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arpan307: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Tue Apr 26, 2011 3:28 am

Help required on a DS problem

by arpan307 » Tue May 17, 2011 8:27 pm

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

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Source: Beat The GMAT — Data Sufficiency | Tue May 17, 2011 8:27 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Tue May 17, 2011 9:10 pm

arpan307 wrote: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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue May 17, 2011 9:11 pm

arpan307 wrote: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

Brent Hanneson - Creator of GMATPrepNow.com

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sourabh33: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Mar 22, 2011 12:01 pm; Thanked: 21 times; Followed by:3 members; GMAT Score:720

by sourabh33 » Tue May 17, 2011 9:14 pm

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

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Blimey72: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Jan 17, 2011 12:40 pm; Thanked: 4 times

by Blimey72 » Fri May 20, 2011 5:56 am

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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Jan 10, 2018 8:10 am

arpan307 wrote: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

Brent Hanneson - Creator of GMATPrepNow.com

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by Scott@TargetTestPrep » Tue Jan 16, 2018 5:03 pm

arpan307 wrote: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