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

 It is currently 26 Jan 2020, 16:04

### 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

# If two 2-digit positive integers have their respective tens digits exc

Author Message
TAGS:

### Hide Tags

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9143
Location: United States (CA)
Re: If two 2-digit positive integers have their respective tens digits exc  [#permalink]

### Show Tags

22 Oct 2019, 19:36
1
dcummins wrote:

I was a bit confused with the last step here.

What are the constraints on the numbers we must choose to determine that the original difference would be 78?

I also solved as (10a + b) - (10c +d) = 10c+b - (10a+d) + 4 to produce (10a -10c) = 2

According to our calculations, as long as the difference between the units digits is 2, the condition of "the difference between the original difference and the difference of the exchanged numbers is 4" is satisfied. That's the constraint of the units digit. For instance, 75 and 43 also satisfy that condition, but those numbers will not give you the greatest possible difference. In order to find "the greatest possible difference", the tens digit of the greater number must be 9 and the tens digit of the smaller number must be 1. As long as these two consitions are satisfied, you can choose any numbers you want (such as 92 and 10, 93 and 11, 94 and 12 etc.) The original difference is always 82 and the new difference is always 78.

In your equation, if 10a + b is the greater number, then after the switch is made, 10a + d will be the greater number; hence the right hand side of your equation should be (10a + d) - (10c + b) + 4.
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP
Joined: 14 Feb 2017
Posts: 1365
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 650 Q48 V31
GMAT 6: 600 Q38 V35
GMAT 7: 710 Q47 V41
GPA: 3
WE: Management Consulting (Consulting)
Re: If two 2-digit positive integers have their respective tens digits exc  [#permalink]

### Show Tags

22 Oct 2019, 21:19
ScottTargetTestPrep wrote:
dcummins wrote:

I was a bit confused with the last step here.

What are the constraints on the numbers we must choose to determine that the original difference would be 78?

I also solved as (10a + b) - (10c +d) = 10c+b - (10a+d) + 4 to produce (10a -10c) = 2

According to our calculations, as long as the difference between the units digits is 2, the condition of "the difference between the original difference and the difference of the exchanged numbers is 4" is satisfied. That's the constraint of the units digit. For instance, 75 and 43 also satisfy that condition, but those numbers will not give you the greatest possible difference. In order to find "the greatest possible difference", the tens digit of the greater number must be 9 and the tens digit of the smaller number must be 1. As long as these two consitions are satisfied, you can choose any numbers you want (such as 92 and 10, 93 and 11, 94 and 12 etc.) The original difference is always 82 and the new difference is always 78.

In your equation, if 10a + b is the greater number, then after the switch is made, 10a + d will be the greater number; hence the right hand side of your equation should be (10a + d) - (10c + b) + 4.

+

thanks scott!
_________________
Here's how I went from 430 to 710, and how you can do it yourself:
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9143
Location: United States (CA)
Re: If two 2-digit positive integers have their respective tens digits exc  [#permalink]

### Show Tags

24 Oct 2019, 19:15
dcummins wrote:
ScottTargetTestPrep wrote:
dcummins wrote:

I was a bit confused with the last step here.

What are the constraints on the numbers we must choose to determine that the original difference would be 78?

I also solved as (10a + b) - (10c +d) = 10c+b - (10a+d) + 4 to produce (10a -10c) = 2

According to our calculations, as long as the difference between the units digits is 2, the condition of "the difference between the original difference and the difference of the exchanged numbers is 4" is satisfied. That's the constraint of the units digit. For instance, 75 and 43 also satisfy that condition, but those numbers will not give you the greatest possible difference. In order to find "the greatest possible difference", the tens digit of the greater number must be 9 and the tens digit of the smaller number must be 1. As long as these two consitions are satisfied, you can choose any numbers you want (such as 92 and 10, 93 and 11, 94 and 12 etc.) The original difference is always 82 and the new difference is always 78.

In your equation, if 10a + b is the greater number, then after the switch is made, 10a + d will be the greater number; hence the right hand side of your equation should be (10a + d) - (10c + b) + 4.

+

thanks scott!

Sure thing!
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15985
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If two 2-digit positive integers have their respective tens digits exc  [#permalink]

### Show Tags

09 Dec 2019, 17:28
1
Hi All,

We're told that if two 2-digit positive integers have their respective TENS digits exchanged, the difference between the pair of integers changes by 4. We're asked for the GREATEST possible difference between the original pair of integers. There are a few different ways to approach this question (and some of them are incredibly "step heavy"). Thankfully, we can solve it rather easily by TESTing THE ANSWERS.

Since we're looking for the GREATEST possible difference between the two 2-digit integers, we should start with Answer E. However, we can use some Number Properties to quickly eliminate a couple of the possibilities first.

The smallest 2-digit number is 10 and the largest is 99, so the difference between those two numbers is 89 (and can only get smaller). Thus, Answers D and E are NOT possible, so we do not have to consider them. Let's TEST Answer C first....

Let's pick two 2-digit numbers that have a difference of 82... the easiest would be 10 and 92.
We already know that the difference between these numbers is 82.
When we switch the TENS digits, we have 90 and 12. The difference between these numbers is 90 - 12 = 78.
The two results (82 and 78) differ by 4 - and this is an exact match for what we were told, so this MUST be the answer.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: If two 2-digit positive integers have their respective tens digits exc   [#permalink] 09 Dec 2019, 17:28

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by