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If y is a negative number greater than -8, is x greater than

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If y is a negative number greater than -8, is x greater than [#permalink] New post 01 Jun 2010, 19:39
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If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ?

(1) On the number line, x is closer to -8 than it is to y.
(2) x = 4y
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Re: 600 level question [#permalink] New post 02 Jun 2010, 04:32
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shekar123 wrote:
If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ?

(1) On the number line, x is closer to -8 than it is to y.
(2) x = 4y


Given: -8<y<0.
Q: is x greater than the average of -8 and x? Or: is x>\frac{-8+y}{2}? --> 2x>-8+y?

-----{-8}-----{average}-----{y} (average of y and -8 is halfway between y and -8).

(1) On the number line, x is closer to -8 than it is to y.

Now, as x is closer to -8 than it (x) is to y, then x is either in the green area, so less than average OR in the red area, so also less than average. Answer to the question is NO.

Sufficient.

(2) x=4y --> is 2x>-8+y? --> is 8y>-8+y? --> is y>-\frac{8}{7}? We don't now that. Not sufficient. (we've gotten that if 0>y>-\frac{8}{7} (for instance if y=-1), then the answer to the question is YES, but if y\leq{-\frac{8}{7}} (for instance if y=-2), then the answer to the question is NO.)

Answer: A.

Similar question: number-line-problem-22709.html#p719532

Hope it helps.
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Re: 600 level question [#permalink] New post 02 Jun 2010, 06:46
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Re: 600 level question [#permalink] New post 02 Jun 2010, 14:19
Bunuel wrote:
shekar123 wrote:
If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ?

(1) On the number line, x is closer to -8 than it is to y.
(2) x = 4y


Given: -8<y<0.
Q: is x greater than the average of -8 and x? Or: is x>\frac{-8+y}{2}? --> 2x>-8+y?

-----{-8}-----{average}-----{y} (average of y and -8 is halfway between y and -8).

(1) On the number line, x is closer to -8 than it is to y.

Now, as x is closer to -8 than it (x) is to y, then x is either in the green area, so less than average OR in the red area, so also less than average. Answer to the question is NO.

Sufficient.

(2) x=4y --> is 2x>-8+y? --> is 8y>-8+y? --> is y>-\frac{8}{7}? We don't now that. Not sufficient. (we've gotten that if 0>y>-\frac{8}{7} (for instance if y=-1), then the answer to the question is YES, but if y\leq{-\frac{8}{7}} (for instance if y=-2), then the answer to the question is NO.)

Answer: A.

Similar question: number-line-problem-22709.html#p719532

Hope it helps.



I still can't get option (2)...:(
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Re: 600 level question [#permalink] New post 02 Jun 2010, 14:52
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shekar123 wrote:
Bunuel wrote:
shekar123 wrote:
If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ?

(1) On the number line, x is closer to -8 than it is to y.
(2) x = 4y


Given: -8<y<0.
Q: is x greater than the average of -8 and x? Or: is x>\frac{-8+y}{2}? --> 2x>-8+y?

-----{-8}-----{average}-----{y} (average of y and -8 is halfway between y and -8).

(1) On the number line, x is closer to -8 than it is to y.

Now, as x is closer to -8 than it (x) is to y, then x is either in the green area, so less than average OR in the red area, so also less than average. Answer to the question is NO.

Sufficient.

(2) x=4y --> is 2x>-8+y? --> is 8y>-8+y? --> is y>-\frac{8}{7}? We don't now that. Not sufficient. (we've gotten that if 0>y>-\frac{8}{7} (for instance if y=-1), then the answer to the question is YES, but if y\leq{-\frac{8}{7}} (for instance if y=-2), then the answer to the question is NO.)

Answer: A.

Similar question: number-line-problem-22709.html#p719532

Hope it helps.



I still can't get option (2)...:(


Stem: -8<y<0.

Statement:(2) x=4y

Based on the above 2 informations can we answer whether: 2x>-8+y? No.
If y=-1>-8, then x=-4 and 2x=-8>-8+y=-8-4=-12 - answer to the question is YES;
If y=-2>-8, then x=-8 and 2x=-16<-8+y=-8-2=-10 - answer to the question is NO.

Two different answers to the question is 2x>-8+y?

Hope it's clear.
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Re: 600 level question [#permalink] New post 02 Jun 2010, 20:59
great explanation.


