When a positive integer n is divided by 29, what is the

[VJesus12]

When a positive integer n is divided by 29, what is the remainder?

1) n-5 is divisible by 29
2) n-29 is divisible by 5

The OA is the option A.

Why the first statement is sufficient and the second one is not? May someone helps me? Please.

[GMATinsight]

When a positive integer n is divided by 29, what is the remainder?

1) n-5 is divisible by 29
2) n-29 is divisible by 5

The OA is the option A.

Why the first statement is sufficient and the second one is not? May someone helps me? Please.

Question : Remainder when Integer n is divided by 29 = ?

Statement 1: n-5 is divisible by 29

i.e. n is 5 greater than a multiple of 29

i,e, when n is divided by 29 then remainder is always 5

SUFFICIENT

Statement 2: n-29 is divisible by 5

i.e. n-29 may be 5 or 10 or 15 etc.
i.e. n may be 34 or 39 or 44 etc.

i.e. when n is divided by 29 then remainder may be 5 or 10 15 etc. respectively

NOT SUFFICIENT

Answer: Option A

[Vincen]

Hello Vjesus12.

I would solve it as follows:

1) n-5 is divisible by 29

This implies that $$n-5=29\cdot k\ \ \ \Leftrightarrow\ \ n=29\cdot k+5$$ and it tells us that when n is divided by 29, the remainder is 5. SUFFICIENT.

2) n-29 is divisible by 5

This tells us that $$n-29=5\cdot k\ \ \ \Leftrightarrow\ \ n=5\cdot k+29.$$ Now, if k=1 then n=34. Therefore, when we divided n by 29, the remainder would be 5.

But if k=2, then n=39 and therefore when we divide n by 29 the remainder would be 10.

This implies that this statement is NOT SUFFICIENT.

Hence, the correct answer is the option A.

[Jeff@TargetTestPrep]

When a positive integer n is divided by 29, what is the remainder?

1) n-5 is divisible by 29
2) n-29 is divisible by 5

We need to determine the remainder of n/29.

Statement One Alone:

n-5 is divisible by 29

We can create the equation:

(n - 5)/29 = Q (where Q is an integer)

n - 5 = 29Q

n = 29Q + 5

Thus:

n/29 = (29Q + 5)/29 = 29Q/29 + 5/29 = Q + 5/29

Since Q is an integer, the remainder must be 5. Statement one alone is sufficient to answer the question.

Statement Two Alone:

n-29 is divisible by 5

(n - 29)/5 = Q (where Q is an integer)

n - 29 = 5Q

n = 5Q + 29

Thus:

n/29 = (5Q +29)/29 = 5Q/29 + 29/29 = 5Q/29 + 1 = 1 + 5Q/29

Since 1 is an integer, the remainder must be 5Q if 5Q < 29. However, the remainder can be 5 (if Q = 1) or 10 (if Q = 2). Therefore, statement two alone is not sufficient to answer the question.

Answer: A

[Brent@GMATPrepNow]

When a positive integer n is divided by 29, what is the remainder?

1) n-5 is divisible by 29
2) n-29 is divisible by 5

Target question: What is the remainder when n is divided by 29?

Statement 1: n-5 is divisible by 29
So, we can say that: n-5 = 29k for some integer k
Add 5 to both sides of the equation to get: n = 29k + 5
We can see that n is 5 greater than some multiple of 29
So, if we divide n by 29, the remainder will equal 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n-29 is divisible by 5
There are several values of n that satisfy statement 2. Here are two:
Case a: n = 39. Notice that 39 - 29 = 10, and 10 IS divisible by 5. When 39 is divided by 29, the remainder is 10. In other words, when we divide n by 29, the remainder will equal 10
Case b: n = 44. Notice that 44 - 29 = 15, and 15 IS divisible by 5. When 44 is divided by 29, the remainder is 15. In other words, when we divide n by 29, the remainder will equal 15
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent