Arithmetic

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tapanmittal: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Fri Apr 10, 2015 4:04 am

by tapanmittal » Fri Jun 19, 2015 10:40 pm

What is the hundreths digit of the decimal m?
(1) The tenths digit of 100m is 5.
(2) The tens digit of 1,000m is 5.

OA is B.
I am unable to understand the question.

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 19, 2015 10:40 pm

mclark30: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Jun 19, 2015 10:13 pm

by mclark30 » Fri Jun 19, 2015 10:55 pm

Hi tapanmittal,

1000m will look like this;

5 _ . _ _ (the blank spaces represent digits that we don't know)

If we then divide by 1000, we'll get m;

_ _ . _ 5 (decimal moves 3 places to the left)

Therefore the hundredths digit of m is 5.

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Fri Jun 19, 2015 11:13 pm

tapanmittal wrote:What is the hundreths digit of the decimal m?
(1) The tenths digit of 100m is 5.
(2) The tens digit of 1,000m is 5.

OA is B.
I am unable to understand the question.

Lets say m = 0.1234
the hundreths digit of m = 2

1)
100 x 0.1234 = 12.34
The tenth digit = 3 and is not equal to the hundreths digit of m which is 2

2)
1000 x 0.1234 = 123.4
The tens digit = 2 which is equal to the hundreths digit of m which is 2
Therefore statement is sufficient

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jun 20, 2015 2:19 am

tapanmittal wrote:What is the hundreths digit of the decimal m?
(1) The tenths digit of 100m is 5.
(2) The tens digit of 1,000m is 5.

Statement 1: The tenths digit of 100m is 5.
Case 1: 100m = 0.5
Here, m = 0.005.
In this case, the hundredth digit of m is 0.

Case 2: 100m = 1.5
Here, m = 0.015.
In this case, the hundredth digit of m is 1.

Since the hundredth digit can be different values, INSUFFICIENT.

Statement 2: The tens digit of 1,000m is 5.
Case 3: 1000m = 50
Here, m = 0.05.
In this case, the hundredth digit of m is 5.

Case 4: 1000m = 152
Here, m = 0.152.
In this case, the hundredth digit of m is 5.

As Cases 3 and 4 illustrate, Statement 2 implies that the hundredth digit of m will always be 5.
SUFFICIENT.

The correct answer is 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 » Sat Jun 20, 2015 8:57 am

Here are a few similar questions to practice with:
- https://www.beatthegmat.com/hundredth-digit-t280191.html
- https://www.beatthegmat.com/digit-ds-que ... 80317.html
- https://www.beatthegmat.com/decimal-ques ... 37999.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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