Integer N

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gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 amFollowed by: 5 members; Thanked: 28 times

by gmatblood » Mon Oct 31, 2011 2:33 pm

How many integers n are there such that
1 < 5n + 5 < 25 ?

(A) Five
(B) Four
(C) Three
(D) Two
(E) One

1 < 5n < 20

1,2,3 only matches!!

[spoiler]IMO:C OA:B[/spoiler]

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GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Mon Oct 31, 2011 2:50 pm

When you subtract 5, you have to subtract it from every part of the inequality. It should be:

1<5n+5<25

-4<5n<20
-4/5<n<4

so n could be 0,1,2, or 3

Pete Ackley
GMAT Math Pro
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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Mon Oct 31, 2011 5:43 pm

-4 < 5n < 20, -4/5 < n < 4, we have 0,1,2,3

gmatblood wrote:How many integers n are there such that
1 < 5n + 5 < 25 ?

(A) Five
(B) Four
(C) Three
(D) Two
(E) One

1 < 5n < 20

1,2,3 only matches!!

[spoiler]IMO:C OA:B[/spoiler]

Success doesn't come overnight!

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Wed Nov 02, 2011 2:03 am

1 < 5n + 5 < 25

You can also substitute in this case !

If 5n + 5 = 0 then n = -1, So we can start from 0 which is the immediate neighbor of -1

n=0 5n + 5 =5
n=1 5n + 5 =10
n=2 5n + 5 =15
n=3 5n + 5 =20
n=4 5n + 5 =25 Stop here, this doesn't satisfy !

so Answer = [spoiler]B) 4[/spoiler]

Anil Gandham
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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Fri Apr 06, 2018 8:02 am

gmatblood wrote:How many integers n are there such that
1 < 5n + 5 < 25 ?

(A) Five
(B) Four
(C) Three
(D) Two
(E) One

Simplifying the inequality, we have:

1 < 5n + 5 < 25

-4 < 5n < 20

-4/5 < n < 4

The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 25.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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