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Manager  Joined: 02 Dec 2012
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If n is a positive integer, what is the tens digit of n ?  [#permalink]

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Question Stats: 65% (01:16) correct 35% (01:39) wrong based on 2625 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
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If n is a positive integer, what is the tens digit of n ?

(1) The hundreds digit of 10n is 6. This implies that the tens digit of n is 6. Sufficient.

(2) The tens digit of n + 1 is 7. If n=70, then the tens digit of n is 7, but if n=69, then the tens digit of n is 6. Not sufficient.

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Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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fozzzy wrote:
How do you solve this one?

(1) The hundreds digit of 10n is 6
SUFFICIENT: If Hundred's place of 10n = 6 then Ten's place of n must be 6
e.g. n=68 tens place 6,
10n=680, hundreds place is 6

(2) The tens digit of n+1 is 7
INSUFFICIENT: If n=69; n+1=70 OR If n=77; n+1=77; i.e. n can have both 6 or 7 as tens place.

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Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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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.

Hence A
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If n is a positive integer, what is the tens digit of n ?  [#permalink]

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If n = 60, then the tens digit is 6
10*n = 600, then the tens digit is 0.

if n = 66, then the tens digit is 6
10*n = 660, then the tens digit is also 6.

Therefore 1. seems (incorrectly) not sufficient to me.

What am I doing wrong?

Damn it, it says "hundreds" digit in 1., not tens digit... :S
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Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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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.

Target question: What is the tens digit of n?

Statement 1: The hundreds digit of 10n is 6
Notice what happens when we multiply any positive integer by 10:
34 x 10 = 340
60 x 10 = 600
128 x 10 = 1280
54629 x 10 = 546290
The tens digit in the original number becomes the hundreds digit in the new number.

So, if we're told that the hundreds digit of 10n is 6, then we know that the tens digit in n must be 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The tens digit of n+1 is 7
There are several values of n that meet this condition. Here are two:
case a: n=69 in which case the tens digit of n is 6
case b: n=74 in which case the tens digit of n is 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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GMAT 1: 470 Q30 V20 GMAT 2: 620 Q42 V33 If n is a positive integer, what is the tens digit of n ?  [#permalink]

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Here is my contribution with the reasoning a little more visual for those still struggling. Attachments Screenshot_20160909-140502.jpg [ 504.88 KiB | Viewed 32563 times ]

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Re: If N is a positive integer, what is the tens digit of N  [#permalink]

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Akuthiala 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 : Hundreds digit of 10N = Tens digit of N = 6. Hence, sufficient.

Statement 2: Tends digit of N+1 = 7.

Now in this case it may happen that Units digit was 9 and when 1 was added, we got Tends digit as 7. In that case answer will be 6. BUT if Units is less than 9, answer would be 7. Hence, Insufficient.
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Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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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.

let the number be in the form

100a+10b+c = n what is 10b

from
1000a+100b+10c + d = 10n , now the 100s digit (b=6) in 10n is the tens in n .......suff

from 2

n+1 = 100a+ 10b+(c+1) ... if c+1>=10 then b = 6 but if c+1<10 b = 7... insuff

A
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If n is a positive integer, what is the tens digit of n ?  [#permalink]

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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.

I am thinking that if we had the question as

If n is a positive number, what is the tenth digit of n?
(1) The hundredth digit of 10n is 6.
(2) The tenth digit of n + 1 is 7

A is no longer sufficient Am I Mistaken?

What do you think guys!
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Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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mohd_int 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.

I am thinking that if we had the question as

If n is a positive number, what is the tenth digit of n?
(1) The hundredth digit of 10n is 6.
(2) The tenth digit of n + 1 is 7

A is no longer sufficient Am I Mistaken?

What do you think guys!

Hello

Yes if you change the question to find the 'tenth' digit rather than 'tens' digit with the same set of statements as in this question, then the answer should be B, I think.

I suggest you post this question of yours to the DS forum.
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If n is a positive integer, what is the tens digit of n ?  [#permalink]

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Bunuel wrote:
If n is a positive integer, what is the tens digit of n ?

(1) The hundreds digit of 10n is 6. This implies that the tens digit of n is 6. Sufficient.

(2) The tens digit of n + 1 is 7. If n=70, then the tens digit of n is 7, but if n=69, then the tens digit of n is 6. Not sufficient.

How can ST ONE be sufficient IF The hundreds digit of 10n is 6

THE NUMBER CAN BE IN THIS CASE 10*60 = 600 the hundreds digits is 6 but tens digit is 0 ? Math Expert V
Joined: 02 Sep 2009
Posts: 59685
Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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dave13 wrote:
Bunuel wrote:
If n is a positive integer, what is the tens digit of n ?

(1) The hundreds digit of 10n is 6. This implies that the tens digit of n is 6. Sufficient.

(2) The tens digit of n + 1 is 7. If n=70, then the tens digit of n is 7, but if n=69, then the tens digit of n is 6. Not sufficient.

How can ST ONE be sufficient IF The hundreds digit of 10n is 6

THE NUMBER CAN BE IN THIS CASE 10*60 = 600 the hundreds digits is 6 but tens digit is 0 ? If 10n = 10*60 = 600, then n = 60. The tens digit of n is 6.
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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.
Can somebody please explain how the ans is A?

Sent from my Mi A1 using GMAT Club Forum mobile app
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Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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sakshi4391 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.
Can somebody please explain how the ans is A?

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Hi sakshi

whenever we multiply any number with 10, the digits of the number shift their places by 1.

eg n=632. 10n=6320
In case of n,
Units Digit: 2
Tens Digit: 3
Hundred's Digit: 6

In case of 10n
In case of n,
Units Digit: 0
Tens Digit: 2
Hundred's Digit: 3

Now coming back to question We need to calculate the tens digit of n.
this will be the same as hundred's digit in 10n.
so using statement 1 we can calculate the answer. Hence Sufficient.

Statement 2 is insufficient because we do not know the units digit.
If the units digit is 9. then in n+1, 1 will be carried over to the tens place and hence increase the value by 1 unit. in this case the answer would be 6.
If the units digit is less than 9, then n+1 wil lhave the same tens digit as n. in this case our ans will be 7

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If n is a positive integer, what is the tens digit of n ?  [#permalink]

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St 1 The hundreds digit of 10n is 6

Note: when we multiply any number by 10 ,value of each digit increase . Eg: 10*60=600 or 72*10=720, 7 was in tens place and 2 in units place in original number before we multiplied to 10. After we multiplied with ten, 7 is now in hundreds place and 2 in tens place.

Same way if 10n has 6 in hundreds place, n should have 6 in tens place only than on multiplying by 10 it will have 6 in hundreds place.

Hence St 1 is Sufficient.

St 2 Tens digit of n+1 is 7

Here lets check cases
if n=69 , n+1 =70
if n=71 , n+1=72

In both the cases above tens digit of n is different satisfying statement two. As we cannot arrive to our goal of finding tens value of n,
Statement 2 is INSUFFICIENT

Don't forget our goal is to find tens digit of n (and not of n+1)

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Re: If n is a positive integer, what is the tens digit of n ?  [#permalink]

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I think we have a problem with the question language for statement (2). It could be perceived in two different ways:

(1) "The tens digit of n" + 1 is 7, or
(2) The tens digit of "n + 1" is 7.

Therefore, perception becomes reality to the reader until we use parentheses properly, or at least some kind of technique to unquestionably clarify the idea being communicated. I think this is even more pertinent given that communication is an essential element in business administration. Re: If n is a positive integer, what is the tens digit of n ?   [#permalink] 25 Jun 2019, 15:32
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