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# The decimal representation of the number n is 0.ab where a and b are d

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Intern
Joined: 08 Jan 2019
Posts: 17
The decimal representation of the number n is 0.ab where a and b are d  [#permalink]

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Updated on: 01 Feb 2019, 03:19
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:46) correct 38% (01:39) wrong based on 31 sessions

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The decimal representation of the number n is 0.ab where a and b are distinct digits. What is the value of b?

(1) 8.2 < 10n < 8.7

(2) 4 < 5n < 4.2

Analyze the Question Stem:

This is a Value question. The digit b represents the hundredths digit of n, where a and b are distinct. For sufficiency, a single value for the hundredths place must be determined.

Evaluate the Statements:

Statement (1): The statement as it is presented, 8.2 < 10n < 8.7, can be simplified by dividing each component by 10. The possible range for n becomes 0.82 < n < 0.87. This means that b could be 3, 4, 5, or 6, and the statement is therefore Insufficient. Eliminate choices (A) and (D).

Statement (2): The statement as it is presented, 4 < 5n < 4.2, can be simplified by dividing each component by 5. The possible range for n becomes 0.8 < n < 0.84. Therefore b could be 1, 2, or 3, and the statement is Insufficient. Eliminate choice (B).

Combined: When taken together the statements are Sufficient. The only digit the two statements share in common is 3, which must be the value of b; Answer Choice (C) is correct.

Finding the logic quite convoluted which yields the answer E . thoughts?

Originally posted by DebbieChats on 01 Feb 2019, 03:15.
Last edited by Bunuel on 01 Feb 2019, 03:19, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 53061
The decimal representation of the number n is 0.ab where a and b are d  [#permalink]

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01 Feb 2019, 03:20
DebbieChats wrote:
The decimal representation of the number n is 0.ab where a and b are distinct digits. What is the value of b?

(1) 8.2 < 10n < 8.7

(2) 4 < 5n < 4.2

Analyze the Question Stem:

This is a Value question. The digit b represents the hundredths digit of n, where a and b are distinct. For sufficiency, a single value for the hundredths place must be determined.

Evaluate the Statements:

Statement (1): The statement as it is presented, 8.2 < 10n < 8.7, can be simplified by dividing each component by 10. The possible range for n becomes 0.82 < n < 0.87. This means that b could be 3, 4, 5, or 6, and the statement is therefore Insufficient. Eliminate choices (A) and (D).

Statement (2): The statement as it is presented, 4 < 5n < 4.2, can be simplified by dividing each component by 5. The possible range for n becomes 0.8 < n < 0.84. Therefore b could be 1, 2, or 3, and the statement is Insufficient. Eliminate choice (B).

Combined: When taken together the statements are Sufficient. The only digit the two statements share in common is 3, which must be the value of b; Answer Choice (C) is correct.

Finding the logic quite convoluted which yields the answer E . thoughts?

Please name topics properly (check rule 3 here: https://gmatclub.com/forum/rules-for-po ... 33935.html) and hide your doubts/questions under the spoilers. Thank you.
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Re: The decimal representation of the number n is 0.ab where a and b are d  [#permalink]

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01 Feb 2019, 03:39
DebbieChats wrote:
The decimal representation of the number n is 0.ab where a and b are distinct digits. What is the value of b?

(1) 8.2 < 10n < 8.7

(2) 4 < 5n < 4.2

Initially i had marked E, but if you look at the combination of both

1) 8.2 < 10n < 8.7
0.82 < n < 0.87, here n can be 0.8345 as well

2) 4 < 5n < 4.2
0.8 < n < 0.84, here n can 0.81 or 0.82 no fix value

Combine both the statements
Here n can be 0.83 or 0.823( I think this cannot exist for the question, because if we round this up to the hundredth place, it wont lie in the range of Statement 1)

Making it C.
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 08 Jan 2019
Posts: 17
Re: The decimal representation of the number n is 0.ab where a and b are d  [#permalink]

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01 Feb 2019, 04:06
0.82 < n < 0.87 --- n = 0.83, 0.84, 0.85, 0.86
0.8 < n < 0.84 n = 0.81, 0.82, 0.83

From the above they are drawing the conclusion that last digit is 3 as 0.83 is the only overlap..

Apply that same logic to an inequality question

Statement 1 - a= 3 or -4
Statement 2 a< -2
1+2 the only overlap is -4 so a = -4 So choice should be C
Here the choice turns out to be E

GMAT logic is very illogical I have to say
VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: The decimal representation of the number n is 0.ab where a and b are d  [#permalink]

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01 Feb 2019, 04:12
DebbieChats wrote:
0.82 < n < 0.87 --- n = 0.83, 0.84, 0.85, 0.86
0.8 < n < 0.84 n = 0.81, 0.82, 0.83

From the above they are drawing the conclusion that last digit is 3 as 0.83 is the only overlap..

Apply that same logic to an inequality question

Statement 1 - a= 3 or -4
Statement 2 a< -2
1+2 the only overlap is -4 so a = -4 So choice should be C

Here the choice turns out to be E

GMAT logic is very illogical I have to say

For the bold part the answer will be a C, only.

But for the question which you had posted previously, there the answer is E because
Statement 1 a= 3 or -4
Statement 2 a< -2 or a> 2 ( you have two range to satisfy)

Even after combining both the statements, you can get 2 values which satisfy both the ranges
3>2 yes and -2>-4 yes

But we were asked to find a value not values
making it an E
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Math Expert
Joined: 02 Sep 2009
Posts: 53061
Re: The decimal representation of the number n is 0.ab where a and b are d  [#permalink]

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01 Feb 2019, 04:13
DebbieChats wrote:
0.82 < n < 0.87 --- n = 0.83, 0.84, 0.85, 0.86
0.8 < n < 0.84 n = 0.81, 0.82, 0.83

From the above they are drawing the conclusion that last digit is 3 as 0.83 is the only overlap..

Apply that same logic to an inequality question

Statement 1 - a= 3 or -4
Statement 2 a< -2
1+2 the only overlap is -4 so a = -4 So choice should be C
Here the choice turns out to be E

GMAT logic is very illogical I have to say

GMAT is very precise.

I tried to explain what you are missing with highlighted question here: https://gmatclub.com/forum/what-is-the- ... l#p2218725
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Joined: 01 Nov 2018
Posts: 72
GMAT 1: 690 Q48 V35
GPA: 3.88
Re: The decimal representation of the number n is 0.ab where a and b are d  [#permalink]

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02 Feb 2019, 05:57
Great Question. Have to play around with the numbers. First statement, 0.83,0.84, 0.85 work so not sufficient. Second statement, 0.82 and 0.83 work so not sufficient. Combined, also 0.83 works meaning b must be the digit 3, hence C.
Re: The decimal representation of the number n is 0.ab where a and b are d   [#permalink] 02 Feb 2019, 05:57
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