Problem Solving

Can someone please help me with this,

I was listening to a GMAT PREP Lesson

And the question was

Is k+5/5 and integer?


Statement 1: When K is divided by 5, the remainder is 1?


Statement 1, was insufficient and they explained it by say 1 divided by 5 is equal to 0 with a remainder of 1.

Are there number property rules I am not understanding because 1/5 is .20

Thank you in Advance

rbansal wrote:Can someone please help me with this,

I was listening to a GMAT PREP Lesson

And the question was

Is k+5/5 and integer?


Statement 1: When K is divided by 5, the remainder is 1?


Statement 1, was insufficient and they explained it by say 1 divided by 5 is equal to 0 with a remainder of 1.

Are there number property rules I am not understanding because 1/5 is .20

Thank you in Advance

Hi,

first thing to note is that if you've reproduced the question correctly, that statement is actually sufficient to answer the question.

Q: is (k+5)/5 an integer?

As with many DS questions, we can make our lives easier by simplifying the question. Let's break up the fraction:

Is k/5 + 5/5 an integer?

Is k/5 + 1 an integer?

Since 1 is already an integer, the question is simply:

Is k/5 an integer?

or

Is k a multiple of 5?

Now the statement:

(1) k/5 has a remainder of 1.

Well, if k/5 has a remainder of 1, then k cannot possibly be a multiple of 5 (if k were a multiple of 5, k/5 would have a remainder of 0 - that's the definition of a multiple!).

So, (1) gives us a definite "no" answer to the question and is sufficient alone.

Now on to your specific question:

Are there number property rules I am not understanding because 1/5 is .20

The short answer is "yes" - you need to brush up on the definition of "remainder".

When you divide one integer by another, one way to express the result is with a quotient and a remainder; the quotient is how many times the divisor goes in and the remainder is how much is left over after the division.

For example:

10/4 can be written as 2 rem 2, since 4 goes into 10 twice (taking up 8 of the 10) with 2 left over (10 minus the 8 that we used up).

27/6 can be written as 4 rem 3, since 6 goes into 27 four times (taking up 24 of the 27) with 3 left over (27 minus the 24 that we used up).

A GMAT trick to watch for is when you have a quotient of 0. For example:

2/7 can be written as 0 rem 2, since 7 goes into 2 zero times (taking up 0 of the 7) with 2 left over (2 minus the 0 that we used up).

So, when a question asks you for a remainder, don't do long division and end up with a decimal - instead, rewrite the fraction as a mixed fraction (and don't simplify!). The number on the numerator of the "left over" unsimplified fraction is the remainder.

Using the same examples as above:

10/4 = 2 2/4 = 2 rem 2
27/6 = 4 3/6 = 4 rem 3
2/7 = 2/7 = 0 rem 2

Things to remember:

Multiple of N +/- Multiple of N = Multiple of N -> Hence divisible by N

Non-Multiple of N +/- Multiple of N = Non-multiple of N -> Hence not divisible by N

**Non-Multiple of N +/- Non-Multiple of N = Could be or not a multiple of N -> Can't tell divisibility (** In this case N = 2 is an exception because ODD + ODD = EVEN -> which is divisible by 2)

Also you can Rephrase the question:
Is (k+5)/5 an Integer?
Is k/5 + 5/5 an Integer?
Is k/5 + 1 an Integer?
Is k/5 an Integer? NO! because when k is divided by 5, the remainder is 1
Statement 1 is sufficient