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

Question

(1) The hundreds digit of 10n is 6.
(2) The tens digit of n + 1 is 7.

BrentGMATPrepNow · Accepted Answer

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:
 3 4 x 10 =  3 40
 6 0 x 10 =  6 00
1 2 8 x 10 = 1 2 80
546 2 9 x 10 = 546 2 90
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

Answer = A

Bunuel · Answer

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.

Answer: A.

PrashantPonde · Answer

(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.

Hence choice(A) is the answer.

gmatkum · Answer

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

felippemed · Answer

Here is my contribution with the reasoning a little more visual for those still struggling. :wink:

eantolovic · Answer

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.

Mits555 · Answer

Isn't it too ambiguous when they say "tens digit of n + 1 = 7"?
I understood that tens digit of n like x, and this x+1=7, so x is 6. Therefore, tens digit of n is 6.

Isn't it also possible to understand the question as I did?

Posted from my mobile device

unraveled · Answer

Mits555 
No.
The way you are saying it x is a single digit number. However, n is a two digit number, the tens digit of which has to be found. 
But, n + 1 ≠ x + 1

Do you mean to say n = x?
No, i guess.

I hope you get the point.

Hovkial · Answer

OFFICIAL GMAT EXPLANATION

(1) Given that the hundreds digit of 10n is 6, the tens digit of n is 6, since the hundreds digit of 10n is always equal to the tens digit of n; SUFFICIENT.

(2) Given that the tens digit of n + 1 is 7, it is possible that the tens digit of n is 7 (for example, n = 70) and it is possible that the tens digit of n is 6 (for example, n = 69); NOT sufficient.

The correct answer is A; statement 1 alone is sufficient .

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=9Vc_s59TP54

ScottTargetTestPrep · Answer

Solution:
 
We need to determine the tens digit of a positive integer n.

Statement One Alone:

Since the hundreds digit of 10n is the tens digit of n, the tens digit of n is therefore 6. Statement one alone is sufficient.

Statement Two Alone:

If the tens digit of n + 1 is 7, the tens digit of n could be 6 or 7. For example, if n = 69, then n + 1 = 70 has a tens digit of 7. In this case, the tens digit of n is 6. On the other hand, if n = 70, then n + 1 = 71 still has a tens digit of 7. In this case, the tens digit of n is 7. Statement two alone is not sufficient.

Answer: A

allezwart · Answer

Statement 1: 10(x)=6xx
needs to be 6x Sufficient

Statement 2: 
Could be 69 (nice) 69+1=70 or could be 71+1=72
since two different tens digit (6 or 7) no good.

Ans->A

Sneha2021 · Answer

Bunuel 
Hi Bunuel,

What if the question didn't mention n is a positive integer. Do you think the answer is still A?

I think even if we consider n is a decimal or a negative number, statement 1 will be sufficient.

Wai22 · Answer

Algebraic approach:

1) 10n = 100(6) + 10(x) + 0 
to make n the subject (since we are trying to find n) we divide the above eq. by 10
 n = 10(6) + x + 0
 n = 10(6) + x

hence, the tens digit is 6 and this statement is sufficient.

2) n+1 = 10(7) + x
 n+1 = 70 + x
 n = 69 + x

now if x (the unit's digit) is 0 then n = 69 
 tens digit of n is 6.
 if x is 1 or greater than 1 then n = 70,71,72......
 tens digit of n is 7.
 
 hence, statement 2 is not sufficient!

totaltestprepNick · Answer

A https://www.youtube.com/watch?v=_t791t9Sb0M Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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GMAT Data Sufficiency (DS) Questions

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

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