GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2019, 03:58

### 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

# The difference between two reversed 2-digit positive integers is a per

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

### Hide Tags

VP
Joined: 07 Dec 2014
Posts: 1230
The difference between two reversed 2-digit positive integers is a per  [#permalink]

### Show Tags

22 Jul 2019, 13:03
3
00:00

Difficulty:

95% (hard)

Question Stats:

24% (02:47) correct 76% (02:07) wrong based on 25 sessions

### HideShow timer Statistics

The difference between two reversed 2-digit positive integers is a perfect square. How many such pairs of integers are there?

A. 8
B. 9
C. 11
D. 12
E. 13
Senior Manager
Joined: 29 Jun 2019
Posts: 326
The difference between two reversed 2-digit positive integers is a per  [#permalink]

### Show Tags

22 Jul 2019, 13:16
(12,21), (32,23), (43,34), (45,54), (56,65), (67,76), (78,87), (89,98): the difference between each of these pairs is 9.
(95,59), (84,48), (73,37),(62,26) , (51,15): the difference between each of these pairs is 36
Option (E)

Posted from my mobile device
_________________
Always waiting
Manager
Joined: 25 Jul 2018
Posts: 211
Re: The difference between two reversed 2-digit positive integers is a per  [#permalink]

### Show Tags

22 Jul 2019, 13:51
1
ab-ba=x^2.(ab, ba -two digit integer)
10a+b-(10b+a)=x^2
10a+b-10b-a=9a-9b=9*(a-b)=x^2

What number do we need to multiply with 9 to get a square of number??
1) a-b=1(9*1=3^2)
2) a-b=4(9*4=6^2)

(a-b=9(9*9=9^2) is also possible, but to get 81, we need 3 digit numbers)

Case1: a-b=1
2-1=1
3-2=1
4-3=1
5-4=1
6-5=1
7-6=1
8-7=1
9-8=1
There are 8 different combinations.

Case2: a-b=4
5-1=4
6-2=4
7-3=4
8-4=4
9-5=4
There are 5 different combinations.

In total, there are 13 different combinations.
Answer choice is E.

Posted from my mobile device
Re: The difference between two reversed 2-digit positive integers is a per   [#permalink] 22 Jul 2019, 13:51
Display posts from previous: Sort by

# The difference between two reversed 2-digit positive integers is a per

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

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