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In the decimal 3.1de

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In the decimal 3.1de

by rsarashi » Sat Jan 21, 2017 9:55 am
In the decimal 3.1de, d and e each represent a digit. If x represents the decimal 3.1de rounded to the nearest tenth, what is the value of x?

1) d=4

2) e=8

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Jan 21, 2017 10:00 am
In The decimal 3.1de, d and e each represent a digit. If X represents the decimal 3.1de rounded to the nearest tenth, what is the value of x?
1) D=4
2) E=8
Target question: What is the value of x?

Given: X represents the decimal 3.1de rounded to the nearest tenth

Statement 1: D = 4
So, the decimal could by 3.140, 3.141, 3.142, 3.143, 3.144, 3.145, 3.146, etc
To round any of these decimals to the nearest tenth, we need only check the hundredths digit.
Since the hundredths digit is 4, ALL of these decimals round to be 3.1
In other words, X must equal 3.1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: E=8
There are several different decimals that meet this condition. Here are two:
Case a: the numbers decimal is 3.128, in which case X = 3.1
Case b: the numbers decimal is 3.168, in which case X = 3.2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by [email protected] » Sat Jan 21, 2017 11:03 am
Hi rsarashi,

Rounding can be done with any digit of a number (to the left of the decimal or to the right of the decimal) - and the rules are the same:

The digits 0-4 are rounded DOWN.
The digits 5-9 are rounded UP.

For example...
12.63 rounded to the nearest TENTH is 12.6 (since '3' is rounded down)
12.63 rounded to the nearest INTEGER is 13 (since '6' is rounded up)
12.63 rounded to the nearest TEN is 10 (since '2' is rounded down)

In this question, we're told that 3.1DE is a number in which D and E are both digits. We're also told X = 3.1DE rounded to the nearest TENTH. We're asked for the value of X.

1) D = 4

With this Fact, we know that the number is 3.14E. Regardless of what E is, we still have round to the nearest TENTH based on the "4", so we know that X = 3.1
Fact 1 is SUFFICIENT

2) E = 8

With this Fact, we know that the number is 3.1D8. Until we know the value of D though, we don't know whether we should round up or round down.
IF....
D = 4, then the number is 3.148 and we round down to 3.1
D = 9, then the number is 3.198 and we round up to 3.2
Fact 2 is INSUFFICIENT

Final Answer: A

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