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

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Manager
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, 06:19
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Difficulty:

75% (hard)

Question Stats:

59% (02:16) correct 41% (01:58) wrong based on 384 sessions

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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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Joined: 02 Sep 2009
Posts: 49496
Re: if k is a 3 digit positive number  [#permalink]

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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 $$345\leq{k}\leq{349}$$.

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

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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

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

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10 Nov 2010, 02:15
1
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, 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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Posts: 49496
Re: if k is a 3 digit positive number  [#permalink]

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10 Nov 2010, 02:51
1
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, 03:45
Perfect! Thank You
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Joined: 26 Oct 2016
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Location: United States
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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, 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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Anaira Mitch

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

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11 Sep 2018, 07:59
I thought about possible "carry overs", i.e. adding an imaginary digit when you do the written method for addition and a sum of digits is >10.

Ex. 18
+ 23

= 41

Here 8+3=11-> 11 is 1 bigger than 10, so you carry the 1 over to the next "column".

Using this approach let us assess the 2 statements:

(1) No info about hundreds digit, thus insufficient.

(2) Assuming no carry over from the tens to the hundreds digit, the hundreds digit could be 3.
However, assuming a carry over of 1 from the tens to the hundreds digit, the hundreds digit could also be 2. Since more than 1 value for the hundreds digtit is possible, statement (2) is insufficient.

(1) & (2) Using the same reasoning from above, combining the 2 statements does not provide any new information. The hundreds digit could still be 3 or 2.

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Re: If k is a 3 digit positive number, what is the hundred digit &nbs [#permalink] 11 Sep 2018, 07:59
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