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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]

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24 Sep 2012, 04:04
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Difficulty:

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Question Stats:

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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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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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

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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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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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24 Sep 2012, 07:43
2
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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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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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28 Sep 2012, 03:55
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]

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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]

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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

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Math Expert
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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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11 Dec 2012, 03:56
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]

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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 ?

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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24 Jun 2013, 04:12
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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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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05 Sep 2013, 22:18
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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 16033 times ]

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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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..

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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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

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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08 May 2016, 13:34
The inequality given is 1 < 5n+5 < 25
it can further reduced to -4 < 5n < 20
finally -4/5 < n < 4
So can only take 5 integer values i.e. 0,1,2,3

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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09 May 2016, 09:57
1
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Expert's post
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

Solution:

1< 5n + 5 < 25 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know, to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality.

1< 5n + 5 < 25

We first subtract 5 from all three parts of the inequality, and we obtain:

-4 < 5n < 20

Next, we divide both sides of the inequality by 5 and we get:

-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.

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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09 Jun 2016, 06:10
Bunuel wrote:
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

We are also told n is greater than 1, than how can we take 0 and 1 in the answer choice???

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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09 Jun 2016, 06:18
Lucky_Rish wrote:
Bunuel wrote:
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

We are also told n is greater than 1, than how can we take 0 and 1 in the answer choice???

We are not told that n is greater than 1. We are told that $$1< 5n +5 < 25$$, which is the same as $$−\frac{4}{5} < n < 4$$.
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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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11 Jun 2017, 21:39
Hi!

To avoid getting into the trap of a -ve number and fractions, we can do the following

Given: $$1 < 5n+5<25$$ ; Subtract throughout by -1

= $$0 < 5n+4 < 24$$ ---> We need all positive integers which satisfies this equation.

= $$4, 9, 14, 19$$ are the possibilities

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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18 Dec 2017, 07:14
Should this question be for 600-700 Difficulty range?
I think it should be moved to 500-600 range.

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Re: How many integers n are there such that 1< 5n +5 < 25? [#permalink]

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18 Dec 2017, 08:12
the minimum n can be is 0. The maximum it can be is 3. So n can be anything from 0 to 3. It can be 0,1,2, or 3 for a total of 4 values.

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Re: How many integers n are there such that 1< 5n +5 < 25?   [#permalink] 18 Dec 2017, 08:12

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