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A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If

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A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If the length of the sides of the rectangle are integers and the area is less than or equal to 20, how many distinct values can a take?

A. 2
B. 5
C. 10
D. 11
E. Any integer ≤ 5 except zero.
[Reveal] Spoiler: OA

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 01 Aug 2017, 01:00
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C 10
a could be negative or positive. But absolute value will be less than equal to 5 and also a cannot be equal to zero. So answer is 10 values from 5 to -5. Excluding zero

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 01 Aug 2017, 01:05
BeingHan wrote:
C 10
a could be negative or positive. But absolute value will be less than equal to 5 and also a cannot be equal to zero. So answer is 10 values from 5 to -5. Excluding zero

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HI BeingHan: Thanks for your reply.Can you please clarify why the answer can't be E.

This is what I have done: LB≤20 >> 4a≤20 >> a≤5.
So, it can take any integral value except zero.

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 01 Aug 2017, 01:43
Hi.
Any integer less than equal to 5 can have values less than -5. Such as -6 ,-7 etc. Which don't support the inequality.

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 01 Aug 2017, 01:46
BeingHan wrote:
Hi.
Any integer less than equal to 5 can have values less than -5. Such as -6 ,-7 etc. Which don't support the inequality.

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Hi,
Values such as -6 ,-7 etc support this inequality a≤5 right?

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 01 Aug 2017, 01:55
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The inequality I referred to here is
Area <= 20. So if we were to use a= -6 , it would lead to area being 24. Hence going against the inequality.

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 01 Aug 2017, 03:41
BeingHan wrote:
The inequality I referred to here is
Area <= 20. So if we were to use a= -6 , it would lead to area being 24. Hence going against the inequality.

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app


Thanks, makes sense.

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 13 Aug 2017, 00:25
Hi,
Could anyone please help me how is the range -5 to 5 excluding zero? How is -6 against the inequality?

Thanks

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 13 Aug 2017, 01:19
The area of rectangle can't be negative.

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Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If [#permalink]

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New post 13 Aug 2017, 02:29
1)4*1
2)4*2
3)4*3
4)4*4
5)4*5
6)4*|-1|
7)4*|-2|
8)4*|-3|
9)4*|-4|
10) 4* |-5|

there will be total of 10?

Kudos [?]: 3 [0], given: 454

Re: A rectangle is formed using the x axis, y axis, x=4 and y=a lines. If   [#permalink] 13 Aug 2017, 02:29
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