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## cube of decimal number

samarthkansal Newbie | Next Rank: 10 Posts
Joined
28 Apr 2014
Posted:
1 messages

#### cube of decimal number

Mon Apr 28, 2014 11:58 am
can anyone please tell me how to find the the answer of (1.04)*(1.04)*(1.04)= ? with shortcut method...

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Apr 28, 2014 12:41 pm
Hi samarthkansal,

This is the Verbal Sub-Forum; you might try posting this in the Math Sub-Forum.

As it stands, the GMAT is unlikely to ask you to perform this type of calculation, so you might consider some alternative approaches (estimation, using the answer choices, etc.) to just doing the math.

GMAT assassins aren't born, they're made,
Rich

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sukriti2hats Junior | Next Rank: 30 Posts
Joined
30 May 2014
Posted:
20 messages
1
Sat May 31, 2014 4:17 am
Hi samarthkansal,

One shortcut of finding (1.03)^3 is by using binomial theorem. In binomial expansion of (1+x)^n

(1+x)ⁿ = 1 + n·x/1! + n(n-1)x²/2! + n(n-1)(n-2)x³/3! + . . . + n(n-1)...(n-k+1)xⁿ/n! + . . . But in this question a simple approximation can be used, (1+ x)^n is approximately equal to 1 + nx.
In this case we can take x=0.04 and n=3 so (1.04)^3=(1 + 0.04)^3 this will approximately be equal to 1+ 3*0.04 = 1+0.12 =1.12

Another method is that, u can split 1.04 into (1 +0.04) and apply the identity of (a+b)^3
The identity : (a+b)^3= a^3 + b^3 + 3ba^2 + 3ab^2 with a=1 and b=0.04

There are many more ways like u can just figure out the last digit of the cube and then eliminate the options one by one. However such type of questions may not be very likely in GMAT.

Regards
Sukriti

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