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DS_Arithmetic

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Source: — Data Sufficiency |

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by Anju@Gurome » Sun Mar 10, 2013 3:26 am
paresh_patil wrote:What is the tenth 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
Clearly none of the statements are individually sufficient.

1 & 2 Together: The number is less than 1/3 = 0.33... but greater than 1/4 = 0.25
Consider the following two cases..
  • The number = 0.29 ---> Tenth's digit = 2
    The number = 0.30 ---> Tenth's digit = 3
Not sufficient

The correct answer is E.
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by GMATGuruNY » Sun Mar 10, 2013 3:30 am
paresh_patil wrote:What is the tenth 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: The number is less than .33333333...
Statement 2: The number is greater than .25.

x=.26 satisfies both statements, in which case the tenths digit is 2.
x=.31 satisfies both statements, in which case the tenths digit is 3.
Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Jeff@TargetTestPrep » Tue Sep 04, 2018 3:59 am
paresh_patil wrote:What is the tenth 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

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 0.2 (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 0.4 (with a tenths place of 4). 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 decimal value is between 0.25 and 0.333.... We could still have decimals values with different tenths places, such as 0.28 or 0.3.

Answer: E

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by Brent@GMATPrepNow » Tue Sep 04, 2018 5:24 am
paresh_patil wrote:What is 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 tenth digit in the decimal representation of a certain number?

Jump straight to.....

Statements 1 and 2 combined
Statement 1 tells us that the number is less than 1/3 (aka 0.333333....)
Statement 2 tells us that the number is greater than 1/4 (aka 0.25)
There are several values that satisfy BOTH statements. Here are two:
Case a: The number is 0.28. In this case, the answer to the target question is the tenths digit is 2
Case b: The number is 0.31. In this case, the answer to the target question is the tenths digit is 3
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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