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tanvis1120: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Sat Dec 28, 2013 8:53 amFollowed by: 5 members; Location: United States; Thanked: 2 times

by tanvis1120 » Mon Aug 04, 2014 10:45 am

3.1n5
Let n represent the hundredth digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
a. 0
b. 2
c. 4
d. 5
e. 6

My first doubt is that 'n' is not the hundredth, but the tens place digit in the target question. How do I proceed?

Thank You!
Tanvi

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Source: Beat The GMAT — Problem Solving | Mon Aug 04, 2014 10:45 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Aug 04, 2014 11:07 am

tanvis1120 wrote:3.1n5
Let n represent the hundredth digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
a. 0
b. 2
c. 4
d. 5
e. 6

My first doubt is that 'n' is not the hundredth, but the tens place digit in the target question. How do I proceed?

Thank You!
Tanvi

CONCEPT : For a Number ABCD.EFG
D is Unit Place
C is Tens Place
B is Hundreds Place
A is Thousands Place

E is Tenths Place
F is Hundredth Place
F is Thousandth Place

Given the Number 3.1n5
Where n is the hundredth Digit

When Thousandth Place is digit 5 or above then the Hundredth Digit is ROUNDED UP Otherwise it remains the same while rounding off the number to the nearest Hundredth

Similarly

When Hundredth Place is digit 5 or above then the Tenth Digit is ROUNDED UP Otherwise it remains the same while rounding off the number to the nearest Tenth

Number = 3.1n5
When the Number is rounded to the nearest Tenth then either the result will have same tenth digit i.e. 1 or the tenth digit will be rounded up if n >5

Therefore the only possibility of Tenth digit are either 1 or 2

2 is available among options therefore

Answer: Option B

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

by Brent@GMATPrepNow » Mon Aug 04, 2014 11:11 am

tanvis1120 wrote:3.1n5
Let n represent the hundredth digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
a. 0
b. 2
c. 4
d. 5
e. 6

n can be any digit from 0 to 9.
Let's try a few.

If n = 0, then 3.105 rounded to the nearest HUNDREDTH is 3.11. Here, the tenths digit is 1
If n = 1, then 3.115 rounded to the nearest HUNDREDTH is 3.12. Here, the tenths digit is 1
If n = 2, then 3.125 rounded to the nearest HUNDREDTH is 3.13. Here, the tenths digit is 1
.
.
we keep getting 1 as the tenths digit until the very end.
.
.
If n = 9, then 3.195 rounded to the nearest HUNDREDTH is 3.20. Here, the tenths digit is 2

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Aug 04, 2014 11:14 am

tanvis1120 wrote:
3.1n5

My first doubt is that 'n' is not the hundredth, but the tens place digit in the target question. How do I proceed?

Thank You!
Tanvi

You should be familier with the following concept first to understand the place name whether it's 'Tenth' or 'Tens' or 'Hundredth'

CONCEPT : For a Number ABCD.EFG
D is Unit Place
C is Tens Place
B is Hundreds Place
A is Thousands Place

E is Tenths Place
F is Hundredth Place
F is Thousandth Place

A few points
1) You are using the word 'Tens' for the place after the decimal which is WRONG
2) Your understanding about the name of the place after decimal point is flawed
First digit after decimal is called 'Tenth'
Second digit after decimal is called 'Hundredth' therefore n is Hundredth digit in given number

I hope it helps you locate your mistake.

All the best!!!

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tanvis1120: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Sat Dec 28, 2013 8:53 amFollowed by: 5 members; Location: United States; Thanked: 2 times

by tanvis1120 » Mon Aug 04, 2014 11:18 am

GMATinsight wrote:
tanvis1120 wrote:
3.1n5

My first doubt is that 'n' is not the hundredth, but the tens place digit in the target question. How do I proceed?

Thank You!
Tanvi
You should be familier with the following concept first to understand the place name whether it's 'Tenth' or 'Tens' or 'Hundredth'

CONCEPT : For a Number ABCD.EFG
D is Unit Place
C is Tens Place
B is Hundreds Place
A is Thousands Place

E is Tenths Place
F is Hundredth Place
F is Thousandth Place

A few points
1) You are using the word 'Tens' for the place after the decimal which is WRONG
2) Your understanding about the name of the place after decimal point is flawed
First digit after decimal is called 'Tenth'
Second digit after decimal is called 'Hundredth' therefore n is Hundredth digit in given number

I hope it helps you locate your mistake.

All the best!!!

Thanks a lot for clarifying the tenth, hundredth, thousandth places for post decimal point digits.

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