The Counting School

[dtweah]

Which range of numbers, including the end values, has the greatest sum?

(a) 100 to 179
(b) 200 to 259
(c) 300 to 339
(d) 400 to 429
(e) 500 to 519

[m&m]

sum is avg * num terms

(a) 100 to 179
S = 139*80

(b) 200 to 259
S=230*60

(c) 300 to 339
S=319*40

(d) 400 to 429
S=414*30

(e) 500 to 519
S=509*20


note that
80 = 2*40 --> a< c
60 = 2*30 --> d< b
40 = 2*20 --> e< c

so compare b and c only --> c>b

answer is C

[avenus]

sum is avg * num terms

(a) 100 to 179
S = 139*80

(b) 200 to 259
S=230*60

(c) 300 to 339
S=319*40

(d) 400 to 429
S=414*30

(e) 500 to 519
S=509*20


note that
80 = 2*40 --> a< c
60 = 2*30 --> d< b
40 = 2*20 --> e< c

so compare b and c only --> c>b

answer is C

c < b

answer is B

[Pranay]

sum is avg * num terms

(a) 100 to 179
S = 139*80

(b) 200 to 259
S=230*60

(c) 300 to 339
S=319*40

(d) 400 to 429
S=414*30

(e) 500 to 519
S=509*20


note that
80 = 2*40 --> a< c
60 = 2*30 --> d< b
40 = 2*20 --> e< c

so compare b and c only --> c>b

answer is C

c < b

answer is B

I agree with Avenues

Another way of solving the problem ..

Evaluate options,

A -> 100 + 101 + ... + 179 => 100*80 + 1 + 2 + 3 ........ 79
B -> 200*60 + 1 + 2 + 3 + ......... + 59
c -> 300*40 + 1 + 2 + 3 + .... 39
D -> 400*30 + 1 + 2 + 3 + ......... 29
E -> 500*20 + 1 + 2 + 3 + ..... 19.

By looking at the options, straight away you can eliminate, A and E.

Now among B,C and D,

CLearly, B has the highest numbers.

Thus B is the answer.

Hope it helps.