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VP  D
Joined: 31 Oct 2013
Posts: 1470
Concentration: Accounting, Finance
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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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11 00:00

Difficulty:   95% (hard)

Question Stats: 31% (03:09) correct 69% (03:03) wrong based on 157 sessions

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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.
Manager  S
Joined: 28 Nov 2017
Posts: 138
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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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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.

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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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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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

Give kudos if you like explanation

Posted from my mobile device
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Intern  B
Joined: 07 Feb 2017
Posts: 26
Location: Singapore
Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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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.

Please correct me if I'm wrong or change the off ans.
Intern  B
Joined: 07 Feb 2017
Posts: 26
Location: Singapore
If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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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

Give kudos if you like explanation

Posted from my mobile device
Manager  B
Joined: 04 Jun 2010
Posts: 87
Location: India
GMAT 1: 660 Q49 V31 GPA: 3.22
Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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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

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.
Intern  B
Joined: 12 Oct 2017
Posts: 15
Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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can any expert clarify this?
Intern  B
Joined: 28 Dec 2018
Posts: 1
Re: If x is an integer between 0 and 10 is y less than the average of x an  [#permalink]

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1

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
Intern  B
Joined: 20 Nov 2018
Posts: 19
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 ?

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 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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