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# SQUARE of any two digit number - shortcut

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Manager
Joined: 19 Apr 2011
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Re: SQUARE of any two digit number - shortcut [#permalink]

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01 Jun 2011, 06:05
Good tip thanks for sharing

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Manager
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Re: SQUARE of any two digit number - shortcut [#permalink]

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01 Jun 2011, 14:29
Can you please explain how you 16+2 and 9+3?

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Intern
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Re: SQUARE of any two digit number - shortcut [#permalink]

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01 Jun 2011, 20:54
bellcurve wrote:
Can you please explain how you 16+2 and 9+3?

Thanks mate for pointing, that is a wrong line. SOme typo there. Please exclude that line

9 | 16 + 2 |5 -- this is wrong (typo)

9 + 3 | 2 |5 - correct

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Manager
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Re: SQUARE of any two digit number - shortcut [#permalink]

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02 Jun 2011, 06:02
This is a pretty cool trick. Thanks!

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Manager
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Re: SQUARE of any two digit number - shortcut [#permalink]

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02 Jun 2011, 21:35
explain it for 29 pls
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Manager
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Re: SQUARE of any two digit number - shortcut [#permalink]

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11 Jun 2011, 09:15
Numbers ending in 5 have a defined rule to square.
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GMAT Tutor
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Re: SQUARE of any two digit number - shortcut [#permalink]

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11 Jun 2011, 09:29
1
KUDOS
Expert's post
arryputtar wrote:

29^2 how to solve this ?

Step 1: Identify the digits

29 - lets say "2" as "a" and "9" as b
So 2-> a and 9-> b

Step 2: Plug into the equation below
a^2 | 2(a*b) | b^2

instead of a -> use 2 and instead of b-> use 9

Step 3:

So by plugging in we get
2^2 | 2(2*9) | 9^2

Step 4:
solve the thing

2^2 => 4
2(2*9) => 36
9^2 => 81

4 | 36 | 81

Step 5:
this is the kewlest thing....all you need to do is carry over from right to left

4| 36 | 81 -> carry over 8 (left most digit just like addition)
4| 36 + 8 | 1 => 44 | 1
now from 44 carry over 4
4 + 4 | 4 | 1

8 | 4 |1 => 29 ^ 2 => 841

Fortunately we rarely (probably never) need to square awkward large numbers on the GMAT. If I need to find the value of 29^2, I'd take advantage of the difference of squares:

29^2 - 1 = (29 + 1)(29 -1) = (30)(28) = 840

so 29^2 = 841.

This would be a fast approach for a number ending in 9 or 1; for other numbers it would still lead to an awkward calculation.
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Re: SQUARE of any two digit number - shortcut   [#permalink] 11 Jun 2011, 09:29
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