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Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10

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Bunuel
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Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   27 Nov 2023, 02:30
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A
B
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D
E

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45% (medium)

Question Stats:

74% (01:59) correct 26% (01:59) wrong based on 53 sessions
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Is \(x - y > −10\) ?

(1) \(5x + 2y > −10\)

(2) \(2y + x > −10\)


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E
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VibhuAnurag
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Re: Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   27 Nov 2023, 13:01
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The answer should be E.

(1) 5x + 2y > -10
This does not tell us whether x - y > -10 --> Insufficient.

(2) 2y + x > -10
Even this option does not confirm whether x - y > -10 --> Insufficient.

Combining:
Add the inequalities --> 6x + 4y > -10.
Even now we don't know whether x - y > -10. Hence, insufficient.
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Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   01 Dec 2023, 03:59
Bunuel wrote:
Is \(x - y > −10\) ?

(1) \(5x + 2y > −10\)

(2) \(2y + x > −10\)




chetan2u Bunuel KarishmaB

From both equation in option (1) & (II)
i am getting X>0 && Y< -5
which satisfies condition that
X-Y > -10

Please clear ,where i am wrong

Thanks
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chetan2u
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Re: Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   01 Dec 2023, 04:13
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CEO2021 wrote:
Bunuel wrote:
Is \(x - y > −10\) ?

(1) \(5x + 2y > −10\)

(2) \(2y + x > −10\)




chetan2u Bunuel KarishmaB

From both equation in option (1) & (II)
i am getting X>0 && Y< -5
which satisfies condition that
X-Y > -10

Please clear ,where i am wrong

Thanks


How did you get the answer.

When you add you get 6x+4y>-20 or 3x+2y>-10

Say x is 10, then 2y>-40 or y>-20.
x=10 and y =100 will give 10-100 or -90
x=10 and y=-10 will give 10-(-10) or 20
So answer will be different.
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CEO2021
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Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   01 Dec 2023, 04:20
chetan2u wrote:
CEO2021 wrote:
Bunuel wrote:
Is \(x - y > −10\) ?

(1) \(5x + 2y > −10\)

(2) \(2y + x > −10\)




chetan2u Bunuel KarishmaB

From both equation in option (1) & (II)
i am getting X>0 && Y< -5
which satisfies condition that
X-Y > -10

Please clear ,where i am wrong

Thanks


How did you get the answer.

When you add you get 6x+4y>-20 or 3x+2y>-10

Say x is 10, then 2y>-40 or y>-20.
x=10 and y =100 will give 10-100 or -90
x=10 and y=-10 will give 10-(-10) or 20
So answer will be different.


chetan2u
but subtracting both equation we get x>0

and multiplying eq(ii) by 5 and then subtracting by eq(1) i am getting y<-5
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chetan2u
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Re: Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   01 Dec 2023, 04:29
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CEO2021 wrote:
chetan2u wrote:

How did you get the answer.

When you add you get 6x+4y>-20 or 3x+2y>-10

Say x is 10, then 2y>-40 or y>-20.
x=10 and y =100 will give 10-100 or -90
x=10 and y=-10 will give 10-(-10) or 20
So answer will be different.


chetan2u
but subtracting both equation we get x>0

and multiplying eq(ii) by 5 and then subtracting by eq(1) i am getting y<-5


No, you never subtract inequalities.

Say 1+5>-10 ……..6>-10 and
-4+(-5)>-10 ………-9>-10
Now how do you subtract
6-(-9)>0….ok
But it can be -9-6>0 or -15>0…Not ok
You can add same sides of inequality but not subtract
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Re: Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   01 Dec 2023, 04:37
chetan2u wrote:
CEO2021 wrote:
chetan2u wrote:

How did you get the answer.

When you add you get 6x+4y>-20 or 3x+2y>-10

Say x is 10, then 2y>-40 or y>-20.
x=10 and y =100 will give 10-100 or -90
x=10 and y=-10 will give 10-(-10) or 20
So answer will be different.


chetan2u
but subtracting both equation we get x>0

and multiplying eq(ii) by 5 and then subtracting by eq(1) i am getting y<-5


No, you never subtract inequalities.

Say 1+5>-10 ……..6>-10 and
-4+(-5)>-10 ………-9>-10
Now how do you subtract
6-(-9)>0….ok
But it can be -9-6>0 or -15>0…Not ok
You can add same sides of inequality but not subtract


OHH...i am unaware of that

Thankyou very much
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KarishmaB
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Re: Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink] New post   04 Dec 2023, 02:36
Expert Reply
CEO2021 wrote:
Bunuel wrote:
Is \(x - y > −10\) ?

(1) \(5x + 2y > −10\)

(2) \(2y + x > −10\)




chetan2u Bunuel KarishmaB

From both equation in option (1) & (II)
i am getting X>0 && Y< -5
which satisfies condition that
X-Y > -10

Please clear ,where i am wrong

Thanks


How did you get the highlighted? Please show your work. It will help me figure out the problem.
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Re: Is x - y > 10 ? (1) 5x + 2y > 10 (2) 2y + x > 10 [#permalink]
04 Dec 2023, 02:36
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Bunuel
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