What two-digit number is less than the sum of the square of : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 10 Dec 2016, 14:38
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What two-digit number is less than the sum of the square of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 03 Sep 2012
Posts: 338
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 16

Kudos [?]: 175 [2] , given: 31

What two-digit number is less than the sum of the square of [#permalink]

Show Tags

New post 15 Nov 2012, 06:03
2
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (02:42) correct 31% (02:02) wrong based on 179 sessions

HideShow timer Statistics

What two-digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 5?

(A) 95
(B) 99
(C) 26
(D) 73
(E) None of the Above
[Reveal] Spoiler: OA

_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35951
Followers: 6865

Kudos [?]: 90118 [3] , given: 10418

Re: What two-digit number [#permalink]

Show Tags

New post 15 Nov 2012, 06:29
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
vomhorizon wrote:
What two-digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 5?

(A) 95
(B) 99
(C) 26
(D) 73
(E) None of the Above


We are told that the two-digit number exceeds doubled product of its digits by 5:

\((10a+b)-2ab=5\) --> \(2a(5-b)-(5-b)=0\) --> \((5-b)(2a-1)=0\) --> \(b=5\) (\(a\) cannot equal to 1/2 since it must be an integer). The only answer choice with 5 as an units digit is A.

Check 95 for the first condition (to eliminate E), which says that the two-digit number is less than the sum of the square of its digits by 11: (9^2+5^2)-95=11. So, the answer is A.

Answer: A.

There is another number satisfying both conditions:

Substitute \(b=5\) in \((a^2+b^2)-(10a+b)=11\) --> \(a^2-10a+9=0\) --> \(a=9\) or \(a=1\). Therefore both 15 and 95 satisfy both conditions.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12907
Followers: 563

Kudos [?]: 158 [0], given: 0

Premium Member
Re: What two-digit number is less than the sum of the square of [#permalink]

Show Tags

New post 12 Jul 2014, 05:29
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 15 Sep 2013
Posts: 44
Concentration: Strategy, Entrepreneurship
GMAT 1: 680 Q47 V36
GMAT 2: 740 Q50 V40
GPA: 3.65
Followers: 0

Kudos [?]: 21 [0], given: 26

GMAT ToolKit User Reviews Badge
Re: What two-digit number is less than the sum of the square of [#permalink]

Show Tags

New post 03 Sep 2014, 00:08
1
This post was
BOOKMARKED
vomhorizon wrote:
What two-digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 5?

(A) 95
(B) 99
(C) 26
(D) 73
(E) None of the Above


Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -11
Thus 2xy +5 = x^2 + y^2 - 11
x^2 + y^2 -2xy = 16
(x-y)^2 = 16
(x-y) = 4 or -4

Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 95
Thus the answer is A
_________________

Please +1 KUDOS if my post helped you in any way

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12907
Followers: 563

Kudos [?]: 158 [0], given: 0

Premium Member
Re: What two-digit number is less than the sum of the square of [#permalink]

Show Tags

New post 12 Feb 2016, 03:34
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: What two-digit number is less than the sum of the square of   [#permalink] 12 Feb 2016, 03:34
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Twice a number is 3 times the square of the number less than one. If mikemcgarry 1 03 May 2016, 09:46
15 Experts publish their posts in the topic The sum of prime numbers that are greater than 60 but less Bunuel 9 23 Jul 2012, 03:39
9 Number S is obtained by squaring the sum of digits of a two feruz77 6 10 Nov 2010, 01:28
2 Experts publish their posts in the topic The number 75 can be written as the sum of the squares of 3 mybudgie 4 02 Nov 2010, 12:53
6 Experts publish their posts in the topic The number 75 can be written as sum of the squares of 3 krishan 6 01 Jan 2009, 22:45
Display posts from previous: Sort by

What two-digit number is less than the sum of the square of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.