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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
If N is a positive, three-digit integer, what is the hundreds digit of  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 44% (02:04) correct 56% (02:03) wrong based on 87 sessions

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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.

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GMAT Club Legend  V
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Re: If N is a positive, three-digit integer, what is the hundreds digit of  [#permalink]

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Bunuel wrote:
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?

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: If N is a positive, three-digit integer, what is the hundreds digit of  [#permalink]

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Bunuel wrote:
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.

N = HTU

FROM STATEMENT - I ( INSUFFICIENT )

HTU + 120 = 7XY

If T > 8 ,H = 5

But, If T < 8 ,H = 6

So, HTU + 120 = 7XY

Thus we ca not have a unique value

FROM STATEMENT - II ( INSUFFICIENT )

HTU + 15 = A9B

If U > 5, T = 7
But if U < 5 , T = 8

Thus we ca not have a unique value

FROM STATEMENT I & II ( INSUFFICIENT )

Since we can not have a unique value of N we can not solve the question using statement I and II...

Thus, Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed , answer will be (E)

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Thanks and Regards

Abhishek....

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