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# For how many integer values of n will the value of the expression 4n +

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
For how many integer values of n will the value of the expression 4n +  [#permalink]

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18 May 2016, 02:19
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:27) correct 42% (01:42) wrong based on 149 sessions

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For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?

A. 48
B. 49
C. 50
D. 51
E. 52

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Joined: 07 Mar 2015
Posts: 108
Location: India
Concentration: General Management, Operations
GMAT 1: 590 Q46 V25
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WE: Engineering (Energy and Utilities)
Re: For how many integer values of n will the value of the expression 4n +  [#permalink]

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18 May 2016, 03:26
1
1
1< 4n+7 < 200

1-7< 4n < 200-7
-6 < 4n < 193
-1.5 < n < 48.25
Since n is an integer -1, 0,1,2,3…………………48

Total 50
Manager
Joined: 18 Jan 2010
Posts: 245
Re: For how many integer values of n will the value of the expression 4n +  [#permalink]

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29 May 2016, 00:50
1
Bunuel wrote:
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?

A. 48
B. 49
C. 50
D. 51
E. 52

From first constraint

4n+7 > 1

4n> -6

n > -(3/2)

n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)

From second constraint

4n+7 < 200

4n< 193

n < 48. 25

n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 48)

Combining the two

-1.5 < n<48.25

n = 1 to 48 (48 integers)
and n = -1 and 0

so 50 integers.
Manager
Joined: 31 Jan 2019
Posts: 172
Location: Switzerland
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GPA: 3.9
Re: For how many integer values of n will the value of the expression 4n +  [#permalink]

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15 Mar 2019, 04:02
Bunuel wrote:
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?

A. 48
B. 49
C. 50
D. 51
E. 52

I used a different approach here.
I used for n integers such as 2, 3 and 4. the results of the expression using the numbers for n were 15, 19 and 23. I assumed that the delta would always be 4 so 200/4=50. Hence c the right answer
Re: For how many integer values of n will the value of the expression 4n +   [#permalink] 15 Mar 2019, 04:02
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