd= [#permalink]

Show Tags

24 Mar 2016, 03:25

Bunuel wrote:

leeto wrote:

papillon86 wrote:

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

In terms of quality of the problem, isn't different names for the variables implies ( implicitly mean ) that the variables is different ? What is the probability that such problem can actually appears in the actual test ? In other words, does creators of the GMAT exam when naming of the different variables with different names assumes ( by default ) that the variables can be equals to each other on special circumstances ( like the problem above ) ?

Unless it is explicitly stated otherwise, different variables CAN represent the same number.

Many thanks, your answer get rid of a lot of doubts.
_________________

I’m not afraid of the man who knows 10,000 kicks and has practiced them once. I am afraid of the man who knows one kick & has practiced it 10,000 times! - Bruce Lee

Please, press the +1 KUDOS button , if you find this post helpful

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

In terms of quality of the problem, isn't different names for the variables implies ( implicitly mean ) that the variables is different ? What is the probability that such problem can actually appears in the actual test ? In other words, does creators of the GMAT exam when naming of the different variables with different names assumes ( by default ) that the variables can be equals to each other on special circumstances ( like the problem above ) ?

Think from a conceptual point of view: A variable is not a stand in for a single value. We put in a variable when the actual value is not known. It is possible that two variables end up having the same value. Often, a variable could take multiple values (e.g. in a quadratic). It is possible that one of its values matches one of the values that another variable can take. Hence, there is no such restriction that two variables cannot take the same value.
_________________

Re: a, b, c and d are four positive real numbers such that abcd= [#permalink]

Show Tags

28 Mar 2016, 23:13

VeritasPrepKarishma wrote:

leeto wrote:

papillon86 wrote:

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

In terms of quality of the problem, isn't different names for the variables implies ( implicitly mean ) that the variables is different ? What is the probability that such problem can actually appears in the actual test ? In other words, does creators of the GMAT exam when naming of the different variables with different names assumes ( by default ) that the variables can be equals to each other on special circumstances ( like the problem above ) ?

Think from a conceptual point of view: A variable is not a stand in for a single value. We put in a variable when the actual value is not known. It is possible that two variables end up having the same value. Often, a variable could take multiple values (e.g. in a quadratic). It is possible that one of its values matches one of the values that another variable can take. Hence, there is no such restriction that two variables cannot take the same value.

I like you analogy with quadratic equation, thank you for this idea.
_________________

I’m not afraid of the man who knows 10,000 kicks and has practiced them once. I am afraid of the man who knows one kick & has practiced it 10,000 times! - Bruce Lee

Please, press the +1 KUDOS button , if you find this post helpful

Re: a, b, c and d are four positive real numbers such that abcd= [#permalink]

Show Tags

11 Sep 2017, 02:24

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.
_________________