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

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Math Expert
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How many integers n are there such that 1< 5n +5 < 25? [#permalink]  24 Sep 2012, 04:04
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Question Stats:

64% (01:40) correct 36% (00:35) wrong based on 757 sessions
How many integers n are there such that 1< 5n +5 < 25?

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

Practice Questions
Question: 50
Page: 158
Difficulty: 600
[Reveal] Spoiler: OA

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Math Expert
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Posts: 31286
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Kudos [?]: 62190 [3] , given: 9444

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  24 Sep 2012, 04:04
3
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Expert's post
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SOLUTION

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

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

$$1< 5n +5 < 25$$ --> subtract 5 from each part: $$-4<5n<20$$ --> divide by 5 each part: $$-\frac{4}{5}<n<4$$. In this range there are 4 integers: 0, 1, 2, and 3.

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Kudos [?]: 549 [1] , given: 241

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  24 Sep 2012, 04:15
1
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1< 5n +5 < 25
-> -4<5n<20
-> -.8<n<4

Four integers are possible
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Kudos [?]: 40 [1] , given: 4

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  24 Sep 2012, 07:43
1
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Bunuel wrote:
How many integers n are there such that 1< 5n +5 < 25?

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

expression can be split into two equations:
1 < 5n + 5 ==> 5n > -4 ==> n > -0.8

5n + 5 < 25 ==> 5n < 20 ==> n < 4

now between -0.8 and 4(excluding) , there exist 4 integers, viz. 0, 1, 2, 3

hence B
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Math Expert
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Posts: 31286
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Kudos [?]: 62190 [0], given: 9444

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  28 Sep 2012, 03:55
Expert's post
SOLUTION

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

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

$$1< 5n +5 < 25$$ --> subtract 5 from each part: $$-4<5n<20$$ --> divide by 5 each part: $$-\frac{4}{5}<n<4$$. In this range there are 4 integers: 0, 1, 2, and 3.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  10 Dec 2012, 03:23
$$1 < 5n +5 < 25$$
$$1 - 5 < 5n + 5 - 5 < 25 -5$$
$$-4 < 5n < 20$$
$$-4/5 < n < 4$$

<===(-1)=-4/5=(0)=(1)=(2)=(3)=(4)==> x-axis

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  11 Dec 2012, 03:14
is it correct?

5*1+5=10
5*2+5=15
5*3+5=20
5*4+5=25 -->n=4
Math Expert
Joined: 02 Sep 2009
Posts: 31286
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Kudos [?]: 62190 [0], given: 9444

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  11 Dec 2012, 03:56
Expert's post
fabrizio1983 wrote:
is it correct?

5*1+5=10
5*2+5=15
5*3+5=20
5*4+5=25 -->n=4

No, that's not correct. n cannot be 4, since 5*4+5=25 and we are told that it must be less than 25.

1< 5n +5 < 25
n=0 --> 5n +5=5;
n=1 --> 5n +5=10;
n=2 --> 5n +5=15;
n=3 --> 5n +5=20.

Thus n can take 4 values: 0, 1, 2, or 3.

Check here: how-many-integers-n-are-there-such-that-1-5n-139474.html#p1124669
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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  24 Jun 2013, 04:06
Bunuel wrote:
SOLUTION

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

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

$$1< 5n +5 < 25$$ --> subtract 5 from each part: $$-4<5n<20$$ --> divide by 5 each part: $$-\frac{4}{5}<n<4$$. In this range there are 4 integers: 0, 1, 2, and 3.

why is it not -1, 0, 1, 2, 3 ?
Math Expert
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Posts: 31286
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Kudos [?]: 62190 [0], given: 9444

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  24 Jun 2013, 04:12
Expert's post
Rs1991 wrote:
Bunuel wrote:
SOLUTION

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

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

$$1< 5n +5 < 25$$ --> subtract 5 from each part: $$-4<5n<20$$ --> divide by 5 each part: $$-\frac{4}{5}<n<4$$. In this range there are 4 integers: 0, 1, 2, and 3.

why is it not -1, 0, 1, 2, 3 ?

Because -1 is LESS than -4/5, and n must be more than -4/5.
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Kudos [?]: 18 [1] , given: 24

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  05 Sep 2013, 22:18
1
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A table showing values of 5n+1 for various values of n. Just need to note the constraint that 1<5n+5<25 (valid values are in green, invalid in red) and count how many valid numbers there are for n.
Attachments

Table.png [ 2.57 KiB | Viewed 8265 times ]

Manager
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Kudos [?]: 19 [0], given: 81

Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  10 Sep 2014, 08:28
Bunuel wrote:
How many integers n are there such that 1< 5n +5 < 25?

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

Practice Questions
Question: 50
Page: 158
Difficulty: 600

1< 5n +5 < 25

-4<5n<20

so n can take 0,1,2,3, totally 4 integers..
Intern
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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]  10 Jul 2015, 23:22
Bunuel wrote:
How many integers n are there such that 1< 5n +5 < 25?

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

Practice Questions
Question: 50
Page: 158
Difficulty: 600

i count only 1,2,and 3
for that reason i choose 3 integer

solution: must be count from 0
so, 0,1,2,and 3
so answer: the range of integer 4
Re: How many integers n are there such that 1< 5n +5 < 25?   [#permalink] 10 Jul 2015, 23:22
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