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Numbers: If n is an integer between 100 and 900

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Numbers: If n is an integer between 100 and 900

by Yaj » Wed Sep 18, 2013 12:04 am
Hi Guys!

Need some help:

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.

[spoiler]OA:A[/spoiler]

Thank You!
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by ganeshrkamath » Wed Sep 18, 2013 1:00 am
Yaj wrote:Hi Guys!

Need some help:

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.

[spoiler]OA:A[/spoiler]

Thank You!

Statement 1:
xyz rounded to nearest ten and then to the nearest hundred differs from xyz rounded to nearest 100.
This can only happen when the number has a tens digit of 4.
example : 145 => 150 => 200 vs 145 => 100
748 => 750 => 800 vs 748 => 700
Sufficient.

Statement 2:
example : 124, 248
They have different tens digit.
Not sufficient.

Choose A

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by sanju09 » Wed Sep 18, 2013 1:05 am
Yaj wrote:Hi Guys!

Need some help:

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.

[spoiler]OA:A[/spoiler]

Thank You!
I. If n is 153 for example. When rounded to nearest ten, it becomes 150, and when 150 is rounded to nearest hundred, it becomes 200. And what happens when 153 is directly rounded to nearest hundred? It still becomes 200. So, n is not this kind of a number, means ten's digit of n is not 5 or more. Let's take n to be 149. When rounded to nearest ten, it becomes 150, and when 150 is rounded to nearest hundred, it becomes 200 as final value. And what happens when 149 is directly rounded to nearest hundred? It becomes 100 by rules of rounding. This shows that the final value differs from the result of rounding n to the nearest hundred. Hence, 149 can be a type that n may assume. We can extend our research taking n to be, 143, 139, or any 3-digit n that carries 4 (or less) in its ones' and tens place, doesn't support the statement. The statement is supported only by those 3-digit n(s) that carry 4 in its tens place and 5 or more in its ones' place. Hence, 4 is the tens digit of n. Sufficient

II. That pretends to be complicated! 248 says it's 4; but 124 says it's 2. [spoiler]Hence insufficient

Take A
[/spoiler]
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by theCodeToGMAT » Wed Sep 18, 2013 1:16 am
Good Question.. took a while to solve..

100<n<900 --> _ _ _

Statement 1: The Middle value should be a value which is acting as a pendulum and is dependent on Unit digits. So, 5

Now, _ 5 _
Lets Validate, Consider Value

454 --> 450 ---> 400 (Applying If n is rounded to the nearest ten and the result is then rounded to the nearest hundred)
454 ---> 500 (Applying the result of rounding n to the nearest hundred)

Hence, the Hundredth Digit is definitely 5 and the Unit Digit varies between 1 to 5 inclusive.

SUFFICIENT

Statement 2:

124
248, etc

hence, Insufficient


ANSWER [A].


Yaj wrote:Hi Guys!

Need some help:

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.

[spoiler]OA:A[/spoiler]

Thank You!
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