|y - r| = p and y

Question

If  |y - r| = p  and  y < r , what is the value of  y - p ?

(A)  r - p 
(B)  p - r 
(C)  r - 2p 
(D)  2p - r 
(E)  p

agrasan · Answer

Since y < r, |y - r| = -(y-r) = r - y

From question, |y-r| = p
r - y = p
y = r - p

So y - p will be r - 2p

(C) is the answer.

shashag · Answer

Just plug in values to solve this. Take y=0 and r=1 (thereby fulfilling the y<r condition)

This will give p=1.

Now test the options; only  Option C  works.

HarishChaitanya · Answer

hi,

as y is less than r(given) the value of y-r is negative.

because modulus function is used for p. here it becomes p= r-y.

from this we get y=r-p

now the value of y-p = r-2p.

thanks i hope my explanation shall be useful to you.

Axwe7 · Answer

If |y - r| = p
Then either:
1) y - r = p (if y >= r)
2) y - r = -p (if y < r)

Since the question specifies y < r, we must only focus on case two.

So; y - r = -p
Hence, 
y + p = r
( By subtracting 2p on both sides )
y - p =  r - 2p

Hence C

nobisvoluptatum · Answer

Could someone please help explain why E is not the answer?

egmat · Answer

Hi nobisvoluptatum,

E gives back p, which is the quantity you were handed. The question asks for  y - p , and that takes one more step.

Since y < r, |y - r| = r - y = p, so y = r - p.

Then y - p = (r - p) - p =  r - 2p .

That second subtraction of p is the step E skips. It reports the given value in place of the expression the question asked for.

Answer: C

|y - r| = p and y < r , what is the value of