Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
17 Aug 2024, 20:11
Kudos
Bookmarks
17 Aug 2024, 23:09
Kudos
Bookmarks
Adarsh_24
A digit is not negative. We have 10 digits from 0 to 9. When we say "a, b, and c are nonzero digits and the three digit number abc..." we mean that abc is a positive 3 digit number with digits a, b and c. To show a negative number, we will need to use -abc.
19 Nov 2024, 05:30
Kudos
Bookmarks
1. Analyze the Difference
Let's represent the 3-digit number 'abc' as 100a + 10b + c and 'cba' as 100c + 10b + a.
The difference 'abc - cba' can be written as:
(100a + 10b + c) - (100c + 10b + a) = 99a - 99c = 99(a - c)
2. Divisibility Rule of 7
For the difference to be divisible by 7, 99(a - c) must be divisible by 7. Since 99 is not divisible by 7, (a - c) must be divisible by 7.
3. Possible Values
Since a and c are non-zero digits, the possible values for (a - c) that are divisible by 7 are:
a - c = 7
a - c = -7
4. Find the Combinations
Case 1: a - c = 7
The possible pairs of (a, c) are (8, 1), (9, 2). For each of these pairs, 'b' can be any of the 9 non-zero digits (1 through 9).
This gives us 2 pairs * 9 options for b = 18 possibilities.
Case 2: a - c = -7
The possible pairs of (a, c) are (1, 8), (2, 9). Similar to case 1, 'b' has 9 possible values.
This gives us another 18 possibilities.
5. Account for Reverse Order
The question asks for numbers where 'abc - cba' is a positive multiple of 7. This means we need to ensure that 'abc' > 'cba'. We've counted possibilities without considering the order. Therefore, we need to divide our current count by 2.
(18 + 18) / 2 = 18
Answer: There are 18 possible 3-digit numbers 'abc' that satisfy the given conditions.
Let's represent the 3-digit number 'abc' as 100a + 10b + c and 'cba' as 100c + 10b + a.
The difference 'abc - cba' can be written as:
(100a + 10b + c) - (100c + 10b + a) = 99a - 99c = 99(a - c)
2. Divisibility Rule of 7
For the difference to be divisible by 7, 99(a - c) must be divisible by 7. Since 99 is not divisible by 7, (a - c) must be divisible by 7.
3. Possible Values
Since a and c are non-zero digits, the possible values for (a - c) that are divisible by 7 are:
a - c = 7
a - c = -7
4. Find the Combinations
Case 1: a - c = 7
The possible pairs of (a, c) are (8, 1), (9, 2). For each of these pairs, 'b' can be any of the 9 non-zero digits (1 through 9).
This gives us 2 pairs * 9 options for b = 18 possibilities.
Case 2: a - c = -7
The possible pairs of (a, c) are (1, 8), (2, 9). Similar to case 1, 'b' has 9 possible values.
This gives us another 18 possibilities.
5. Account for Reverse Order
The question asks for numbers where 'abc - cba' is a positive multiple of 7. This means we need to ensure that 'abc' > 'cba'. We've counted possibilities without considering the order. Therefore, we need to divide our current count by 2.
(18 + 18) / 2 = 18
Answer: There are 18 possible 3-digit numbers 'abc' that satisfy the given conditions.
