Problem Solving

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

[x] is the greatest integer less than or equal x, what is the value of [√30]+[√40]+[√50]?

A. 12
B. 15
C. 16
D. 18
E. 20

GIVEN: [x] is the greatest integer less than or equal x
For example, [3.2] = 3, since 3 is the greatest integer that is less than (or equal) to 3.2
Likewise, [8.7] = 8, since 8 is the greatest integer that is less than (or equal to) 8.7

Now onto the question....
√25 = 5
√36 = 6
√49= 7
√64 = 8

Since √30 is BETWEEN √25 (aka 5) and √36 (aka 6), we know that √30 = 5.something
So, [√30] = 5

Since √40 is BETWEEN √36 (aka 6) and √49 (aka 6), we know that √40 = 6.something
So, [√40] = 6

Since √50 is BETWEEN √49 (aka 7) and √64 (aka 8), we know that √50 = 7.something
So, [√50] = 7

So, [√30]+[√40]+[√50] = 5 + 6 + 7 = 18

Answer: D

Cheers,
Brent

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

[x] is the greatest integer less than or equal x, what is the value of [√30]+[√40]+[√50]?

A. 12
B. 15
C. 16
D. 18
E. 20

√30 is about 5.4, so [√30] = 5.

√40 is about 6.3, so [√40] = 6.

√50 is about 7.1, so [√50] = 7.

Thus, [√30]+[√40]+[√50] = 5 + 6 + 7 = 18.

Alternate Solution:

The greatest integer whose square is less than 30 is 5 (because 5^2 = 25, but 6^2 = 36 > 30). Therefore, [√30] = 5.

Similarly, the greatest integer whose square is less than 40 is 6 and greatest integer whose square is less than 50 is 7; therefore [√40] = 6 and [√50] = 7.

Thus, [√30]+[√40]+[√50] = 5 + 6 + 7 = 18.

Answer: D