Arithmetic

[John fran kennedi]

Hi guys
Do you have some logic math to solve this question ?
Because I don't understand the answer explanation, Expecially if the number is less than 0,3333......, the tenths digit can be 0,1,2, or 3;

[fcabanski]

Statement 1: Numbers less than 1/3 (.333333) include .3, .2, .1, -1.0, -2.4,... -10.9. Any digit could be in the tenths place of this number.

Statement 1 is not sufficient.

Statement 2: Numbers greater than 1/4 (.25) include .3, .4, 1.5, 2.6...9.9, 10.0. Again, any digit (0-9)could be in the tenths place.

Statement 2 is not sufficient.

Taken together: 1/4 < n < 1/3 --> .25 < n < .333333...

n could be .26, or .3, so once again the tenths digit isn't certain.

Both statements together are not sufficient.

[John fran kennedi]

Could you please give me one example with the answer explanation to make me understand perfectly ?

[fcabanski]

The answer explanation ends up leading to the correct answer, but the explanation doesn't account for negative numbers.

I provided examples of numbers less than 1/3, that have different tenths digits.

0: .01 < .33...
1: .10 < .33...
2: .23 < .33...
3: .30 < .33...
4: -.4 < .33... (-.5, -.6, -.7, -.8 -.9 are also < .33...)

Numbers greater than 1/4 (.25)

0: 1.0
1: 1.1
2: 1.2
3: 1.3
4: 1.4
5-9 (1.5, 1.6, 1.7, 1.8, 1.9)

I provided examples of numbers with 2 and 3 in the tenths digit for the statements taken together.

[Brent@GMATPrepNow]

Question- What is the the tenths digit in the decimal representation of a certain number?

(1) The number is less than 1/3
(2) The number is greater than 1/4

statement 1: if the number is less than 1/3, then there are many possible values for that number
case a) the number = 0.31, in which case the value of the tenths digit is 3
case b) the number = 0.298, in which case the value of the tenths digit is 2
Since these tenths digit can have more than 1 value, statement 1 is NOT SUFFICIENT

statement 2: if the number is greater than 1/4, then there are many possible values for that number
case a) the number = 0.31, in which case the value of the tenths digit is 3
case b) the number = 0.298, in which case the value of the tenths digit is 2
Since these tenths digit can have more than 1 value, statement 2 is NOT SUFFICIENT


statements 1 & 2 combined: if the number is greater than 1/4 and less than 1/3, then there are many possible values for that number
case a) the number = 0.31, in which case the value of the tenths digit is 3
case b) the number = 0.298, in which case the value of the tenths digit is 2
Since these tenths digit can have more than 1 value, statements 1 & 2 combined are NOT SUFFICIENT

So, the answer is E

[John fran kennedi]

Now I understand perfectly, thank you so much, guys.