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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Of all the numbers less than 100,000 and greater than [#permalink]

Show Tags

09 Apr 2007, 11:37

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Of all the numbers less than 100,000 and greater than 50,000, how many, when read from left to right, or right to left, add up to the same amount? (For example: 56,365)

vikramjit_01, your reasoning is right except that you did not take into account that the penultimate digit on the right can take the value of either the value of the first digit or the value of second digit(for eg 54145 or 54154). Thus the value would become

5*10*10*2*1

(5 as values between 50,000 and 100000 --> 5,6,7,8,9)

Shouldn't the number be a palindrome? Cuz any number would add up to the same number when read from both ways. For example, 123 when read from left to right adds up to 6, and when read from right to left adds up to 6 as well... (duh!) So I'm assuming that the number IS a palindrome otherwise the question doesn't make sense...

Therefore, First and last digits have to be the same.
There are 10 choices for the second digit and 10 for the middle digit.
So that's 10*10 = 100 for 50,000~59995
So for 5, 6, 7, 8, 9 = 5
100*5 = 500
E

What is the OA?
Please correct my reasoning if there's any error.

Shouldn't the number be a palindrome? Cuz any number would add up to the same number when read from both ways. For example, 123 when read from left to right adds up to 6, and when read from right to left adds up to 6 as well... (duh!) So I'm assuming that the number IS a palindrome otherwise the question doesn't make sense... :?

Therefore, First and last digits have to be the same. There are 10 choices for the second digit and 10 for the middle digit. So that's 10*10 = 100 for 50,000~59995 So for 5, 6, 7, 8, 9 = 5 100*5 = 500 E

What is the OA? Please correct my reasoning if there's any error. :wink:

The question's wording is confusing. When I first read it, I assumed that I need to calculate the number of palindromes but since the question asks for sum, i am confused.

Btw, if all we need to do is count palindromes then it is indeed 500

I agree the post is ambiguous when you use the word 'add up to the same amount when read from left to right and right to left'. This phrase qualifies all numbers, because all digits in a number would add up to be the same either way you read it. But the example given in the question suggests it's looking for a palindrome.

The range given to us is 50001 - 99999, so we're dealing with 5 digit numbers.

The first digit can be 5-9 -> so 5 choices
The second digit can be 0-9 -> so 10 choices
The third digit can be 0-0 -> so 10 choices
The fourth digit must be the same as the second, so only 1 choice
The fifth digit must be the same as the first, so only 1 choice

If you read carefully, only palindromes can satisfy the condition.
The phrase- 'when read from left to right, or right to left, add up to the same amount' means when you read like first 3 numbers and last three numbers, the sum should be equal. Or if you read first two and last two, the sum should be same. This condition can be satisfied if and only if the number is palindrome.

If you read carefully, only palindromes can satisfy the condition. The phrase- 'when read from left to right, or right to left, add up to the same amount' means when you read like first 3 numbers and last three numbers, the sum should be equal. Or if you read first two and last two, the sum should be same. This condition can be satisfied if and only if the number is palindrome.

Not nescessary. To me, a phrase that says adds up to the same when read right to left or left to right means just this:

Say the number is 5678, then from left to right, the sum is 26, and from right to left, the sum is also 26, but 5678 is a palindrome. When you say 'sum', the arithmetic addition comes into mind. If I wanted to meant a palindrome, I would just say the number is the same when read right to left and left to right (leaving out the word 'sum' to avoid confusion). Anyway, I digress....