Data Sufficiency

If K is a positive 3 digit integer, what is value of hundredth digit of K?

1. Hundredth digit of K+150 if 4
2. Tens digit of K+25 is 7

1 is insufficient. Consider k = 250: k + 150 will have the hundredth digit 4, but k has the hundredth digit 2. But take k = 349; again, k + 150 will have the hundredth digit 4, but now k has the hundredth digit 3. Notice that I have given you the smallest and the largest possible values for k (250 and 349).

2. again, insufficient. Tens digit of k + 25 is 7 means that the tens digit of k is either 4 (think of 45 + 25 = 70) or 5 (think of 54 + 25 = 79). This means that the last two digits of k are between 45 and 54 inclusive, but we don't know anything about the hundreds digits.

Put both statements together and you still can't say for sure. Take 254 and 345 to prove that there are at least two sets of answers.

Thanks Dana, you offered the most clear explaination ! E it is.

IMO (E)

1. If the hundreds digit of K+150 is 4, then K + 150 is from 400 to 499 and thus K is between 250 and 349. So, it's hundreds digit could be 2 or 3.

Option A and D ruled out.

2. Ten's digit of K + 25 is 7, which is even more arbitrary. K can have any digit from 1 to 9 on the hundreds place.

Option B also ruled out.

Lets try to combine the two statements.
If K is between 250 and 349, K + 25 is between 275 and 374. The tens digit has to be 7 so K + 25 can be (275,....279,371,...374) or K can be (250,..254, 346,...349)
So, again, the hundreds place of K can be 2 or 3.

No conclusive answer yet.
so, (E) is the correct option.

It took me close to the full 2 mins to conclude on E. I took the approach of plugging in.

(i). We get a range of numbers for this value. K can be any number between 250 (K+150=400) to 349 (K+150=499).

(ii). Since there is no restriction on the Hundreds digit we get a large range of values for every hundred i.e. X45 to X54.

Together, we get two values 254 and 345 i.e. there is not a distinct value. Hence E.

A: insufficient - K can be any number between 250 and 349.
B: insufficient - As it doesnot give any information about hundreds digit.

Put together, take 250 and 349, which satifies A and add 25 to them.
250+25 = 275
349+25 = 374
both satifies B, but still no definite answer for K's hundred digit.

Hence option E is the correct answer.

off lost patience to thoroughly evaluate C !

Since a positive 3-digit integer does not have a hundredth digit, I suspect that the problem should read as follows:

sakurle wrote:If K is a positive 3 digit integer, what is value of hundredth digit of K?

1. Hundreds digit of K+150 is 4
2. Tens digit of K+25 is 7

Plug in RANGES for K+150 and K+25.
Then subtract 150 and 25 from these ranges to determine the possible values of K.

Statement 1: The hundredth digit of K+150 is 4
K+150 = 400...499
Subtracting 150 from this range, we get:
K = 250...349.
Since the hundreds digit of K can be 2 or 3, INSUFFICIENT.

Statement 2: Tens digit of K+25 is 7
K+25 = 170...179, 270...279, 370...379, etc.
Subtracting 25 from these ranges, we get:
K = 145...154, 245...254, 345...354, etc.
Since the hundreds digit of K can be different values, INSUFFICIENT.

Statements 1 and 2 combined:
250...254 and 345..349 satisfy both statements.
Since the hundreds digit of K can be 2 or 3, INSUFFICIENT.

The correct answer is E.

E the answer.

let the three digit numbers be 345 and 354

345+150=495 and 345+25=370

254+150=404 and 254+25=279

GMATGuruNY wrote:

sakurle wrote:If K is a positive 3 digit integer, what is value of hundredth digit of K?

1. Hundredth digit of K+150 is 4
2. Tens digit of K+25 is 7

Plug in RANGES for K+150 and K+25.
Then subtract 150 and 25 from these ranges to determine the possible values of K.

Statement 1: The hundredth digit of K+150 is 4
K+150 = 400...499
Subtracting 150 from this range, we get:
K = 250...349.
Since the hundreds digit of K can be 2 or 3, INSUFFICIENT.

Statement 2: Tens digit of K+25 is 7
K+25 = 170...179, 270...279, 370...379, etc.
Subtracting 25 from these ranges, we get:
K = 145...154, 245...254, 345...354, etc.
Since the hundreds digit of K can be different values, INSUFFICIENT.

Statements 1 and 2 combined:
250...254 and 345..349 satisfy both statements.
Since the hundreds digit of K can be 2 or 3, INSUFFICIENT.

The correct answer is E.

Hi Mitch,

Please correct me - Hunderedth digit is 2digit to the right of decimal point.

so as per that Answer should be A.

nikhilgmat31 wrote: Hi Mitch,

Please correct me - Hunderedth digit is 2digit to the right of decimal point.

so as per that Answer should be A.

Good catch.
The problem was posted with a typo.
Since K is a positive 3-digit integer -- and an integer does not have a hundredth digit -- statement 1 should read as follows:
The HUNDREDS digit of K+150 is 4.
In my post above, I've corrected the typo.

GMATGuruNY wrote:

nikhilgmat31 wrote: Hi Mitch,

Please correct me - Hunderedth digit is 2digit to the right of decimal point.

so as per that Answer should be A.

Good catch.
The problem was posted with a typo.
Since K is a positive 3-digit integer -- and an integer does not have a hundredth digit -- statement 1 should read as follows:
The HUNDREDS digit of K+150 is 4.
In my post above, I've corrected the typo.

So the answer should be A, right ?

nikhilgmat31 wrote:
So the answer should be A, right ?

The correct answer is not A but E.
When the two statements are combined, the hundreds digit of K could be 2 or 3, as shown in my post above.
Thus, the two statements combined are INSUFFICIENT.

GMATGuruNY wrote:

nikhilgmat31 wrote:
So the answer should be A, right ?

The correct answer is not A but E.
When the two statements are combined, the hundreds digit of K could be 2 or 3, as shown in my post above.
Thus, the two statements combined are INSUFFICIENT.

Thanks Mitch, Now I misread it