Data Sufficiency

If k is a positive three-digit integer, what is the hundreds digit of k?

1) The hundreds digit of K +150 is 4

2) The tens digit of K + 25 is 7

OA is E

Please explain

tj123 wrote:If k is a positive three-digit integer, what is the hundreds digit of k?

1) The hundreds digit of K +150 is 4

2) The tens digit of K + 25 is 7

OA is E

Please explain

IMO C

From 1.

If K = 704, K+ 150 = 854 - Hundred Digit = 4, Also hundred Digit of K = 4
If K= 990, K + 150 = 1140 - Hundred Digit = 4 , But hundred digit of K =0

From 2.

Clearly, we say of hundred digit, just from tens' digit.

Combining I and II, ten's digit should always be 5. Hundred should be 4.And Unit's digit can vary.

K=154
K+25=179
K+150=304

I cannot think of any number, which satisfies I and II, and its hundredth digit is not 4.

I think it is E.

1)
XXX + 150 = 4XX

The numbers that satisfy this condition range from:

250 to 349.

So therefore the hundreds digit can be 2 or 3 and Insufficient.

2)
XXX + 25 = X7X

The numbers that satisfy this condition range from:

X45 to X54.

So therefore the hundreds digit can be 1 to 9 and Insufficient.

Combined:

Using the info above the range of numbers are:

250 to 254 or 345 to 349.

So therefore the hundreds digit can be 2 or 3.

Therefore E.