Decimals

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sat Nov 12, 2011 3:52 am

If 0.0abababab.... = 2/55, then what is the value of a*b?

A) 10
B) 18
C) 27
D) 36
E) 42

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Source: Beat The GMAT — Problem Solving | Sat Nov 12, 2011 3:52 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Nov 12, 2011 4:04 am

shankar.ashwin wrote:If 0.0abababab.... = 2/55, then what is the value of a*b?

2/55 = (2000/55)/1000

Now, 2000/55 = 400/11 = 36.36...
Hence, 2/55 = (36.36...)/1000 = 0.03636...

Comparing this with the expression given, a = 3 and b = 6

Therefore, a*b = 3*6 = 18
[spoiler]
The correct answer is B.[/spoiler]

Last edited by Anurag@Gurome on Sat Nov 12, 2011 4:36 am, edited 1 time in total.

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by Anurag@Gurome » Sat Nov 12, 2011 4:08 am

Another Approach:
If someone is fast enough to do the division and see the pattern they can go for the traditional approach of attacking recurring decimal problems.

--> 0.0abababab... = 2/55
--> 10*(0.0abababab...) = 0.abababab... = 20/55 .............. (1)
--> 1000*(0.0abababab...) = ab.abababab... = 2000/55 ....... (2)

Subtracting (1) from (2), ab = 1980/55 = 36

Hence, a = 3 and b = 2
Therefore, a*b = 3*6 = 18

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sat Nov 12, 2011 4:26 am

The way i did it,

2/55 = x/100

x = 200/55 = 40/11 = 3.6363..

Wasnt sure if it was the fastest way to do it.

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Sat Nov 12, 2011 5:17 am

2/55 = 4/110 = 36/990 = 3.6/99 = 0.0363636
so 3*6 = 18

user123321

Just started my preparation

Want to do it right the first time.

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rooster: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Aug 25, 2010 12:23 am; Thanked: 6 times

by rooster » Mon Nov 14, 2011 2:56 am

2/55= 0.036

We know the pattern is .0ababababa....

Thus we already know. multiply 3*6 and presto!

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Mon Nov 14, 2011 7:22 am

shankar.ashwin wrote:If 0.0abababab.... = 2/55, then what is the value of a*b?

A) 10
B) 18
C) 27
D) 36
E) 42

2/55 => 2/( 5 * 11 )

2/5 = 0.4

Again we have 0.4/11

We know 1/11 => 0.09090909.....{ We can memorize some key reciprocals till 1/20 for quicker calculations}

So, 0.4/11 => 0.09090909..... * 0.4 => 0.036363636363636.....

Here a = 3 and b = 6

So , a * b => 3 * 6 = 18...

Abhishek

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