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Gmat Prep divisibilty remainders

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Gmat Prep divisibilty remainders

by sdotcruz » Sat Nov 27, 2010 6:00 am
this problem is from the Gmat Prep software. I understand what is being asked, but do not know how to determine the value.


If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1. n+1 is divisible by 3

2. n>20


OA: A
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by shovan85 » Sat Nov 27, 2010 6:28 am
sdotcruz wrote: If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1. n+1 is divisible by 3

2. n>20
Option 1:

n+1 is divisible by 3

So, n+1 = 3k (k is any integer)

=> n = 3k - 1

Now, 4 + 7n

= 4 + 7(3k - 1)

= 4 + 21k - 7

= 21k - 3

for any value of k, 21k - 3 is divisible by 3. Thus r = 0. Sufficient.

Option 2: n > 20

Then 4 + 7n can be any value with n greater than 20.

When n = 21, 4 + 7n = 151. Thus remainder = 1

When n = 22, 4 + 7n = 158. Thus remainder = 2

So we do not have a concrete value of r. Thus, Not sufficient.

IMO A
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by Rahul@gurome » Sat Nov 27, 2010 6:31 am
sdotcruz wrote:If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?
1. n+1 is divisible by 3
2. n>20

OA: A
Given: When (7n + 4) is divided by 3, the remainder is r.

Statement 1: (n + 1) is divisible by 3.
Implies 7(n + 1) is divisible by 3.
=> (7n + 7) is divisible by 3.
=> (7n + 4 + 3) is divisible by 3.
=> (7n + 4) is divisible by 3.

This is because if a number x is divisible by 3, then (x - 3) will also be divisible by 3.

Thus r = 0.

Sufficient.


Statement 2: n > 20
Value of r may be 0, 1 or 2 according to the value of n.

Not sufficient.

The correct answer is B.
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by rishab1988 » Sat Nov 27, 2010 7:32 am
Here is how I approached this problem and most GMAT problems.Simplify the prompt as much as you can.

We know n is an integer and (4+7n)/3 will give a remainder r.

Lets assume n=1 11/3. Rem =2
n=2 18/3 rem=0
n=3 25/3 rem =1
n=4 32/3 rem =2
n=5 39/3 rem =0


You can see a pattern : 2,0,1,2,0,1,2... So if we know n we can find what the remainder is.

When the term is 2nd,5th,8th,11th the rem =0
When the term is 1st,4th,7th,10th the rem =2
When the term is 3rd,6th,9th the rem =1

1) n+1 divisible by 3. if n =2 .n+1 is divisible by 3. Rem @ n=2 is 0.

When n+1=6 or n =5 rem 0

n+1=9 n-> 8 rem = 0

In general you can say n->2,5,8,11,14.See it matches with value 0

Sufficient.

2) This is clearly insufficient as n could be 21,or 22,or 23 or anything.

For 21. rem =1
For 22 rem =2.

Multiple values.hence insufficient.

Answer should be A
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by rishab1988 » Sat Nov 27, 2010 7:40 am
Alternatively,you can also use this logic ; when you either add or subtract a multiple of a number X to another multiple of same number X.

Eg: 22 is a multiple of 11 right?

we also know 110 is a multiple of 11.

Add 22 to 110 .You get 132-another multiple of 11.

Subtract 22 from 110,you get 88-another multiple of 11.

Prompt "IS (4+7n)/n = integer"?

1) n+1 is a multiple of 2.

Now if subtract a multiple a multiple of 3 from another multiple of 3,the result too would be a multiple of 3 right?

Applying this (4+7n)-(n+1) = 6n+3 = 3(2n+1).

Since it has a factor of 3.We can say that it is divisible by 3.Therefore 4+7n too is.

2) n>20

use n=30 -> 4+210 = 214. Sum of digits -> 7 .remainder must be 1.
use n=40 -> 4+280 = 284 Sum of digits -> 14 .remainder must be 2.

Insufficient.

Hence A
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by tomada » Sun Nov 28, 2010 5:17 pm
FYI, you accidentally typed that the correct answer is B.

Rahul@gurome wrote:
sdotcruz wrote:If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?
1. n+1 is divisible by 3
2. n>20

OA: A
Given: When (7n + 4) is divided by 3, the remainder is r.

Statement 1: (n + 1) is divisible by 3.
Implies 7(n + 1) is divisible by 3.
=> (7n + 7) is divisible by 3.
=> (7n + 4 + 3) is divisible by 3.
=> (7n + 4) is divisible by 3.

This is because if a number x is divisible by 3, then (x - 3) will also be divisible by 3.

Thus r = 0.

Sufficient.


Statement 2: n > 20
Value of r may be 0, 1 or 2 according to the value of n.

Not sufficient.

The correct answer is B.
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