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General rule certain interval.

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by lenagmat » Wed Oct 26, 2011 5:00 am
If n is a positive integer between 30 and 60, inclusive, what is the value of n?
(1) When n is divided by 4, the remainder is 1.
(2) When n is divided by 5, the remainder is 2.

Answer: E

Here my solution. Please, could you help me where exactly I am wrong because I have answer C ?
Step by step:

1. N=4a+1
2. N=5b+2
3. a=(5b+1)/4
4. b=3, a=4
5. N=4*4+1=17
6. Now the General rule:
X=20c+17 by formula
7. 30=<20c+17<=60
8. 0....=<c<=20....
it means N=17, is ok for this interval.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Oct 26, 2011 5:37 am
lenagmat wrote:If n is a positive integer between 30 and 60, inclusive, what is the value of n?
(1) When n is divided by 4, the remainder is 1.
(2) When n is divided by 5, the remainder is 2.

Answer: E

Here my solution. Please, could you help me where exactly I am wrong because I have answer C ?
Step by step:

1. N=4a+1
2. N=5b+2
3. a=(5b+1)/4
4. b=3, a=4 - this is 1 solution. There are more: (b=7, a=9) and (b=11, a=14) etc.
5. N=4*4+1=17 - we are told that n is between 30 and 60 inclusive
6. Now the General rule:
X=20c+17 by formula
7. 30=<20c+17<=60
8. 0....=<c<=20....
it means N=17, is ok for this interval.
My comments above.

Cheers,
Brent
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by Brent@GMATPrepNow » Wed Oct 26, 2011 5:46 am
lenagmat wrote:If n is a positive integer between 30 and 60, inclusive, what is the value of n?
(1) When n is divided by 4, the remainder is 1.
(2) When n is divided by 5, the remainder is 2.
Given the small range of possible values for n, it might be easiest to list possible values here.
Rule: If K divided by D leaves remainder R, then the possible values of K are: R, R+D, R+2D, R+3D, ... (assuming K, D and R are positive integers)

Statement 1: When n is divided by 4, the remainder is 1.
Possible values of n (within the given range): 33, 37, 41, 45, 49, 53, 57
Insufficient

Statement 2: When n is divided by 5, the remainder is 2.
Possible values of n (within the given range): 32, 37, 42, 47, 52, 57
Insufficient

Statements 1 & 2:
From statement 1, the possible values of n are: 33, 37, 41, 45, 49, 53, 57
From statement 2, the possible values of n are: 32, 37, 42, 47, 52, 57
Since n can equal 37 or 57, the combined statements are still insufficient.
Answer: E

Cheers,
Brent
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by neelgandham » Wed Oct 26, 2011 5:53 am
lenagmat wrote:If n is a positive integer between 30 and 60, inclusive, what is the value of n?
(1) When n is divided by 4, the remainder is 1.
(2) When n is divided by 5, the remainder is 2.

Answer: E

Here my solution. Please, could you help me where exactly I am wrong because I have answer C ?
Step by step:

1. N=4a+1
2. N=5b+2
3. a=(5b+1)/4
4. b=3, a=4
5. N=4*4+1=17
6. Now the General rule:
X=20c+17 by formula
7. 30=<20c+17<=60
8. 0....=<c<=20....
it means N=17, is ok for this interval.
From the statement marked bold above 30=<20c+17<=60 ,
if c = 1, 30<=37<=60, satisfies the inequality
if c = 2,30<=57<=60, satisfies the inequality.
i.e both 37 and 57 satisfy the given two conditions. Hence E !

My Approach

(1)When n is divided by 4, the remainder is 1.
n can be 33,37,41,45,49,53,57 - Insufficient

(2)When n is divided by 5, the remainder is 2.
n can be 32,37,42,47,52,57 - Insufficient

1 and 2
37 and 57 both satisfy the conditions ! Hence E
Anil Gandham
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by user123321 » Wed Oct 26, 2011 6:13 am
lenagmat wrote:If n is a positive integer between 30 and 60, inclusive, what is the value of n?
(1) When n is divided by 4, the remainder is 1.
(2) When n is divided by 5, the remainder is 2.

Answer: E

Here my solution. Please, could you help me where exactly I am wrong because I have answer C ?
Step by step:

1. N=4a+1
2. N=5b+2
3. a=(5b+1)/4
4. b=3, a=4
5. N=4*4+1=17
6. Now the General rule:
X=20c+17 by formula
7. 30=<20c+17<=60
8. 0....=<c<=20....
it means N=17, is ok for this interval.
clearly A & B are not proper choices as you already found out.
But when
n=4a + 1 &
n=5b + 2
then it should be of the form...n=20k + 17
so we get 37 & 57 between the range provided then E should be the answer

user123321
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