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21 Feb 2020, 05:57
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C
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Difficulty:
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73% (03:01) correct
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If [x] is the greatest integer less than or equal to x, what is the value of [√1] + [√2] + [√3] + … + [√49] + [√50] ?
A. 187
B. 189
C. 217
D. 287
E. 317
Are You Up For the Challenge: 700 Level Questions
A. 187
B. 189
C. 217
D. 287
E. 317
Are You Up For the Challenge: 700 Level Questions
QuabityAssurance
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Schools: McCombs '23 (D) Foster '24 (II) Darden '24 (D) Goizueta '24 (I) Jones Tuck '24 (S) Tepper '24 (S)
GRE 1: Q166 V159
GRE 2: Q165 V156
GRE 3: Q166 V159
Posts: 693
21 Feb 2020, 06:14
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Greatest Integer Function denotes that one has to procedd on the left side of the number line where the nearest integer is.
For eg. root(2) =1.41 , and thus the nearest integer on left hand side of 1.41 is 1 which means GIF[root2] is 1
1=1
So from 2 till 4 GIF , would be 1 so 2*1 =2
From 4 till 8 GIF would be 2 , so 5*2 =10
From 9 till 15 , GIF would be 3 , so 7*3 =21
From 16 til 24 , GIF would be 4 so 9*4=36
From 25 till 35 , 11*5 =55
From 36 till 48 , 13*6= 78
From 49 till 50 , 2*7=14
1+2+10+21+36+55+78+14= 217
For eg. root(2) =1.41 , and thus the nearest integer on left hand side of 1.41 is 1 which means GIF[root2] is 1
1=1
So from 2 till 4 GIF , would be 1 so 2*1 =2
From 4 till 8 GIF would be 2 , so 5*2 =10
From 9 till 15 , GIF would be 3 , so 7*3 =21
From 16 til 24 , GIF would be 4 so 9*4=36
From 25 till 35 , 11*5 =55
From 36 till 48 , 13*6= 78
From 49 till 50 , 2*7=14
1+2+10+21+36+55+78+14= 217
General Discussion
21 Feb 2020, 07:14
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The greatest integer function [] returns the largest integer less than or equal to x. In essence, it rounds down a real number to the nearest integer. Also, if x is an integer, [x]= x
[√1] = 1
[√2] = [1.414] = 1
[√3] = [1.732] = 1
[√4] = [2] = 2
hence we need to check the perect square from 1 to 50. for perfect square [n^2] = n and for (n-1)^2<x<n^2 , [x]= n-1
Perfect squares less than 50 are
1 [1]=1, for x= 1,2,3 [x]= 1
: sum of [x] from x = 1 to 3 = 3*1 = 3
4, for x = 4 to 8, [x] = 2
sum of [x] from x = 4 to 8 = 5*2 = 10
9, for x = 9 to 15, [x] =3
sum of [x] from x = 9 to 15 = 3*7 = 21
16, x = for 16 to 24, [x] = 4
sum of [x] from x = 16 to 24 = 4*9 = 36
25, x = for 25 to 35, [x] = 5
sum of [x] from x = 25 to 35 = 5*11 = 55
36, for x = 36 to 48, [x] = 6
sum of [x] from x = 36 to 48 = 6*13 = 78
49, for x = 49 & 50, [x] =7
sum of [x] from x =49 to 50 = 2*7 = 14
total sum = 217
Answer = C
Bunuel
