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tens digit of n

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by nidhis.1408 » Sat Nov 12, 2011 11:57 am
If n is a positive integer, what is the tens digit of n?

1. the hundreds digit of 10n is 6.
2. the tens digit of n+1 is 7.
This is OG pg 348, ques-167


I need a better explanation for this.
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by shankar.ashwin » Sat Nov 12, 2011 12:09 pm
let n = ABCD

tens digit = C

1. 10n = ABCD0
given, hundreds digit = 6 (or) C = 6 - sufficient

2. tens digit of n+1 = 7.

consider CD = 69 -> CD+1 = 70 -> C=6 (or)

consider CD = 71 ->CD+1 = 72 -> C = 7

2 cases possible - insuff.

A IMO
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by Anurag@Gurome » Sat Nov 12, 2011 10:40 pm
nidhis.1408 wrote:If n is a positive integer, what is the tens digit of n?

1. the hundreds digit of 10n is 6.
2. the tens digit of n+1 is 7.
Statement 1: If we multiply any positive integer with 10, all the digits of the of the integer shifts one place to the left. Hence, tens digit of n is same as the hundreds digit of 10n.

Sufficient

Statement 2: Say, n = 69 ---> (n + 1) = 70 --> Tens digit are different
But if n = 68 ---> (n + 1) = 69 --> Tens digit are same

Not sufficient

The correct answer is A.
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by melguy » Tue May 07, 2013 4:19 am
Anurag@Gurome wrote:
nidhis.1408 wrote:If n is a positive integer, what is the tens digit of n?

1. the hundreds digit of 10n is 6.
2. the tens digit of n+1 is 7.
Statement 1: If we multiply any positive integer with 10, all the digits of the of the integer shifts one place to the left. Hence, tens digit of n is same as the hundreds digit of 10n.

Sufficient

Statement 2: Say, n = 69 ---> (n + 1) = 70 --> Tens digit are different
But if n = 68 ---> (n + 1) = 69 --> Tens digit are same

Not sufficient

The correct answer is A.
Hello

Thanks for your response. Kindly confirm one thing. The question states "2. the tens digit of n+1 is 7." but if we take n = 68 ---> (n + 1) = 69 (in this case 10's digit is not 7).

n = 69 ---> (n + 1) = 70
n = 70 ---> (n + 1) = 71

Please correct me if I am wrong but is the above what you wanted to write?

Thanks
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by Blue_Skies » Tue May 07, 2013 11:44 am
Whenever you multiple by 10, you are moving the digits to left hand side. So after multiplication the tenth digit becomes hundredths digits. Hence A gives the answer.

B) units digit can be 9 and this will affect the tenth digit. It can be 6 or 7.
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