Can you square 97 in 5 seconds and 989 in 5 seconds? ONLY 5

Question

just 10 seconds

1)9519-885691 2)9409-978121 3)9849-744121 4)9939-432111 5)9479-834871

BenchPrepGURU · Answer

Yep. It's an old school trick:
97^2 = (100 - 3)^2 = 10,000 - 2(3)(100) + 9 = 10,000 - 600 + 9 = 9,409
989^2 = (1,000 - 11)^2 = 1,000,000 - 2(11)(1,000) + 121 = 1,000,000 - 22,000 + 121 = 978,121

BenchPrepGURU

pike · Answer

Yes, this was my method as well, but I certainly couldn't do all that in 5 seconds.

varunmaheshwari · Answer

I even tried the same method.. :-D

Can square 97 in 5 seconds but guess 989 may take 10 to 15 secs.. :lol:

saeedt · Answer

BenchPrepGURU you are rather right but some calculations you did are unncessary, making it more than 5 seconds to solve.

Look, for 97 square, we have a -3 difference to the base right? apply that -3 to 97. It makes up the first two digits of the answer, which is 94. Then just square that difference, -3, to earn 9 . Now, because our base had two zeros, we should put a 0 before 9 to have a two-digit number as well. The only thing left to do is to put that 09 beside 49. So, you saw no need to all that 600 and 10,000 you did.

Now imagine we are squaring 92. 
1) the difference is -8.
2) Apply that -8 to the original number to earn the first two digits: 84
3) Now square that difference and just put it to the right side of 84: 84 64 
* because 64 is two digit (equal to number of zeros in our base, no addition of 0 is required)

Now what about 989. varunmaheshwari you can solve it in 5 seconds with the same method provided that you know the square of 11 to 20, which we are expected to know for GMAT.

1) the difference is -11. The base obviously is 1000 here. The base number of digits correspond to the number of digits in our original number.

2) Apply that -11 to the original number to earn the first three digits: 978

3) square the difference to earn 121 and put that on the right side of 978 to reach the final answer,  978121

Lets do it with 991, too.

1) difference is -9
2) the 3 first digits are therefore 982
3) square of -9 is 81, which after adding a 0 must be put on the right side of 982 to make the total of 982081

I think this method is great and reduces at least 10 seconds compared to BenchPrepGURU's method and about 30 seconds compared to the novice method of multiplying a three digit number by the same three digit number to get the square, disregarding the more error probability in those methods.

Can you square 97 in 5 seconds and 989 in 5 seconds? ONLY 5

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