Data Sufficiency

Hi Two questions from GMAT prep s/w, looking for the best method to solve it:

#A) If X and Y are integers & Y=|X+3| + |4-X|, does Y=7?
(1) X<4
(2) X>-3

[Answer is C]


#B) If both X and Y are non-zero numbers, what is the value of Y/X?

(1) X=6
(2) Y^2=X^2

[Answer is E]

aditi_bc wrote:Hi Two questions from GMAT prep s/w, looking for the best method to solve it:

#A) If X and Y are integers & Y=|X+3| + |4-X|, does Y=7?
(1) X<4
(2) X>-3

[Answer is C]

Y=|X+3| + |4-X|
Y = lX-(-3)l + l4-Xl

this can be deciphered as Y is equal to addition of distance between x and -3 and distance between 4 and x on a number line.

Therefore, if y=7, x has to be between -3 and 4

The question is basically asking -3<x<4 ?

Statement (1) & (2) gives us exactly that.

Thus, C is the answer.

#B) If both X and Y are non-zero numbers, what is the value of Y/X?

(1) X=6
(2) Y^2=X^2

[Answer is E]

Y/X

statement (1) X=6, we dont know anything about Y. Insufficient.

statement (2) Y^2 = X^2

X^2/Y^2 = 1

X/Y = +1 OR -1
Insufficient.

Combining (1) & (2)

X=6
6/Y = -1
6/Y = +1
Insufficient.

Thus, E is the answer.

Thanks Morgoth!

Is there any other way of working with the expression Y=|X+3| + |4-X|?

aditi_bc wrote:Thanks Morgoth!

Is there any other way of working with the expression Y=|X+3| + |4-X|?

Morgoth, could you please elaborate your approach to these expression?
How you deducted that it is the same as -3<x<4 ?

4meonly wrote:

aditi_bc wrote:Thanks Morgoth!

Is there any other way of working with the expression Y=|X+3| + |4-X|?

Morgoth, could you please elaborate your approach to these expression?
How you deducted that it is the same as -3<x<4 ?

Here is the process:

Let the two points be -2 and 2

Let x is the distance between -2 and 2 = l-2-2l = 4 or l2-(-2)l = 4

if y is the point between -2 and 2

X = ly-(-2)l + l2-yl

X = ly+2l + l2-yl

for any value of y between the -2 and 2, X will always be 4

Let me know if you still have any doubts.

wow, great explanation Morgoth. Thx

insane explanation morgoth!