How many integers n are there such that 1

Question

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

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

Bunuel · Accepted Answer

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.

Answer: B.

dexerash · Answer

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

fabrizio1983 · Answer

is it correct?

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

Bunuel · Answer

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

imperfectdark · Answer

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.

JeffTargetTestPrep · Answer

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.

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=FqLx-ZSZUMw Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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

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