If n is a positive integer, what is the ten digit of n?
1) The hundreds digit of 10n is 6
2) The tens digit of n+1 is 7
OAA
Please explain
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ten digit of n
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Statement 1:Needgmat wrote:If n is a positive integer, what is the ten digit of n?
1) The hundreds digit of 10n is 6
2) The tens digit of n+1 is 7
10n = 600, 610, 620, 630...
If we divide both sides by 10, we get the following options for n:
n = 60, 61, 62, 63...
In every case, the tens digit of n is 6.
SUFFICIENT.
Statement 2:
n+1 = 70, 71, 72...
If we subtract 1 from both sides, we get the following options for n:
n = 69, 70, 71...
If n=69, then its tens digit is 6.
If n=70, then its tens digit is 7.
Since the tens digit can be different values, INSUFFICIENT.
The correct answer is A.
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Brent@GMATPrepNow
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Target question: What is the tens digit of n?Needgmat wrote:If n is a positive integer, what is the ten digit of n?
1) The hundreds digit of 10n is 6
2) The tens digit of n+1 is 7
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
Answer = A
Cheers,
Brent
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Hi Needgmat,
Both Mitch's and Brent's explanations are right-on, so I won't rehash them here. The issue in this question is basically a "decimal shift" issue, which is something you'll see on the GMAT as least once. You will also have to deal with this issue any time the answers having shifting decimals:
For example
210
21
2.1
.21
.021
This is essentially a test of your "accounting" ability - it's really easy to get this question correct and really easy to screw it up. To get the 700+ that everyone's after, you have to be perfect on these questions (in addition to all of the other questions that you need to get correct).
GMAT assassins aren't born, they're made,
Rich
Both Mitch's and Brent's explanations are right-on, so I won't rehash them here. The issue in this question is basically a "decimal shift" issue, which is something you'll see on the GMAT as least once. You will also have to deal with this issue any time the answers having shifting decimals:
For example
210
21
2.1
.21
.021
This is essentially a test of your "accounting" ability - it's really easy to get this question correct and really easy to screw it up. To get the 700+ that everyone's after, you have to be perfect on these questions (in addition to all of the other questions that you need to get correct).
GMAT assassins aren't born, they're made,
Rich
Hello Mitch Hunt and other experts......
I understood your explanations. Please help me in my below logic where I go wrong..
Statement 1. hundreds digit of 10n is 6...So, let n=61-> so 10n=610.. hundred digit is 6 but ten digit is 1.
let n=62-> .. hundred digit of 10n=620 but ten digit of n is 2.. So INSUFFICIENT.
Statement 2.The tens digit of n+1 is 7. If n is a 2 digit positive integer (to get tens digit atleast) n has to be 69, to get 69+1=70.. so 69...let n=169 so n+1=170.. so still tens digit is 7, but n is 169.. Hence in sufficient..
Both together will say that only with number n=69, 10n=690.. so Statement 1 sufficient and 69+1=70.. So Statement 2 sufficient...
So OA shoudl be C.
Please explain where I go wrong in above explanation.
Regards,
Mrudang
I understood your explanations. Please help me in my below logic where I go wrong..
Statement 1. hundreds digit of 10n is 6...So, let n=61-> so 10n=610.. hundred digit is 6 but ten digit is 1.
let n=62-> .. hundred digit of 10n=620 but ten digit of n is 2.. So INSUFFICIENT.
Statement 2.The tens digit of n+1 is 7. If n is a 2 digit positive integer (to get tens digit atleast) n has to be 69, to get 69+1=70.. so 69...let n=169 so n+1=170.. so still tens digit is 7, but n is 169.. Hence in sufficient..
Both together will say that only with number n=69, 10n=690.. so Statement 1 sufficient and 69+1=70.. So Statement 2 sufficient...
So OA shoudl be C.
Please explain where I go wrong in above explanation.
Regards,
Mrudang
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Brent@GMATPrepNow
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My comments are abovemjmehta81 wrote:Hello Mitch Hunt and other experts......
I understood your explanations. Please help me in my below logic where I go wrong..
Statement 1. hundreds digit of 10n is 6...So, let n=61-> so 10n=610.. hundred digit is 6 but ten digit is 1. Here n = 61 and 10n = 610. The question asks for the tens digit of n, not 10n. The tens digit of n is 6
let n=62-> .. hundred digit of 10n=620 but ten digit of n is 2.. So INSUFFICIENT.
Here n = 62 and 10n = 620. The question asks for the tens digit of n, not 10n. The tens digit of n is 6
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Matt@VeritasPrep
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This is a totally reasonable and common objection, but remember that you don't have to tell us *everything* about n: you only have to give us what the question seeks. Since we're only asked for the tens digit of n, the units digit of n (the tens digit of 10n) is irrelevant.mjmehta81 wrote: Statement 1. hundreds digit of 10n is 6...So, let n=61-> so 10n=610.. hundred digit is 6 but ten digit is 1.
let n=62-> .. hundred digit of 10n=620 but ten digit of n is 2.. So INSUFFICIENT.
It's nice to be complete and thorough, but that instinct can get us in real trouble in DS.
