GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 07 Apr 2020, 16:33

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

The sum of the squares of the digits of a two digit number is 65. How

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
G
Joined: 20 Aug 2019
Posts: 45
GPA: 3.9
The sum of the squares of the digits of a two digit number is 65. How  [#permalink]

Show Tags

New post 30 Dec 2019, 09:24
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

84% (02:09) correct 16% (02:03) wrong based on 50 sessions

HideShow timer Statistics

The sum of the squares of the digits of a two digit number is 65. How much should be added to this number to get another two digit number in which the digits are in the reverse order?
(A) 59
(B) 25
(C) 63 or 27
(d) 21
(E) 32
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3348
Re: The sum of the squares of the digits of a two digit number is 65. How  [#permalink]

Show Tags

New post 30 Dec 2019, 09:42
2
2
Given this specific option choices, this question can be solved without any calculation.

    • For any two-digit number, the number and its reverse will always have a gap, which is a multiple of 9 [if we have AB, then reverse of it is BA. BA – AB = 10B + A – 10A – B = 9(B – A)]

From the given choices, only one option is a multiple of 9

Hence, the correct answer is option C

From observation, the numbers are 18 (18 + 63 = 81) or 47 (47 + 27 = 74)
_________________
Intern
Intern
avatar
B
Joined: 05 Oct 2019
Posts: 11
Re: The sum of the squares of the digits of a two digit number is 65. How  [#permalink]

Show Tags

New post 30 Dec 2019, 10:29
1
First let's take a look at the squares of figures:

1 = 1
2 = 4
3= 9
4 = 16
5 = 25
6 = 36
7 = 49
8 = 64

There are a 2 combinations that gives 65: 1 & 8, 4 & 6; hence the possibilities are:

18 to 81, or 46, 64; hence answer is (C).
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 2503
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
Re: The sum of the squares of the digits of a two digit number is 65. How  [#permalink]

Show Tags

New post 30 Dec 2019, 11:47
1
naju wrote:
The sum of the squares of the digits of a two digit number is 65. How much should be added to this number to get another two digit number in which the digits are in the reverse order?
(A) 59
(B) 25
(C) 63 or 27
(d) 21
(E) 32


Let us assume, two digit number to be of the format xy where x is tenth digit and y is unit digit.
x^2 + y^2 = 65
(x,y) = {(1,8),(4,7)}

If xy = 18 -> yx=81; 81-18 = 63
If xy = 47 -> yx =74; 74-47 = 27

IMO C
Manager
Manager
avatar
B
Joined: 04 Aug 2019
Posts: 54
Location: Viet Nam
Concentration: Organizational Behavior, Strategy
Schools: Desautels
WE: Research (Other)
Re: The sum of the squares of the digits of a two digit number is 65. How  [#permalink]

Show Tags

New post 24 Feb 2020, 01:20
naju wrote:
The sum of the squares of the digits of a two digit number is 65. How much should be added to this number to get another two digit number in which the digits are in the reverse order?
(A) 59
(B) 25
(C) 63 or 27
(d) 21
(E) 32


Method 1: x = BA (the larger) - AB (the smaller) --> x = 10B + A - 10A - B = 9(B-A) --> x must be a multiple of 9 --> (C)
Method 2: A^2 + B^2 = 65 and A<B --> B max = 8.
(1) If B = 8, A = 1. --> x = 81 - 18 = 63
(2) If B = 7, A = 4 --> x = 74 - 47 = 27
--> (C)
_________________
"The devil is in the detail"
GMAT Club Bot
Re: The sum of the squares of the digits of a two digit number is 65. How   [#permalink] 24 Feb 2020, 01:20
Display posts from previous: Sort by

The sum of the squares of the digits of a two digit number is 65. How

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





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