happymanocha wrote:How many integers are there between c and d?

(1) Neither c nor d is an integer.

(2) c - d = 3

OA is C but according to me it should be E. Can someone explain?

Source : Grockit

Hi happymanocha!

It might be easiest to pick some numbers to illustrate what we are told in each statement.

Statement (1): Neither c nor d is an integer.

Let's make c=1.5 and d=1.5, then there are 0 integers between them.
Now move them apart, c=1.5 and d=2.1, now there is 1 integer between them.

[spoiler]2 different answers = NOT sufficient[/spoiler]


Statement (2): c - d = 3

Now, remember that statement 1 told us that c & d were NON integers. This should be a hint to try integer AND non-integer values for c & d when using this choice.

Integers: c=5 then d=2, there are 2 integers between them (3 and 4)
Non-Integers: c=5.5 then d=2.5, now there are actually 3 integers between them (3, 4 & 5)

[spoiler]2 different answers = NOT Sufficient[/spoiler]

Statement (1+2): c&d are non-integers that are 3 units apart
Let's pick a couple of examples:

c=5.5, d=2.5: between {3, 4, 5}
c=1.1, d=-1.9: between {-1, 0, 1}
c=-3.7, d=-6.9: between {-6, -5, -4}

So we see that when we have 2 non-integers that are 3 units apart, there will be 3 integers between them. SUFFICIENT - the answer is C.

You can sketch it on a number line to prove it to yourself as well.

<--|--(#)--|-----|-----|--(#)--|----->

Hope this helps clear up the confusion!

Whit