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If x is an integer between 0 and 10 is y less than the average of x an

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If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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If x is an integer between 0 and 10 is y less than the average of x and 10 ?

(1) (10-y) < y - (x +10)/2
(2) y is 4 times as large as x

Originally posted by KSBGC on 26 Apr 2018, 20:31.
Last edited by Bunuel on 26 Apr 2018, 23:12, edited 1 time in total.
Edited the question and the tags.
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Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 26 Apr 2018, 21:51
1
selim wrote:
If x is an integer between 0 and 10 is y less than the average of x and 10 ?

1. (10-y) < y - (x +10) / 2
2. y is 4 times as large as x


(2) If \(x=1\), then \(y=4\).
So, \(\frac{(1+10)}{2}>4\).

If \(x=2\), then \(y=8\).
So, \(\frac{(2+10)}{2}<8\).

Hence, not suff.

(1) \(2(10-y)<2y-(x+10)\)
\(4y>x+30\).

Let's take extreme values of \(x\) (\(0\) and \(10\)).

If \(x=0\), then \(4y>30\) --> \(y>7.5\)
Clearly, \(\frac{(0+10)}{2}<y\).

If \(x=10\), then \(4y>40\) --> \(y>10\)
Clearly, \(\frac{(10+10)}{2}<y\).

Hence, suff.

Answer: A

Please correct me if I'm wrong or change the off ans.
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Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 27 Apr 2018, 01:15
selim wrote:
If x is an integer between 0 and 10 is y less than the average of x and 10 ?

(1) (10-y) < y - (x +10)/2
(2) y is 4 times as large as x


Ans: A

We know that x is between 0 and 10 so the average of x and 10 is going to be between 5 and 10. 5<(x+10)/2<10
we need to find is y<(x+10)/2

Stat 1) (10-y) < y - (x +10)/2
after solving this we get y> 1/2 ((x+10)/2)+ 5
now here we know that y will alway be greater than 5. we can put different values of x get avg and value of y and we see that this is always true that y>the avg of x qnd 10

so this is sufficient.

Stat: 2 y =4x
start putting values if x=1 : y=4 and avg of x and 10 is 5.5 : y<avg
x=2 ; y=8 ; avg =6 y>avg
stat 2 not sufficient:

Ans A
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If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 15 May 2018, 07:04
1
selim wrote:
If x is an integer between 0 and 10 is y less than the average of x and 10 ?

(1) (10-y) < y - (x +10)/2
(2) y is 4 times as large as x



I) 2(10−y)<2y−(x+10)

4y>x+30
Not sufficient as we can't say anything about y<(x+10)/2

II)y=4x
Not sufficient .we don't know values of x and y

Combining both we got
16x>x+30
x>2 then y=4x>8

X=3 y=12 so 12<10+3/2 No
X=4 Y=16 so 16<10+4/2 No
X=10 Y=40 so 40<10+10/2 No

So every value from x=3 to 10 we get same result from equation as No

So sufficient
Answer is C

Give kudos if you like explanation

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Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 08 Jun 2019, 14:22
This is wrong

X cannot be 10 since this integer from 0 to 10 exclusive

Tulkin987 wrote:
selim wrote:
If x is an integer between 0 and 10 is y less than the average of x and 10 ?

1. (10-y) < y - (x +10) / 2
2. y is 4 times as large as x


(2) If \(x=1\), then \(y=4\).
So, \(\frac{(1+10)}{2}>4\).

If \(x=2\), then \(y=8\).
So, \(\frac{(2+10)}{2}<8\).

Hence, not suff.

(1) \(2(10-y)<2y-(x+10)\)
\(4y>x+30\).

Let's take extreme values of \(x\) (\(0\) and \(10\)).

If \(x=0\), then \(4y>30\) --> \(y>7.5\)
Clearly, \(\frac{(0+10)}{2}<y\).

If \(x=10\), then \(4y>40\) --> \(y>10\)
Clearly, \(\frac{(10+10)}{2}<y\).

Hence, suff.

