Hi rsarashi,

The first Fact in this DS question is rather 'densely' worded, so you would likely find it helpful to TEST VALUES so that you can clarify what is 'allowed' and what is not.

We're told that N is an integer and that 100 < N < 900. We're asked for the TENS DIGIT of N.

1) If N is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value DIFFERS from the result of rounding N to the nearest hundred.

With this Fact, we're told to round TWICE (first to the nearest 10 and THEN to the nearest 100). Consider a couple of examples....

IF.... N = 425
Rounding to the nearest ten.... 430.... then rounding to the nearest hundred.... 400

vs.

Just rounding to the nearest hundred... 400

The two 'end' results would be the SAME, but Fact 1 states that they have to be DIFFERENT. So... what type of value of N would lead to different results... You need a number that would naturally round 'down' but rounds 'up' if you round it in two steps...

IF.... N = 445
Rounding to the nearest ten.... 450.... then rounding to the nearest hundred.... 500

vs.

Just rounding to the nearest hundred... 400

Now the results are DIFFERENT. This type of result will only occur when the TENS digit is 4 AND the UNITS DIGIT is 5 or higher (you can try as many examples as you like and you'll see). Thus, the answer to the question is ALWAYS FOUR.
Fact 1 is SUFFICIENT.

2) The tens digit of N is half the units digit of N and is twice the hundreds digit of N.

IF....
N = 124, then the answer to the question is TWO.
N = 248, then the answer to the question is FOUR.
Fact 2 is INSUFFICIENT.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

rsarashi wrote:If n is an integer between 100 and 900, what is the tens digit of n?

(1) If n is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value differs from the result of rounding n to the nearest hundred.

(2) The tens digit of n is half the units digit of n and is twice the hundreds digit of n.

OAA[spoiler][/spoiler]

We have: 100 < n < 900

Question: What's the value of tens digit?

Statement 1: If n is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value differs from the result of rounding n to the nearest hundred.

We must test critical value for tens digit, for example, 3, 4, and 5. The result for '3' would be the same for tens digits 0, 1, and 2, and the result for '5' would be the same for tens digit 6, 7, 8, and 9.

Say n = 139.

Rounding to the nearest ten and the result is then rounded to the nearest hundred: 139 --> 140 --> 100
Rounding to the nearest hundred: 139 --> 100

Since the result does not differ, the tens digit cannot be 0, 1, 2, or 3.

Say n = 149.

Rounding to the nearest ten and the result is then rounded to the nearest hundred: 149 --> 150 --> 200
Rounding to the nearest hundred: 149 --> 100

Since the result differs, '4' can be tens digit.

Say n = 169.

Rounding to the nearest ten and the result is then rounded to the nearest hundred: 169 --> 170 --> 200
Rounding to the nearest hundred: 169 --> 200

Since the result does not differ, the tens digit cannot be 6, 7, 9, or 9.

So, the tens digit is '4.' Sufficient.

Statement 2: The tens digit of n is half the units digit of n and is twice the hundreds digit of n.

Let's think of a few numbers. They are 124 and 248. No unique answer. Insufficient.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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