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What is [2.45 + 1/100] + [2.45 + 2/100] +….+ [2.45 + 99/100] + [2.45 + 100/100]? ([x] means the greatest inte

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What is [2.45 + 1/100] + [2.45 + 2/100] +….+ [2.45 + 99/100] + [2.45 + 100/100]? ([x] means the greatest inte

by Max@Math Revolution » Wed Jan 29, 2020 11:43 pm

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[GMAT math practice question]

What is [2.45 + 1/100] + [2.45 + 2/100] +….+ [2.45 + 99/100] + [2.45 + 100/100]? ([x] means the greatest integer less than or equal to x)

A. 233
B. 242
C. 246
D. 254
E. 256
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Re: What is [2.45 + 1/100] + [2.45 + 2/100] +….+ [2.45 + 99/100] + [2.45 + 100/100]? ([x] means the greatest inte

by Max@Math Revolution » Sun Feb 02, 2020 6:22 pm
=>

Since 2 ≤ 2.45 + 1/100 < 3, we have [2.45 + 1/100] = 2.
Since 2 ≤ 2.45 + 2/100 < 3, we have [2.45 + 2/100] = 2.
…
Since 2 ≤ 2.45 + 54/100 < 3, we have [2.45 + 50/100] = 2.

Since 3 ≤ 2.45 + 55/100 < 4, we have [2.45 + 1/100] = 3.
Since 3 ≤ 2.45 + 56/100 < 4, we have [2.45 + 2/100] = 3.
…
Since 3 ≤ 2.45 + 100/100 < 4, we have [2.45 + 50/100] = 3.

Then, we have
[2.45 + 1/100] + [2.45 + 2/100] +….+ [2.45 + 99/100] + [2.45 + 100/100]
= ( 2 + 2 + … + 2 ) + ( 3 + 3 + … + 3 )
= 2*54 + 3*(100 - 55 + 1) = 108 + 138 = 246.

Therefore, C is the answer.
Answer: C
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Re: What is [2.45 + 1/100] + [2.45 + 2/100] +….+ [2.45 + 99/100] + [2.45 + 100/100]? ([x] means the greatest inte

by Pyunika » Tue Feb 04, 2020 1:53 am
[2.45] = 2

[2.45+x] will remain 2 as long as 2.45+x<3 thereafter it will become 3
x<0.55=55/100
[2.45+x]will remain 2 for 54 terms.
For the remaining it will be = 3

Thus, required sum
=54∗2+46∗3=108+138
= 246

Answer C
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