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

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Manager
Joined: 14 Mar 2007
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Of all the numbers less than 100,000 and greater than [#permalink]  09 Apr 2007, 10:37
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)

(A) 450
(B) 1500
(C) 1000
(D) 900
(E) 500

Solve and explain.
Manager
Joined: 02 Jan 2007
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I'll go with (E)

total ways to choose such a number:
10 * 10 * 10 * 1 * 1

1 & 1 because the last digit must be same as the first & the second-last must be same as the second digit.

So thats' 1,000 ways.
And we want number's > 50, 000
Thats half of them
and thats 500.
Intern
Joined: 09 Apr 2007
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I must say I would go with C.

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)

= 1000
Senior Manager
Joined: 11 Feb 2007
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Hmmm...the posts confuse me...

I naively thought E was the answer.

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.
Manager
Joined: 28 Feb 2007
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Location: California
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ricokevin wrote:
Hmmm...the posts confuse me... :?

I naively thought E was the answer.

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
GMAT Club Legend
Joined: 07 Jul 2004
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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

Total = 500.
Director
Joined: 14 Jan 2007
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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.
GMAT Club Legend
Joined: 07 Jul 2004
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vshaunak@gmail.com wrote:
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....
Manager
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Hi people, this one got lots of comments. Nice...indeed the right one is 500!!!
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