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Seven different numbers are selected from the integers 1 to

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Seven different numbers are selected from the integers 1 to

by mitzwillrockgmat » Thu May 20, 2010 7:42 am
Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?

(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Can someone please explain why stat 1 doesnt work? Thanks! :)
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by liferocks » Thu May 20, 2010 7:47 am
when any number is divided by 7 reminder can be 0,1,2,3,4,5,6

From 1,
range is 6 that mean in the set of reminders 0 and 6 is present ..but others can be any number from 0 to 6..not sufficient

From 2

only possibility of the reminders is 0,1,2,3,4,5,6..sufficient

Ans option B
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by mitzwillrockgmat » Thu May 20, 2010 7:57 am
liferocks wrote:when any number is divided by 7 reminder can be 0,1,2,3,4,5,6

From 1,
range is 6 that mean in the set of reminders 0 and 6 is present ..but others can be any number from 0 to 6..not sufficient

From 2

only possibility of the reminders is 0,1,2,3,4,5,6..sufficient

Ans option B
sorry i dont understand! :(

range = highest no - lowest no. hence, the highest value in the set can be let's say 36 & the lowest hence will have to be 30 for range to be 6. therefore, the no.s in the set are 36,35,34,33,32,31 & 30. all of these divided by 7 give remainders; 1,0,6,5,4,3,2. sum is 21.

can you show me a set that doesnt equal 21 & has range 6??

thanks!
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by indiantiger » Thu May 20, 2010 7:58 am
set of numbers is between 1 to 100

need to find the sum of remainders : ?
Statement 1. range of seven remainders is 6

lets try to find 6 numbers that we divide by 7, these can be

case 1 : 14,28,33,35,42,49,77

for all above except 33 remainder is 0 and for 33 remainder is 6 sum of remainders is 6

case 2 : 4,28,33,35,42,48,77

for all above remainder is zero except 48 and 33, which a remainder 6

sum is 6+6 = 12

Statement 2: The seven numbers selected are consecutive integers.

You can take any 7 consecutive numbers (for the given set) and they will have the following remainders
0,1,2,3,4,56

Lets check for 46,47,48,49,50,51,52.
remainders as follows : 4,5,6,0,1,2,3

Hence (B)
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by mitzwillrockgmat » Thu May 20, 2010 8:01 am
indiantiger wrote:set of numbers is between 1 to 100

need to find the sum of remainders : ?
Statement 1. range of seven remainders is 6

lets try to find 6 numbers that we divide by 7, these can be

case 1 : 14,28,33,35,42,49,77

for all above except 33 remainder is 0 and for 33 remainder is 6 sum of remainders is 6

case 2 : 4,28,33,35,42,48,77

for all above remainder is zero except 48 and 33, which a remainder 6

sum is 6+6 = 12

Statement 2: The seven numbers selected are consecutive integers.

You can take any 7 consecutive numbers (for the given set) and they will have the following remainders
0,1,2,3,4,56

Lets check for 46,47,48,49,50,51,52.
remainders as follows : 4,5,6,0,1,2,3

Hence (B)
oh oh just got it! i kept reading the range of the numbers rather than the range of the REMIANDERS!! ugghh :s

thanks very much for the replies! :)
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by liferocks » Thu May 20, 2010 8:02 am
mitzwillrockgmat wrote:
liferocks wrote:when any number is divided by 7 reminder can be 0,1,2,3,4,5,6

From 1,
range is 6 that mean in the set of reminders 0 and 6 is present ..but others can be any number from 0 to 6..not sufficient

From 2

only possibility of the reminders is 0,1,2,3,4,5,6..sufficient

Ans option B
sorry i dont understand! :(

range = highest no - lowest no. hence, the highest value in the set can be let's say 36 & the lowest hence will have to be 30 for range to be 6. therefore, the no.s in the set are 36,35,34,33,32,31 & 30. all of these divided by 7 give remainders; 1,0,6,5,4,3,2. sum is 21.

can you show me a set that doesnt equal 21 & has range 6??

thanks!
option 1 says The range of the seven remainders is 6..the bold part is imp..it does not say that The range of the seven number is 6
Hope this will clarify the doubt
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