Last visit was: 14 Jul 2024, 21:31 It is currently 14 Jul 2024, 21:31
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640855 [10]
Given Kudos: 85011
Send PM
Most Helpful Reply
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11470
Own Kudos [?]: 34321 [7]
Given Kudos: 322
Send PM
General Discussion
Senior Manager
Senior Manager
Joined: 09 Mar 2017
Posts: 361
Own Kudos [?]: 839 [2]
Given Kudos: 646
Location: India
Concentration: Marketing, Organizational Behavior
WE:Information Technology (Computer Software)
Send PM
Intern
Intern
Joined: 23 Oct 2017
Posts: 46
Own Kudos [?]: 20 [0]
Given Kudos: 23
Send PM
Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink]
Option D.
a,b,c
=> b2, b, c
c=b*(b+1)

Product of 2 consecutive +ve integers
30 &72

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19130
Own Kudos [?]: 22631 [1]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink]
1
Kudos
Expert Reply
Bunuel wrote:
a, b and c are positive integers. If b equals the square root of a, and if c equals the sum of a and b, which of the following could be the value of c?

I. 21
II. 30
III. 72

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III


We have the following equations:

b = √a

b^2 = a

and

c = a + b

Thus,

c = a + a^2

So c is the sum of an integer + that integer squared.

Statement I is not true, since 4^2 + 4 = 20 and 5^2 + 5 = 30; thus the value of a that satisfies a^2 + a = 21 is not an integer, but some real number between 4 and 5.

Looking at the answer choices we see that II and III can work since 30 = 5 + 25, and 72 = 8 + 64.

Answer: D
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17015 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink]
Expert Reply
If b equals the square root of a => \(b^2 = a\)

If c equals the sum of a and b => \(c = a + b = b^2 + b = b ( b + 1)\)

Therefore, c is the product of two consecutive integers

I. 21 = 4 * 5 = 20 - NOT POSSIBLE

II. 30 = 5 * 6 = 30 - POSSIBLE

III. 72 = 8 * 9 = 72 - POSSIBLE

Only Option II and III are possible.

Answer D
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33972
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink]
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.
GMAT Club Bot
Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink]
Moderator:
Math Expert
94342 posts