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1.4ab5

by j_shreyans » Tue Sep 30, 2014 9:03 am

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In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 - x?

(1) If x is rounded to the nearest hundredth, then 10 - x = 8.56.

(2) If x is rounded to the nearest thousandth, then 10 - x = 8.564.

how OA B

Pls explain me guys.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Sep 30, 2014 9:52 am

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j_shreyans wrote:In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 - x?

(1) If x is rounded to the nearest hundredth, then 10 - x = 8.56

(2) If x is rounded to the nearest thousandth, then 10 - x = 8.564
Target question: What is the value of 10 - x?

Given: X = 1.4ab5

Statement 1: If x is rounded to the nearest hundredth, then 10 - x = 8.56
10 - 1.44 = 8.56
So, x rounded to the nearest HUNDREDTH = 1.44
So, x COULD equal 1.4355, 1.4365, 1.4375, 1.4385, 1.4395, 1.4405, 1.4415, 1.4425, 1.4435 OR 1.4445
Given all of the different possible values of x, 10 - x could have MANY different values.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If x is rounded to the nearest thousandth, then 10 - x = 8.564
10 - 1.436 = 8.564
In other words, x rounded to the nearest THOUSANDTH = 1.436
This tells us that a must equal 3, leaving us with 1.43b5
If 1.43b5 rounded to the nearest THOUSANDTH = 1.436, then b MUST equal 5
So, x must equal 1.4355, which means 10 - x MUST equal 8.5645
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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by Brent@GMATPrepNow » Tue Sep 30, 2014 9:56 am

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Here are 2 similar questions:
- https://www.beatthegmat.com/decimal-ques ... 37999.html
- https://www.beatthegmat.com/manhattan-de ... 70519.html

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by [email protected] » Sat Feb 25, 2017 1:11 am

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agreed
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Rounding off Q Solution

by Vipul1991 » Sat Aug 12, 2017 11:53 am

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10.0000-1.4ab5= 8.5(9-a)(9-b)5

Our number is 8.5(9-a)(9-b)5
1) we know 10-x = 8.56
then the no can be 8.5615 & 8.5565 and still yield on rounding to nearest hundredth digit 8.56 hence Unsufficient
2) 10-x = 8.564
9-a = 6
In 8.5(9-a)(9-b)5, When we round it to nearest thousandth 9-b must become (9-b)+1
hence the number must be 8.5635 which rounds up to 8.564
Hence Sufficient
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by Brent@GMATPrepNow » Mon Jan 15, 2018 9:29 am

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j_shreyans wrote:In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 - x?

(1) If x is rounded to the nearest hundredth, then 10 - x = 8.56.

(2) If x is rounded to the nearest thousandth, then 10 - x = 8.564.

Target question: What is the value of 10 - x?

Given: X = 1.4ab5

Statement 1: If x is rounded to the nearest hundredth, then 10 - x = 8.56
10 - 1.44 = 8.56
So, x rounded to the nearest HUNDREDTH = 1.44
So, x COULD equal 1.4355, 1.4365, 1.4375, 1.4385, 1.4395, 1.4405, 1.4415, 1.4425, 1.4435 OR 1.4445
Given all of the different possible values of x, 10 - x could have MANY different values.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If x is rounded to the nearest thousandth, then 10 - x = 8.564
10 - 1.436 = 8.564
In other words, x rounded to the nearest THOUSANDTH = 1.436
This tells us that a must equal 3, leaving us with 1.43b5
If 1.43b5 rounded to the nearest THOUSANDTH = 1.436, then b MUST equal 5
So, x must equal 1.4355, which means 10 - x MUST equal 8.5645
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Brent
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by masoom j negi » Fri Dec 21, 2018 8:35 pm

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Statement 1. If x is rounded to nearest hundredth digit, then 10 - x = 8.56 i.e. x = 1.44
This is possible for (a , b) = (3, >5) and (4 , <5). Hence, Insufficient.
Statement 2. If x is rounded to nearest thousandth digit, 10 - x= 8.564 i.e. x = 1.436
This is only possible when a = 3 and b = 5. Hence, Sufficient.
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