1001 claims

Algebra Level 1

A boy claims that he can multiply any three digit no. by 1001 instantly. If his friend said "715", he'd say the answer immediately. Compute the answer and justify.

Credit-" Algebra " by I. M. Gelfand and A. Shen

no clue 715001, 'cause he is fast at multiplication 71634,' cause multiplication with 1001 is easy 715715, 'cause he is first multiplying by 1000 and then by one and adding it together

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3 solutions

If we multiply an n n digit number a a by 1 0 n 10^n , we get n n zeros to the right of that number. When we add that number with the product, we get a number of the form a a \overline {aa} . So, by multiplying an n n digit number a a with 1 0 n + 1 10^n+1 , we get the number a a \overline {aa} . In this example, by multiplying 715 715 with 1001 1001 we get 715715 715715 .

Awesome way of tackling the problem

Nethra Ramakrishnan - 1 year ago

Since '715' is the friend's answer - we will assume that 715 is the number.

So 715 1001 715 * 1001 = 715 1000 715 * 1000 + 715 1 715 * 1 = 715715 715715 . Therefore (715715, 'cause he is first multiplying by 1000 and then by one and adding it together.) is the answer.

oof this hard

Vishal S - 12 months ago

Well it was easy what you have to do it just muplitpy 1001 times 715 or do the divsion way 715715 divdie by 715

https://brilliant.org/problems/do-you-really-know-about-bacteriophage/

OOFMATION ANIMATION - 1 year ago

there's got to be an easier explanation

Nethra Ramakrishnan - 1 year ago

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thats great

OOFMATION ANIMATION - 1 year ago

well the easy way i found it just do 1001 times 715 math not my stuff i more as science and social studies

OOFMATION ANIMATION - 1 year ago

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