Answer: A

Please correct me if I'm wrong or change the off ans.
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If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 08 Jun 2019, 14:28
The answer is right but reasoning a little bit flawed.

X cannot be neither 0 nor 10 since this is integer from 0 to 10

X can be only 4 while taking both stms into consideration


push12345 wrote:
selim wrote:
If x is an integer between 0 and 10 is y less than the average of x and 10 ?

(1) (10-y) < y - (x +10)/2
(2) y is 4 times as large as x



I) 2(10−y)<2y−(x+10)

4y>x+30
Not sufficient as we can't say anything about y<(x+10)/2

II)y=4x
Not sufficient .we don't know values of x and y

Combining both we got
16x>x+30
x>2 then y=4x>8

X=3 y=12 so 12<10+3/2 No
X=4 Y=16 so 16<10+4/2 No
X=10 Y=40 so 40<10+10/2 No

So every value from x=3 to 10 we get same result from equation as No

So sufficient
Answer is C

Give kudos if you like explanation

Posted from my mobile device
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Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 08 Jun 2019, 23:41
1
kebab1990 wrote:
The answer is right but reasoning a little bit flawed.

X cannot be neither 0 nor 10 since this is integer from 0 to 10

X can be only 4 while taking both stms into consideration


push12345 wrote:
selim wrote:
If x is an integer between 0 and 10 is y less than the average of x and 10 ?

(1) (10-y) < y - (x +10)/2
(2) y is 4 times as large as x



I) 2(10−y)<2y−(x+10)

4y>x+30
Not sufficient as we can't say anything about y<(x+10)/2

II)y=4x
Not sufficient .we don't know values of x and y

Combining both we got
16x>x+30
x>2 then y=4x>8

X=3 y=12 so 12<10+3/2 No
X=4 Y=16 so 16<10+4/2 No
X=10 Y=40 so 40<10+10/2 No

So every value from x=3 to 10 we get same result from equation as No

So sufficient
Answer is C

Give kudos if you like explanation

Posted from my mobile device



I think A is sufficient for any value of X from 0 to 10 exclusive.
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Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 10 Jun 2019, 09:14
can any expert clarify this?
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Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 13 Jun 2019, 07:06
1
The correct answer is C

St1 : (10-y) < y - (x +10)/2
2(10-y)<2y-(x+10)
20-2y<2y-(x+10)
4y>x+30
As we get same values for x and y if we take x=10( i think between includes 0 and 10 because it doesn't say exclusive)
So St1 is insufficient

St2 : y is 4 times as large as x
y=4x
Insufficient as it doesn't give any other information

Combining 1&2

4y>x+30
4(4x)>x+30 (sub y=4x)
16x>x+30
15x>30
Therefore, x>2

Question stem is y<x+10/2
4x<x+10/2
8x<x+10
7x<10
x<10/7
Is x<1.4

Therefore we got the answer that x is greater than 2. Sufficient
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If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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New post 26 Jul 2019, 13:46
If x is an integer between 0 and 10 is y less than the average of x and 10 ?

From the question steam, the only available info about X is that its an integer and 0<X<10.

And the question is whether (10+X)/2>Y


(1) (10-y) < y - (x +10)/2



2(10-Y)<2Y-(X+10)
20-2Y<2Y-X-10
X-4Y+30<0

Now think about it, the whole term is less than zero and for that Y must be positive and the expression -4Y must be greater than (X+30)
So the values of X and Y can be :-

X=(1,2,3,4,5,6,7,8,9)
Y=(8,9,10)


INSUFFICIENT

(2) y is 4 times as large as x



Clearly INSUFFICIENT , Y could be any value which is a multiple of 4.

But When we take these 2 statements together we can clearly see that out of values of Y provided by statement 1, only Y=8 is a multiple of 4.(since X is an integer between 0 and 10)
So X must be equal to 2(according to statement 2)

and then (10+2)/2>4. So, both statement together is sufficient. Ans C
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If x is an integer between 0 and 10 is y less than the average of x an   [#permalink] 26 Jul 2019, 13:46
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