Last visit was: 05 Nov 2024, 08:34 It is currently 05 Nov 2024, 08:34

Close

GRE Prep 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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29891
Own Kudos [?]: 36122 [13]
Given Kudos: 25919
Send PM
Most Helpful Community Reply
avatar
Intern
Intern
Joined: 11 Jan 2018
Posts: 44
Own Kudos [?]: 104 [13]
Given Kudos: 0
Send PM
General Discussion
avatar
Intern
Intern
Joined: 08 Dec 2017
Posts: 40
Own Kudos [?]: 69 [5]
Given Kudos: 0
Send PM
avatar
Manager
Manager
Joined: 15 Feb 2018
Posts: 53
Own Kudos [?]: 34 [6]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
6
a = 5b^2 - 10b + 7
Subtract b from both sides
a - b = 5b^2 - 11b + 7
Since the coefficient of b^2 is positive the RHS is >0.

So a-b>0 --> a>b.

Answer: A
avatar
Intern
Intern
Joined: 17 Feb 2018
Posts: 9
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
gremather wrote:
a = 5b^2 - 10b + 7
Subtract b from both sides
a - b = 5b^2 - 11b + 7
Since the coefficient of b^2 is positive the RHS is >0.

So a-b>0 --> a>b.

Answer: A


great approach, didn't think of that
avatar
Intern
Intern
Joined: 28 Dec 2019
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
Here in one explanation, it is mentioned that, since CO-efficient of b^2 is positive, therefore RHS is positive. Why?

Posted from my mobile device Image
avatar
Intern
Intern
Joined: 08 Mar 2020
Posts: 13
Own Kudos [?]: 23 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
gremather wrote:
a = 5b^2 - 10b + 7
Subtract b from both sides
a - b = 5b^2 - 11b + 7
Since the coefficient of b^2 is positive the RHS is >0.

So a-b>0 --> a>b.

Answer: A


This is a false approach. Let a = 5b^2 - 10b

In that case, a-b = 5b^2 - 11b. Coefficient of b^2 is positive, but the RHS isn't always positive.

Consider b = 1, the RHS equals -6. The only thing you can say for certain when b^2 has a positive coefficient is that the RHS will be positive as b tends to infinity.
avatar
Intern
Intern
Joined: 08 Mar 2020
Posts: 13
Own Kudos [?]: 23 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
1
mosshiur wrote:
Here in one explanation, it is mentioned that, since CO-efficient of b^2 is positive, therefore RHS is positive. Why?



It's not true. Read my other comment. The actual way to solve this problem is by finding the global minima of a-b = 5b^2 - 11b + 7, which can be found by differentiating the RHS wrt b and noting that the minima is a positive value, thus a-b is always positive.
User avatar
Intern
Intern
Joined: 30 Mar 2020
Posts: 27
Own Kudos [?]: 26 [0]
Given Kudos: 0
WE:Research (Health Care)
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
What does RHS stand for?
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [0]
Given Kudos: 136
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
FunkyMonk0 wrote:
What does RHS stand for?


Right hand side
avatar
Intern
Intern
Joined: 27 Feb 2020
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
gremather wrote:
a = 5b^2 - 10b + 7
Subtract b from both sides
a - b = 5b^2 - 11b + 7
Since the coefficient of b^2 is positive the RHS is >0.

So a-b>0 --> a>b.

Answer: A



Hello,

I didnt understad after you -b from both sides, kindly explain in detail, I was not able to follow
Verbal Expert
Joined: 18 Apr 2015
Posts: 29891
Own Kudos [?]: 36122 [0]
Given Kudos: 25919
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
1
Expert Reply
Put this way

\(5b^2-10b+7\)

Now simplify

\(b^2-5b+7\)

\(b(b-5)+7\)

Basically \(b=0\)
OR
\(b=5\)

Substitute

If \(b=0\) in the equation \(b(b-5)+7\), then \(a=7\)

If \(b=5\), \(a\) is still \(= 7\)

A is always greater than b

Hope now is more clear
avatar
Intern
Intern
Joined: 18 Apr 2020
Posts: 14
Own Kudos [?]: 29 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
1
Another method

a ? b
5b^2 -10b +7 ? b
5b^2-11b+7 ? 0

First derivative of the eqn on LHS will be
10b-11 = 0.........=> b = 11/10=1.1 gives the min or max for the function.
Second derivative is
10 which implies at b=1.1 the function has the minimum value

put b=1.1 in the eqn we will get a + number therefore A>B.....which is the answer.

Cheers
avatar
Intern
Intern
Joined: 26 Jan 2020
Posts: 38
Own Kudos [?]: 35 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 – 10b + 7 [#permalink]
1
The given equation is an upward facing parabola. The minimum value of this parabola occurs at b=1 -> where the value of equation is 2. From the point the quadratic equation grows exponentially and quantity A will always be greater.
Intern
Intern
Joined: 11 Jun 2022
Posts: 38
Own Kudos [?]: 25 [0]
Given Kudos: 187
Send PM
Re: a = 5b^2 10b + 7 [#permalink]
Carcass how did you reach the step of simplification of 5b^2 - 10b + 7 to b^2 -5b +7? Could you please walk through the question once again and also, if not too inconvenient, share similar questions for practice?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29891
Own Kudos [?]: 36122 [1]
Given Kudos: 25919
Send PM
Re: a = 5b^2 10b + 7 [#permalink]
1
Expert Reply
iASindia wrote:
Carcass how did you reach the step of simplification of 5b^2 - 10b + 7 to b^2 -5b +7? Could you please walk through the question once again and also, if not too inconvenient, share similar questions for practice?



basically it is a binomial expression + 7.

Here more https://gre.myprepclub.com/forum/gre-math- ... tml#p81624

If you have a look under the quick reply under every discussion, you will have always similar topic to practice


Attachment:
screenshot.791.jpg
screenshot.791.jpg [ 127.49 KiB | Viewed 3039 times ]


Or you can use the tag algebra to find tons of questions that are similar and NOT https://gre.myprepclub.com/forum/search.ph ... &tag_id=10
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: a = 5b^2 10b + 7 [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
Re: a = 5b^2 10b + 7 [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne