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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

\(1< 5n +5 < 25\) --> 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.

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.

Answer: B.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

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.

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.

Answer: B.

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

Because -1 is LESS than -4/5, and n must be more than -4/5.
_________________

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

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05 Sep 2013, 22:18

1

This post received KUDOS

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.

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 Correct answer - B

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

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09 May 2016, 09:57

1

This post received KUDOS

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.

The answer is B.
_________________

Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

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