Statement:(2) x=4y

Based on the above 2 informations can we answer whether: 2x>-8+y? No.
If y=-1>-8, then x=-4 and 2x=-8>-8+y=-8-4=-12 - answer to the question is YES;
If y=-2>-8, then x=-8 and 2x=-16<-8+y=-8-2=-10 - answer to the question is NO.

Two different answers to the question is 2x>-8+y?
great explanation
Hope it's clear.[/quote]
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Re: Number line question [#permalink] New post 19 Sep 2010, 15:19
A is enough... Basically it is asking if x is closer to y or -8?, A gives us the answer...

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Re: Number line question [#permalink] New post 19 Sep 2010, 15:23
zisis wrote:
If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ?

(1) On the number line, x is closer to -8 than it is to y.

(2) x = 4y


A is enough, if x is closer to -8 than y and y>-8 then x will be less than the average of -8 and y (answering NO to the question)

B is not enough. Eg. y=-0.5, x=-2, avg=-4.25 x is greater; y=-6, x=-24, avg=-16 x is lesser

Hence, ans is A
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Re: Number line question [#permalink] New post 19 Sep 2010, 15:24
zisis wrote:
If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ?

(1) On the number line, x is closer to -8 than it is to y.

(2) x = 4y


I just substituted numbers in each of the choices and arrived at A. But it took me 3:05 mins to solve this...I am always taking extra time in solving such problems...ANyone please suggest a short cut in solving such type of problems...Always when I substitute values in these kind of problems I take a minimum of 3 minutes.. :(
Any suggestion is greatly appreciated.

Choice (A)
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Re: Number line question [#permalink] New post 19 Sep 2010, 15:28
vigneshpandi wrote:
I just substituted numbers in each of the choices and arrived at A. But it took me 3:05 mins to solve this...I am always taking extra time in solving such problems...ANyone please suggest a short cut in solving such type of problems...Always when I substitute values in these kind of problems I take a minimum of 3 minutes.. :(
Any suggestion is greatly appreciated.

Choice (A)


In this question, if you draw a number line, most of the answer will just come to you as obvious
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Re: 600 level question [#permalink] New post 19 Sep 2010, 15:53
Thank you guys..I will use it going forward...
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Re: 600 level question [#permalink] New post 14 Oct 2010, 18:49
A

1) x is closer to -8 than y so x is towards -8 away from mid-point (=avg). so x is < avg ==> SUFF

2) x = 4y

y=-7 => x=-28 --> no
y=1 => x=4 ---> yes
no and yes ==> INSUFF
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Re: 600 level question [#permalink] New post 17 Jan 2011, 09:40
'A' can't be the correct answer -

given --> -8<y<0

so , when y =-1 , [-1+(-8)] /2=-4.5
when y=-7, [-7+(-8)]/2= -7.5

now if x is closer to -8 means , x<-4.5

but there is no connection between values of X and Y [ie, value of x is independent of Y] so,
if x=-4.6 then , x>-7.5 [where -7.5 is one of the values of average of y and -8]
if x=-7.8 then , x<-7.5 [where -7.5 is one of the values of average of y and -8]

but if x=4y is also considered then x will always be greater than average of y and -8

so correct ans must be C .

please correct me if i'm wrong
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Re: 600 level question [#permalink] New post 17 Jan 2011, 09:52
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reg wrote:
'A' can't be the correct answer -

given --> -8<y<0

so , when y =-1 , [-1+(-8)] /2=-4.5
when y=-7, [-7+(-8)]/2= -7.5

now if x is closer to -8 means , x<-4.5

but there is no connection between values of X and Y [ie, value of x is independent of Y] so,
if x=-4.6 then , x>-7.5 [where -7.5 is one of the values of average of y and -8]
if x=-7.8 then , x<-7.5 [where -7.5 is one of the values of average of y and -8]

but if x=4y is also considered then x will always be greater than average of y and -8

so correct ans must be C .

please correct me if i'm wrong


OA (official answer) for this question is A. not C.

If you consider y=-7 so that the average of -8 and y to be -7.5 then x=-4.6 is not a proper value for x as (1) says that x is closer to -8 than it (x) is to y.

Refer to the correct solutions above.
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Re: If y is a negative number greater than -8, is x greater than [#permalink] New post 31 Aug 2013, 05:22
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Re: If y is a negative number greater than -8, is x greater than   [#permalink] 31 Aug 2013, 05:22
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