M41-14

Question

If  a ,  b , and  c  are positive constants, how many different numbers  y  are there such that  a*y + b = c ?

A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information

Bunuel · Answer

Official Solution:

If  a ,  b , and  c  are positive constants, how many different numbers  y  are there such that  a*y + b = c ?

A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information

Since  a  is nonzero, then  y = \frac{c - b}{a} = \frac{c - b}{nonzero \ number} .
 
As a result, regardless of the value of  c - b , the equation  a*y = c - b  will always have only one solution, given by:  y =\frac{c - b}{nonzero \ number} .

Answer: B

Josvit · Answer

a*y+b=c

a= 1, b=2, c=3; y=1
a=2, b=3, c=7; y=2
a=3, b=4, c=13; y=3

.... and so on.

Because the question is not asking about y in terms of a,b or c. Perhaps, some additional details might be good for this. thanks.

Bunuel · Answer

We are told that a, b, and c are constants, meaning that each has one fixed value.

prabhatshahi9 · Answer

Is there no possibility that c=b? In this case, y=0, otherwise with all constants>0, y would have a fixed solution. If we do consider the first case too, then there would be 2 possible values of y

Bunuel · Answer

c can be equal to b; however, this changes nothing. Again, a, b, and c are constants, meaning that each has a single fixed value. Therefore, regardless of their specific values, there is exactly one possible value for y. If you claim that there will be two values of y possible, then please provide specific values for a, b, and c such that, when substituted into a * y + b = c, the equation yields two distinct values for y.

prabhatshahi9 · Answer

Thanks for the detailed explanation, got it now

SaiJ1011 · Answer

I came across a similar question which just had "different constants" instead of "positive constants" in the question.
That question had the answer of Cannot be Determined.

How much of a difference does this make can you please explain? Didn't understand this quite well.

Thanks

Bunuel · Answer

Positive constants  means constants are positive. However, in general, they can be equal.

Different constants  just means they are not equal to each other, but any of them could be negative, zero, or positive.

SaiJ1011 · Answer

Thanks got it!

pavanhra · Answer

Can someone explain me this.

if a =1 b = 2 c = 10 Y = 10-2/1 = 8
if a = 2 b = 3 c = 15 Y = 15-3/2 = 4

different values are possible for right? how 1 value is the solution here? Y = (c-b)/a

Bunuel · Answer

a, b, and c are constants, meaning they have fixed values. Once these values are set, the equation a*y + b = c has only one solution for y, given by y = (c - b)/a. The value of y changes if a, b, or c changes, but for any fixed set, there is only one y. So the answer is B: 1.

needforspeed112 · Answer

I did not quite understand the solution. they asked different numbers not ..... number of solutions 
and through combinations of a,b,c we can get as many different numbers as we want

Bunuel · Answer

Please check again:

If  a ,  b , and  c  are positive constants, how many   different numbers  y    are there such that  a*y + b = c ?

750rest · Answer

I did not quite understand the solution. Couldn't understand how value of Y will be only one

Bunuel · Answer

Since a is a positive constant, a is not 0.

So once a, b, and c are fixed, the equation a * y + b = c forces y to have one specific value.

For example, if 2 * y + 3 = 11, then y must be 4. No other value of y can work.

Same logic here: because y is multiplied by a nonzero number, there is only one possible value of y.

M41-14

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