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How many integers n are there such that v<n<w?

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How many integers n are there such that v<n<w? [#permalink] New post 14 Mar 2012, 05:13
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How many integers n are there such that v<n<w?

(1) v and w are positive integers?
(2) w-v=4

How is it even possible that v<w when v-w=4?

from gmathacks
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Mar 2012, 04:23, edited 2 times in total.
Edited the question
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Re: How many integers are there such that v<n<w? [#permalink] New post 14 Mar 2012, 05:33
Expert's post
BN1989 wrote:
How many integers n are there such that v<n<w?

1) v and w are positive integers?
2) v-w=4

How is it even possible that v<w when v-w=4?

from gmathacks


(2) should read: w-v=4.

How many integers n are there such that v<n<w?

Notice that if w and v are integers, for example w=5 and v=1 then there will be 3 integers between them: 2, 3, and 4. But if w and v are NOT integers for example w=5.5 and v=1.5 then there will be 4, so one more, integers between them: 2, 3, 4 and 5.

(1) v and w are positive integers. Not sufficient.
(2) w-v=4. Not sufficient.

(1)+(2) According to above reasoning since v and w are positive integers then there are 3 integers between them (case 1). Sufficient.

Similar question to practice: how-many-integers-n-are-there-such-that-r-n-s-101917.html

Hope it helps.
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Re: How many integers are there such that v<n<w? [#permalink] New post 17 Mar 2012, 04:21
BN1989 wrote:
How many integers are there such that v<n<w?

(1) v and w are positive integers?
(2) w-v=4

How is it even possible that v<w when v-w=4?

from gmathacks


The question stem seems to ask how many integral triplets exists which are bound by v<n<w?
Whereas the intent is to ask how many integral values of n exist such that v<n<w ?

Only if we are interested in finding the no. of integral values n can take then we can get the answer
by combining 1&2 (as Bunnel stated)
But if we are interested in finding integers then obeying 1&2 we can take any natural no. as v and accordingly our w will get fixed and then we can choose any 3 no.s between w and v to get n.So infinite no. of triplets can be formed.

@Bunnel: I would be thankful if you clarify
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Re: How many integers are there such that v<n<w? [#permalink] New post 17 Mar 2012, 04:25
Expert's post
jach2012 wrote:
BN1989 wrote:
How many integers are there such that v<n<w?

(1) v and w are positive integers?
(2) w-v=4

How is it even possible that v<w when v-w=4?

from gmathacks


The question stem seems to ask how many integral triplets exists which are bound by v<n<w?
Whereas the intent is to ask how many integral values of n exist such that v<n<w ?

Only if we are interested in finding the no. of integral values n can take then we can get the answer
by combining 1&2 (as Bunnel stated)
But if we are interested in finding integers then obeying 1&2 we can take any natural no. as v and accordingly our w will get fixed and then we can choose any 3 no.s between w and v to get n.So infinite no. of triplets can be formed.

@Bunnel: I would be thankful if you clarify


The question should read: "How many integers N are there such that v<n<w?" There was a typo in the original post, which is now edited.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: How many integers are there such that v<n<w?   [#permalink] 17 Mar 2012, 04:25
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