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If n is an integer, what is the remainder when n is divided [#permalink]
 31 May 2009, 10:07
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If n is an integer, what is the remainder when n is divided by 7?
(1) n+1 is divisible by 7
(2) n+8 is divisible by 7
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Question: what is the remainder when n is divided by 7 ?
(1) if n+1 has a remainder of 0 when divided by 7, then, if positive, n has a remainder of six, but, if negative, it has a remainder of one. insufficient
(2) if n+8 has a remainder of 0 when divided by 7, the same discrepancy between negative and positive numbers occurs. insufficient.
(1+2) if n+8 and n+1 have remainders of 0, then if n is positive, n still has a remainder of six, and, negative, n still has a remainder of one. Either is possible. insufficient.
The answer, therefore, is E.
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Agree,
If N = 13, Remainder = 6
If N = -15, Remainder = -1
Therefore, Insufficient.
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IMO E. Nice expln dk94588.
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vcbabu wrote: If n is an integer, what is the remainder when n is divided by 7?
1) n+1 is divisible by 7
2) n+8 is divisible by 7 D. Reminder(s) can never be negative but is(are) always: 0 <= r =< 7. Lets say n = ax + r, where a = 7, x is quotient, and r is reminder. Or, n = 7x + r Then in each case above, r = 6. 1) If n = 7x + r, n+1 = (7x+r) + 1. If so, r must be 6. Suff............ If "n= 7x + r" is -ve, x has to be -ve. Then n +1 = (7x + r) + 1 If suppose x = -1, n+1 = 7(-1) + r + 1 = -6+r. What has to be r to have (n+1) divisible by 7? r = +6. Somebody might say -1 but remember r can never be -ve. So what is the minimum r can be 6 because r must be >0 but smaller than 7. 2) If n = 7x + r, n+8 = (7x+r) + 8. Or, n+8 = 7(x+1) + r +1 Now the equation is similar to the eq. in 1. Therefore r = 6 again. Suff................ So d.
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yes but even if the remainder is always positive, but either expression could make the remainder either 1 or 6. n is not necessarily always positive, and if n+1 is divisible by 7, n could easily be -50 or 48, giving you two different remainders, whether they are 1<= r <= 7 .
Still say E.
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dk94588 wrote: yes but even if the remainder is always positive, but either expression could make the remainder either 1 or 6. n is not necessarily always positive, and if n+1 is divisible by 7, n could easily be -50 or 48, giving you two different remainders, whether they are 1<= r <= 7 .
Still say E. Still D even if n = -50 or 48 because r = 6 in either case. n +1 = 7(-8) + (r + 1) where (r+1) = 7 or r = 6. n +1 = -56 + 7 n = -49-1 = -50 Simple logic, if n+1 is divided by 7 leaves reminder 0, then n/7 must have 6 reminder no matter n is +ve or -ve..
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D Question: (N/7 remainder)? (1) (N+1)/7 = X, where X is any integer N+1=7X N = 7X-1 = 7(X-1)+7-1 = 7(X-1) + 6 Remainder of 6. (2) Same thing as 2, (N+8)/7 = X, where X is any integer N+8=7X N = 7X-8 = 7X - 7 - 1 = 7(X-1) - 1 = 7X - 1 (same as A) Final Answer, D.
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Although there is a better method, my Finding The Pattern method-- when in doubt, FTP!!!!!!!! Because there is always a pattern. Question: (N/7 remainder?) (1)N+1 is divisible by 7 N=6,13,20,27,34,... Question=6,6,6,6,6,...... Sufficient (2)N+8 is divisible by 7 N=6,13,20,27,34,... Question=6,6,6,6,6... Sufficient General rule of thumb generate the possible values and check the remainder really fast... if it changes insufficient, otherwise sufficient.
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Agree with Hades, D is the answer.
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Agree with GMAT Tiger
Answer is D
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I obviously need to brush up on division skills I guess.
pls explain how -50/7 has a remainder 6.
wouldn't it be -7 Remainder 1, because it divides seven times and has a remainder of 1, or would it be -8 Remainder 6, since it divides 8 times (-56) and has a positive 6 remainder?
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Generally a remainder has to be between 0 & what you're dividing by--it can be negative, but you can always convert it to a positive integer. So as a rule of thumb on the GMAT, work with positive remainders. If you do get a negative remainder you can always convert it to a positive one. For example, what's the remainder when -83 is divided by -3? -83 = -3*(27) - 2 or -83 = -3*(28) + 1 The remainder is -2 or 1.
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dk94588 wrote: I obviously need to brush up on division skills I guess.
pls explain how -50/7 has a remainder 6.
wouldn't it be -7 Remainder 1, because it divides seven times and has a remainder of 1, or would it be -8 Remainder 6, since it divides 8 times (-56) and has a positive 6 remainder? pls explain how -50/7 has a remainder 6. Q & R are integers -50/7 = 7*(-6) - 8 -50/7 = 7*(-7) - 1 -50/7 = 7*(-8) + 6 -50/7 = 7*(-9) + 13 But generally we want the remainder to be 0<=R<7, so we'd go with remainder of 6.
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so in data sufficiency problems, we do assume that the remainder is the lowest possible positive integer?
because if it could be -1 then it would be insufficient
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Hades wrote: Generally a remainder has to be between 0 & what you're dividing by--it can be negative, but you can always convert it to a positive integer. So as a rule of thumb on the GMAT, work with positive remainders.
If you do get a negative remainder you can always convert it to a positive one.
For example, what's the remainder when -83 is divided by -3?
-83 = -3*(27) - 2
or
-83 = -3*(28) + 1
The remainder is -2 or 1. Does the OG has this rule in it ?
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goldeneagle94 wrote: Hades wrote: Generally a remainder has to be between 0 & what you're dividing by--it can be negative, but you can always convert it to a positive integer. So as a rule of thumb on the GMAT, work with positive remainders.
If you do get a negative remainder you can always convert it to a positive one.
For example, what's the remainder when -83 is divided by -3?
-83 = -3*(27) - 2
or
-83 = -3*(28) + 1
The remainder is -2 or 1. Does the OG has this rule in it ? I just checked, it doesn't look like it's in the Quant review. I've never seen a remainder question where you're given negative numbers...
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Hades wrote: goldeneagle94 wrote: Hades wrote: Generally a remainder has to be between 0 & what you're dividing by--it can be negative, but you can always convert it to a positive integer. So as a rule of thumb on the GMAT, work with positive remainders.
If you do get a negative remainder you can always convert it to a positive one.
For example, what's the remainder when -83 is divided by -3?
-83 = -3*(27) - 2
or
-83 = -3*(28) + 1
The remainder is -2 or 1. Does the OG has this rule in it ? I just checked, it doesn't look like it's in the Quant review. I've never seen a remainder question where you're given negative numbers... There is one PS question, I guess, discussed on the forum but I do not remember whether it is from OG. I could not find it.  .
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Hades wrote: D
Question: (N/7 remainder)?
(1) (N+1)/7 = X, where X is any integer
N+1=7X
N = 7X-1 = 7(X-1)+7-1 = 7(X-1) + 6
Remainder of 6.
(2) Same thing as 2,
(N+8)/7 = X, where X is any integer
N+8=7X
N = 7X-8 = 7X - 7 - 1 = 7(X-1) - 1 = 7X - 1 (same as A)
Final Answer, D. interesting approach
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Good guestion..
Agree the answer is D..
n+1 and n+8 will leave the same remainder when divided by 7..
and if n+1 is evenly divided by 7, then the n will defnitely remain a remainder of 6 i.e falling short of 1.
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close
