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

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Joined: 07 Feb 2010
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If k is a 3 digit positive number, what is the hundred digit [#permalink]

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09 Nov 2010, 05:19
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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
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 43894
Re: if k is a 3 digit positive number [#permalink]

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09 Nov 2010, 05:29
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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 $$345\leq{k}\leq{349}$$.

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

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10 Nov 2010, 01:09
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

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

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10 Nov 2010, 01:15
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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

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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10 Nov 2010, 01:28
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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10 Nov 2010, 01:51
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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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10 Nov 2010, 02:45
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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30 Oct 2013, 17:05
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Re: If k is a 3 digit positive number, what is the hundred digit [#permalink]

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12 Nov 2014, 08:41
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Re: If k is a 3 digit positive number, what is the hundred digit [#permalink]

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23 Jan 2016, 01:46
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Re: If k is a 3 digit positive number, what is the hundred digit [#permalink]

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12 Feb 2017, 17:27
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Re: If k is a 3 digit positive number, what is the hundred digit [#permalink]

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12 Feb 2017, 17:28
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, 17:28
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