Consective Integers

[THANU.KG]

Hi,

Since I cannot point out the question from the Official Guide that I have a question on and the explanation provided in the OG archer, I hope I can ask this question so it is generic.

If I am asked to count the number of integers between two integers (first and last not included) in a DS question, how can I come to a conclusion that they are consecutive integers. For example:

If my set is {1,2,3,4,5,6,7,8,9,10}, then last-first = 9 - 1 = 8 is the number of integers.

But, if my set is {11,13,46,34}, then last-first = 23 - 1 = 22 is NOT the number of integers.

Can someone please help? The OG archer says "If we know the values of r and s, we can calculate the number of integers between them. This WILL form a consecutive integers set" How?

[kyle_proctor]

Hi:

I will let the experts explain the mechanics of the rules. However, your reasoning below is incorrect. You can easily count the number of terms in a set of consecutive integers OR evenly-spaced sets:

Consecutive Integers:

1,2,3,4,5,6,7,8,9,10 ----> (Last Term - First Term) + 1
----> (10 - 1) = 9 + 1 => 10 TERMS

Evenly-Spaced Sets:

2,4,6,8,10,12 ----> [(Last Term - First Term) / 2] + 1
----> [(12-2) = 10 / 2] = 5 + 1 => 6 TERMS

We are dividing by "2" above because each term is two units apart. If each term were three units apart, you would divide by three. For evenly-spaced sets, the spacing is irrelevant as long as each unit is the same number of units apart:

Without counting, count the number of terms in the set below using our formula above:

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60

[kyle_proctor]

One additional thought. If you were asked to count the number of even terms from 200 to 500, non-inclusive.

You would need to count the number of even terms from 202 to 498.

Applying our formula from the previous post:

[(Last Term - First term) / 2] +1

----> [(498-202) = 296/2 = 148 ] + 1 = 149 TERMS

Hope this helps.

[tim]

thanks Kyle!

[THANU.KG]

Thanks much Kyle for the detailed explanation.

However, my question was more around when are asked to count the numbers between 2 numbers, can you assume that it is a consecutive integers set. But i read the question again, I guess they were referring to 2 points on a number line...

[kyle_proctor]

I think the forum will agree that is is NEVER safe to assume anything on the GMAT. I imagine a question would indicate with specific language that a range of integers is either consecutive or evenly-spaced.

[tim]

thanks Kyle. let us know if there are any further questions on this one..

[ly.priv]

could someone help me explain the logic behind dividing with 2 if 2 units apart and 3 if 3 units apart .

I can definitely memorize this rule but can't seem to conceptualise the logic behind, too abstract for me.

[RonPurewal]

could someone help me explain the logic behind dividing with 2 if 2 units apart and 3 if 3 units apart .

I can definitely memorize this rule but can't seem to conceptualise the logic behind, too abstract for me.

^^ honestly, if the rule is "too abstract", then you may want to just count the numbers on your fingers. if there are fewer than twenty or thirty numbers, there will be NO significant difference in time (maybe a few seconds, at the very most).

__

in any case... just think about "matching up" the numbers with a list that goes 1, 2, 3, etc.

if you have the list 2, 4, 6, 8, 10, 12, 14—and you divide each of these numbers by 2—then you get 1, 2, 3, 4, 5, 6, 7.
there are clearly 7 numbers in this list.

that's the logic here: if you do this sort of division, then you create a list that literally just COUNTS numbers. does that make sense?