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

Question

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

Bunuel · Answer

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.

rockroars · Answer

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

Bunuel · Answer

Red part is not correct. OA for this question is E, not A. Refer for the solution to my post above.

rockroars · Answer

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?

Bunuel · Answer

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.

rockroars · Answer

Perfect! Thank You

anairamitch1804 · Answer

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.

laulau · Answer

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.

Hence, the answer is E.

If you liked this post, feel free to hit Kudos!

Probus · Answer

Hi,

here are my two cents for this question.

We need to determine the hundred's digit of a given number.

K= _ _ _

We are told that K+150 , the hundreds digit is 4, this means if there is no carry bought in by tens digit then the value is 3 else the value is 2

from statement 2 we have k+25 , the tens digit is 7 . Similarly if there is if there is no carry bought in by ones digit then the value is 5 else the value is 4

Combining 1 and 2 we have 
if tens digit of k is 4 and k+150 has hundreds digit as 4 then hundreds digit of k is 3.

if tens digit of k is 5 and k+150 has hundreds digit as 4 then hundreds digit of k is 2.

So we cannot conclusively say if hundred's digit is 2 or 3

Hence E

Probus

Rocknrolla21 · Answer

Hello, Bunuel!

We know that the tenths digit is a 4 or a 5 and that 250 <= K <= 349. Hence, K could equal anything from 250-259 or 340-349 and the hundreds digit could still be 2 or 3.

Why just 250≤k≤254 or 345≤k≤349 ?

Thank you!

bumpbot · Answer

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

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