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# If each term in the sum A1 + A2 + .....+ An is either 7 or

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Director
Joined: 08 Jun 2007
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If each term in the sum A1 + A2 + .....+ An is either 7 or [#permalink]

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15 Dec 2007, 20:26
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If each term in the sum A1 + A2 + .....+ An is either 7 or 77 and the sum equals 350
,which of the following could be equal to n ?

A 38
B 39
C 40
D 41
E 42
CEO
Joined: 29 Mar 2007
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15 Dec 2007, 21:58
ashkrs wrote:
If each term in the sum A1 + A2 + .....+ An is either 7 or 77 and the sum equals 350
,which of the following could be equal to n ?

A 38
B 39
C 40
D 41
E 42

I get C.

Took me about 1min 30 sec, but it seems to work...

Just tried values 7*38=266 +77=343 +7

So 39*7 +77=350.

Unless Im missin somethin.
Director
Joined: 08 Jun 2007
Posts: 578
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15 Dec 2007, 22:06
GMATBLACKBELT wrote:
ashkrs wrote:
If each term in the sum A1 + A2 + .....+ An is either 7 or 77 and the sum equals 350
,which of the following could be equal to n ?

A 38
B 39
C 40
D 41
E 42

I get C.

Took me about 1min 30 sec, but it seems to work...

Just tried values 7*38=266 +77=343 +7

So 39*7 +77=350.

Unless Im missin somethin.

no u are not missin anythin....OA is C.
but how did you arrived..on 7*38=266 +77=343 +7

i tried plugging too ..but tool hell lotta time for me to put all combinations ..before i arrived at c ..just wanted to know whats the best way to do this..
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 573

Kudos [?]: 3972 [0], given: 360

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16 Dec 2007, 02:32
C.

other way.

350/7=50 but 50 is out of answer cases.

we add one 77 and exclude eleven 7, so 350=(50-11)*7+1*77 ==> n=50-11+1=40
Manager
Joined: 12 Jun 2006
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17 Dec 2007, 00:26
walker wrote:
C.

other way.

350/7=50 but 50 is out of answer cases.

we add one 77 and exclude eleven 7, so 350=(50-11)*7+1*77 ==> n=50-11+1=40
Sorry I didn't understand how you came up with the above equation? Plz elaborate
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 573

Kudos [?]: 3972 [0], given: 360

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17 Dec 2007, 00:40
lonesome307 wrote:
Sorry I didn't understand how you came up with the above equation? Plz elaborate

step 1. we can represent 350 as a sum of only 7. 350=50*7. So, we should sum 50 terms - out of answers.

step 2. we add one 77 and exclude eleven 7 to balance the sum: 350=50*7+1*77-11*7=50*39+1*77. we have 40 terms.

we had gone to the next step if 40 would not be answer.

possible step: add next 77 and exclude eleven 7 to balance question:
350=50*7+2*77-22*7=50*28+2*77. we have 30 terms.
Manager
Joined: 03 Sep 2006
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17 Dec 2007, 01:35
1
KUDOS
Late, but C:

350 = 7*50 (but we don't have such answer)
350-77 = 273 (and 273/7 = 39), so answer is 40.

walker, nice trick - noted!
17 Dec 2007, 01:35
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