## Hundred digit of N

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### Hundred digit of N

by j_shreyans » Wed Sep 10, 2014 10:38 pm
If N is a positive, three-digit integer, what is the hundreds digit of N?

(1) The hundreds digit of N+120 is 7.

(2) The tens digit of N+15 is 9

OA[/spoiler]E[spoiler][/spoiler]

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by [email protected] » Wed Sep 10, 2014 10:48 pm
If N is a positive, three-digit integer, what is the hundreds digit of N?

(1) The hundreds digit of N+120 is 7.
(2) The tens digit of N+15 is 9
Target question: What is the hundreds digit of N?

We can find the quick answer (which is E) by looking for conflicting values that satisfy the statements.

Let's jump straight to . . .

Statements 1 and 2 combined
There are several values of N that meet the given conditions. Here are two:
Case a: N = 580, in which case the hundreds digit is 5
Case b: N = 675, in which case the hundreds digit is 6
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent

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by [email protected] » Wed Sep 10, 2014 10:49 pm
If N is a positive, three-digit integer, what is the hundreds digit of N?

(1) The hundreds digit of N+120 is 7.
(2) The tens digit of N+15 is 9
Here's the rationale behind my answer above.

Target question: What is the hundreds digit of N?

Statement 1: The hundreds digit of N+120 is 7
Let's examine the range of possible values for N.
N can be as small as 580 (since 580+120=700) and N can be as large as 679 (since 679+120=799)
So, 580 < N < 679
As we can see, the hundreds digit of N can be either 5 or 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The tens digit of N+15 is 9
Since there's no information about the hundreds digit, we immediately know that statement 2 is NOT SUFFICIENT.
However, let's see what we can conclude from statement 2.
If the tens digit of N+15 is 9, then N can be as small as ?75 (since ?75+15=?90), and N can be as large as ?84 (since ?84+15=?99)
Aside: The question mark represents the unknown hundreds digit
So, ?75 < N < ?84

Statements 1 and 2 combined
Statement 1 tells us that 580 < N < 679
Statement 2 tells us that ?75 < N < ?84

At this point, we can spot some possible values of N that will yield conflicting answers to the target question.
Case a: N = 582, in which case the hundreds digit is 5
Case b: N = 679, in which case the hundreds digit is 6
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent

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### Re: Hundred digit of N

by BeatGmatEdgar » Fri Apr 09, 2021 1:31 pm
Hi, this is my approach,

Since N is a three digits number, 0 < hundreds digit <= 9.
So, hundreds digit could be (1,2,3,4,5,6,7,8,9)

St#1: The hundreds digit of N+120 is 7
As we do not have information about tens digit of N, so the hundreds digit of N could be 5 or 6. --->Not sufficient.

St#2: The tens digit of N+15 is 9
As we do not have information about de units digits of N, so the tens digit of N could b 7 or 8. And this does not give information about the hundreds digit of N ---> Not sufficient.

St#1 & St#2
Combining the 2 statements, we have that, N could be 57U, 58U, 67U or 68U, where U= units digits of N.

If I take 9 as units digit of N to to complete the number 57U we have: 579. Adding 579+120 we have 699 so, that contradicts St#1: The hundreds digit of N+120 is 7 , ( 6)

If I take 9 as units digit of N to to complete the number 58U we have: 589. Adding 589+120 we have 709 so, that confirms St#1: The hundreds digit of N+120 is 7 (7). .

If I take 9 as units digit of N to to complete the number 67U we have: 679. Adding 679+120 we have 799 so, that confirms St#1: The hundreds digit of N+120 is 7 , ( 7)

If I take 9 as units digit of N to to complete the number 68U we have: 689. Adding 689+120 we have 809 so, that contradicts St#1: The hundreds digit of N+120 is 7 (8).

---> Not sufficient because we have 5 or 6 in the hundreds digit of N

Do you think that my approach is correct?
Thanks

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