BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

f(x) denotes the number of positive integers less than or equal

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

f(x) denotes the number of positive integers less than or equal

by Max@Math Revolution » Wed Feb 19, 2020 1:11 am
[GMAT math practice question]

f(x) denotes the number of positive integers less than or equal to \(\sqrt{x}\) . What is f(1) + f(2) + f(3) +…+ f(50)?

A. 131
B. 217
C. 228
D. 307
E. 339
Top
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: f(x) denotes the number of positive integers less than or equal

by Max@Math Revolution » Fri Feb 21, 2020 12:41 am
=>

Since 1 < √2 < √3 < 2, we have f(1) = f(2) = f(3) = 1.
Since 2 < √5 < √6 < √7 < √8 < 3, we have f(4) = f(5) = … = f(8) = 2.
Since 3 < √10 < √11 < √12 < … < √15 < 4, we have f(9) = f(10) = … = f(15) = 3.
Since 4 < √17 < √18 < √19 < … < √24 < 5, we have f(16) = f(17) = … = f(24) = 4.
Since 5 < √26 < √27 < √28 < … < √35 < 6, we have f(25) = f(26) = … = f(35) = 5.
Since 6 < √37 < √38 < √39 < … < √48 < 7, we have f(36) = f(37) = … = f(48) = 6.
Since 7 < √50, we have f(49) = f(50) = 7.

Then, f(1) + f(2) + f(3) + … + f(50) = 1*3 + 2*5 + 3*7 + 4*9 + 5*11 + 6*13 + 7*2 = 3 + 10 + 21 + 36 + 55 + 78 + 14 = 217.

Therefore, B is the answer.
Answer: B
Top
Post new topic Post Reply
• Page 1 of 1