Help required on a DS problem

[arpan307]

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

This is a problem from OG 12 and the OA is E
i didn't really get the concept. could someone explain it please

[Anurag@Gurome]

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

This is a problem from OG 12 and the OA is E
i didn't really get the concept. could someone explain it please

(1) The number is less than 1/3 implies it is less than 0.333... So, the tenths digit can be 0, 1, 2, or 3. But since we don't have a definite answer.
So, (1) is NOT SUFFICIENT.

(2) The number is greater than 1/4 implies it is greater than 0.25. SO, the tenths digit can be 2, 3, 4, 5, 6, 7, 8, or 9. Again we don't have a definite answer.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), number < 0.333... and > 0.25. This implies tenths digit can be 2 or 3. But we need a definite answer. So, again the given info is NOT SUFFICIENT.

The correct answer is E.

[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

This is a problem from OG 12 and the OA is E
i didn't really get the concept. could someone explain it please

Hi arpan307,

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

[sourabh33]

Let the number be 0.ABC where A represents the tenth digit in the decimal. We need to find the value of A in this question

1. Evaluating Statement A

number is less than 1/3 --> 0.ABC < 0.3333
Now in this A could be 3,2,1 or 0 so the statement is insufficient

2. Evaluating Statement B

Number is greater than 1/4 --> 0.ABC > 0.25
Now in this A could be 9,8,7,6,5,4,3 or 2 so the statement is insufficient

Combining 1 & 2
0.25 < 0.ABC < 0.333
Now A could still be 2 or 3 therefor insufficient.

Hence the Answer should be E

[Blimey72]

Another point to note is that the question doesn't restrict the number to positive values.
So for statement 1, counting down, the tenth's digit could be 3,2,1,0,1,2,3,4 (as in -0.4),5 (-0.5),6,... i.e. all integers.

[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

Target question: What is the tenths digit in the decimal representation of a certain number?

Statement 1: The number is less than 1/3
There are several values that satisfy statement 1. Here are two:
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 we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 1: The number is greater than 1/4
There are several values that satisfy statement 2. Here are two:
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 we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
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 we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

[Scott@TargetTestPrep]

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 /quote]

We need to determine the value of the tenths place of a particular number.

Statement One Alone:

The number is less than 1/3.

Since the number is less than 1/3, it is less than 0.333.... Thus, we could have values such as 0.3 (with a tenths place of 3) or 0.28 (with a tenths place of 2). Statement one is not sufficient to answer the question.

Statement Two Alone:

The number is greater than 1/4.

Since the number is greater than 1/4, it is greater than 0.25. Thus, we could have values such as 0.3 (with a tenths place of 3) or 0.28 (with a tenths place of 2). Statement two does not provide enough information to answer the question.

Statements One and Two Together:

From statements one and two we know that the number is between 0.25 and 0.333.... We could still have numbers with different tenths places, such as 0.28 or 0.3.

Answer: E