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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