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Properties of number

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Durgaa
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Properties of number [#permalink] New post   02 Sep 2021, 21:33
Hi I need help with this question. specifically part (b) and (d)

๐’™ and ๐’š are two integers such thatโˆ’5(๐’™^2+๐’š) is a positive number. Determine whether each of the following expression is positive, negative, 0, or โ€œNo unique answerโ€.

a)๐’š - negative
b)๐’™+๐’š - negative
c)โˆ’๐’š - positive
d)๐’™โˆ’๐’š - positive
e)(๐’™^2+๐’š)/๐’š - positive
f)๐’™^2 - no unique answer
g)๐’™^2+๐’š^2 - positive

Thank you
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sivatx2
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Re: Properties of number [#permalink] New post   02 Sep 2021, 21:53
๐’™ and ๐’š are two integers such thatโˆ’5(๐’™^2+๐’š) is a positive number. Determine whether each of the following expression is positive, negative, 0, or โ€œNo unique answerโ€.

a)๐’š - negative
b)๐’™+๐’š - negative
c)โˆ’๐’š - positive
d)๐’™โˆ’๐’š - positive (INCORRECT: Must be No unique answer)
x could be negative. Note, square of a negative number is always positive.Also, it could be a very very large number, "negatively". and could make x-y a negative value. Since both positive and negative values are possible, the choice would be "No unique answer".
e)(๐’™^2+๐’š)/๐’š - positive
[color=#ff0000]f)๐’™^2 - no unique answer (INCORRECT: Must be positive)
Irrespective of whether x is positive or negative integer, x^2 is always a positive integer.
[/color]
g)๐’™^2+๐’š^2 - positive
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Durgaa
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Re: Properties of number [#permalink] New post   02 Sep 2021, 21:57
Hi

The answers I have written are correct. I need an explanation as to why parts b and d have such answers.
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ash124
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Re: Properties of number [#permalink] New post   03 Sep 2021, 05:50
Durgaa wrote:
Hi

The answers I have written are correct. I need an explanation as to why parts b and d have such answers.

From
๐’™ and ๐’š are two integers such thatโˆ’5(๐’™^2+๐’š) is a positive number

from this equation:
โˆ’5(๐’™^2+๐’š)

๐’™^2 is always +tive and to negative sign given outside of brackets
๐’™^2+๐’š < 0
you can take some numbers as well

y = -10(y will always be a -tive integer as ๐’™^2 is always +tive and we need a negative (๐’™^2+๐’š) )
x can be positive or negative but ๐’™^2 should be less than |y|
x = 2 or -2
๐’™^2 = 4



b)๐’™+๐’š - negative
as ๐’™^2 should be less than |y|

-2-10 = -12
2-10 = -8
always -tive

d)๐’™โˆ’๐’š - positive

in same way
-2+10 = 8
2+10 = 12
always +tive
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Durgaa
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Re: Properties of number [#permalink] New post   04 Sep 2021, 00:33
Hi ash124

i understand now. thank you.
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ash124
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Re: Properties of number [#permalink] New post   04 Sep 2021, 09:11
Durgaa wrote:
Hi ash124

i understand now. thank you.


Good to know :)

Thanks for asking
GMAT Club Bot
gmatclubot
Re: Properties of number [#permalink]
04 Sep 2021, 09:11
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