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If k is a 3 digit positive number, what is the hundred digit

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If k is a 3 digit positive number, what is the hundred digit [#permalink]

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New post 09 Nov 2010, 06:19
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If k is a 3 digit positive number, what is the hundred digit of k?

(1) The hundred digit of k+150 is 4
(2) The tens digit of k+25 is 7
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Re: if k is a 3 digit positive number [#permalink]

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New post 09 Nov 2010, 06:29
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If k is a positive three-digit integer, what is the hundreds digit of k?

(1) The hundreds digit of K +150 is 4 --> \(400\leq{k+150}\leq{499}\) --> \(250\leq{k}\leq{349}\), not sufficient, as hundreds digit of k can be 2 or 3.

(2) The tens digit of K + 25 is 7 --> \(x70\leq{k+25}\leq{x79}\) --> \(x45\leq{k}\leq{x54}\). Clearly insufficient to get \(x\).

(1)+(2) Hundreds digit still can be 2 (for example if k=250) or 3 (for example if k=345). Not sufficient.

Basically we have that: \(250\leq{k}\leq{254}\) or \(345\leq{k}\leq{349}\).

Answer: E.
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Re: if k is a 3 digit positive number [#permalink]

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New post 10 Nov 2010, 02:09
Let us assume that the k="ABC" => K= 100 (A) +10 (B) + C

According to statement 1: The hundred digit of k+150 is 4
K+150= 100 (A) +10 (B) + C + 150
k+150= 100 (A) + 100 + 10 (B) + 50 + C
K+150= 100 (A+1) +10 (B+5) + C

A+1=4 => A=3

Statement 1 is sufficient.

According to statement 2: The tens digit of k+25 is 7

K+25= 100 (A) +10 (B) + C + 25
= 100 (A) + 10 (B+2) + (C+5)

B+2=7 => B=5

Statement 2 is insufficient because it tell us nothing about the hundreds place



Answer is A
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Re: if k is a 3 digit positive number [#permalink]

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New post 10 Nov 2010, 02:15
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rockroars wrote:
Let us assume that the k="ABC" => K= 100 (A) +10 (B) + C

According to statement 1: The hundred digit of k+150 is 4
K+150= 100 (A) +10 (B) + C + 150
k+150= 100 (A) + 100 + 10 (B) + 50 + C
K+150= 100 (A+1) +10 (B+5) + C

A+1=4 => A=3

Statement 1 is sufficient.

According to statement 2: The tens digit of k+25 is 7

K+25= 100 (A) +10 (B) + C + 25
= 100 (A) + 10 (B+2) + (C+5)

B+2=7 => B=5

Statement 2 is insufficient because it tell us nothing about the hundreds place



Answer is A


Red part is not correct. OA for this question is E, not A. Refer for the solution to my post above.
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Re: if k is a 3 digit positive number [#permalink]

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New post 10 Nov 2010, 02:28
Thank You for your response, I will go through the solution provided by you.

But I am interested to know why the red part highlighted by you is not correct?
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Re: if k is a 3 digit positive number [#permalink]

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New post 10 Nov 2010, 02:51
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rockroars wrote:
Thank You for your response, I will go through the solution provided by you.

But I am interested to know why the red part highlighted by you is not correct?


Note that when you represent 3-digit number as \(100A+10B+C\): A, B and C must be digits from 0 to 9 (for A from 1 to 9).

Now, when you get \(K+150=100(A+1)+10(B+5)+C\) you can not say that it's a representation of 3-digit number where A+1 is hundreds digit, B+5 tens digit and C units digit as we don't know whether B+5 is in the range from 0 to 9, because if it's more than 9 then you'll have A+1 plus 1 hundreds: A+1+1=4 --> A=2.

Hope it's clear.
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Re: if k is a 3 digit positive number [#permalink]

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New post 10 Nov 2010, 03:45
Perfect! Thank You :)
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Re: If k is a 3 digit positive number, what is the hundred digit [#permalink]

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New post 12 Feb 2017, 18:28
In general, with problems like this one, just consider the EXTREMES of any possible range they throw at you.

If the hundreds digit of (k + 150) is 4, then take that to mean that
400 <= k + 150 <= 499
or
250 <= k <= 349.

Therefore, the hundreds digit of k can be either 2 or 3, so this statement is insufficient.

Note that you don't have to set up the inequalities to solve the problem: you can just notice that the biggest possible value for (k + 150) is 499, and that the smallest possible value for that expression is 400.

Hence E.
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Re: If k is a 3 digit positive number, what is the hundred digit   [#permalink] 12 Feb 2017, 18:28
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