Data Sufficiency

selango 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

Source:Grockit

+1 for A

Looking for OA!!

Hi:

Y is between -8 and 0 (given that it is negative and greater than -8). Arithmetic mean of Y and -8 is a no halfway between Y and -8 ==> is a negative no

#1 --> x is closer to -8 than Y means that X could be <-8 or x could be between -8 and Y.
If X is <-8 than it is < average of -8 and Y (which is -8 < MEAN < Y)
If X is >-8 and is closer to -8 than Y then it is less than MEAN (which is equidistant from -8 and Y)
So #1 = sufficient

#2 --> X = 4Y. If Y== -1 than X=-4 and is > -4.5 (MEAN of -8 and Y)
If Y == -5 then X=-20 and is <MEAN
So not sufficient


HENCE ans = A

Here is the original source of this problem that is based on GMATPrep and discussed in the following post:

https://www.beatthegmat.com/gmat-prep-in ... 89109.html

Read gmatboost and bblast's explanations.

Dabral

selango 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

Source:Grockit

To Fabio:

In your explanation you state that y < 2x+8 or y < 8(y+1) or (y+1)/y < 1/8.

I understand how you got y < 2x+8 but where did you get y < 8(y
+1)? I think I am missing something there.

+1 for A

From stem we are asked, Is x>(y-8)/2 given y >-8 and its negative i.e. 0>y>-8.

From, Statement 2, x=4y
0>y>-8 From stem
0>4y>-32 Multiply throughout by 4
0>x>-32

Now if x=-1, y = -8 , Is x>(y-8)/2? YES
Now if x=-31, y = -8 , Is x>(y-8)/2? NO

So, statement 2 is INSUFFICIENT.

From, Statement 1, x is closer to -8 than it is to y.
|x+8|<|x-y|
Is x>(y-8)/2? given i.e. 0>y>-8.

Now if y = -1, x = -7 --> Is x>(y-8)/2? NO
Now if y = -4, x = -7 --> Is x>(y-8)/2? NO
Now if y = -6, x = -7.5 --> Is x>(y-8)/2? NO

Answer should be A.
I did it in 2.5 minutes, any shortcuts?

Well I do not know how am I not getting the answer as A. I am getting the answer as E.

watever explanation u have given i read those but i have a doubt in this question...

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


Statement 1:

lets say that if y = -6 and x = -7, then the average of -6 and -8 is -7.

also x = -7

hence it can't be said that x will always be closer than the mean of y and -8.

according to me the answer is E......

I hope this helps...!!!

[email protected] wrote:Well I do not know how am I not getting the answer as A. I am getting the answer as E.

watever explanation u have given i read those but i have a doubt in this question...

answer is A
-8<y<0, Question: Is 2x>y-8?

st(1) implies distance between x and -8 is shorter than the distance between x and y OR |x-(-8)|<|x-y|, Tip~ mode is convenient for measuring distance between the numbers on the number line.

|x+8|<|x-y|, Solve by squaring both sides, this will be quicker. x^2+16x+64<x^2-2xy+y^2, y^2-2xy-16x-64>0, y^2-2x(y+8)-64>0, (y^2-64)/(y+8)>2x, (y-8)(y+8)/(y+8)>2x, y-8>2x Sufficient to answer No

st(2) provides x=4y and by multiplying both sides by 2 we get 2x=8y. From the question we know -8<y<0 and for example two cases considered:
case a) y=-1, x=-4 and to answer the question 2x>y-8 we test -8>-1-8, Yes
case b) y=-7, x=-28 and test 2x>y-8 returns -56>-7-8, No
Not Sufficient.

~Tip, you can directly answer st(2) Not Sufficient as x=4y implies literally x and y can be everything and contradicts our question's constraint -8<x<0

Make number line to answer these questions.
(A) is the answer.

IMO (A)
QED

answer is E

A is the ans!!

D in answer

A in answer