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

 It is currently 24 Feb 2017, 17:50

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
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 [?]: 183 [2] , given: 31

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

### Show Tags

15 Nov 2012, 06:03
2
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:43) correct 31% (02:02) wrong based on 182 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

Math Expert
Joined: 02 Sep 2009
Posts: 37108
Followers: 7254

Kudos [?]: 96538 [3] , given: 10753

### Show Tags

15 Nov 2012, 06:29
3
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.

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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13957
Followers: 590

Kudos [?]: 167 [0], given: 0

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

### Show Tags

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.
_________________
Intern
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

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

### Show Tags

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
_________________

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13957
Followers: 590

Kudos [?]: 167 [0], given: 0

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

### Show Tags

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.
_________________
Re: What two-digit number is less than the sum of the square of   [#permalink] 12 Feb 2016, 03:34
Similar topics Replies Last post
Similar
Topics:
1 The sum of the digits of a two-digit number is 12, and the ten’s digit 4 02 Jan 2017, 11:42
4 Twice a number is 3 times the square of the number less than one. If 1 03 May 2016, 09:46
16 The sum of prime numbers that are greater than 60 but less 9 23 Jul 2012, 03:39
3 The number 75 can be written as the sum of the squares of 3 4 02 Nov 2010, 12:53
6 The number 75 can be written as sum of the squares of 3 6 01 Jan 2009, 22:45
Display posts from previous: Sort by