If a, b, and c are constants, how many different numbers y are there

Question

If  a ,  b , and  c  are constants, how many different numbers  y  are there such that  a*y + b = c ?
 
(1)  c >b 
 
(2)  a > 1

M39-36

chetan2u · Answer

We are looking for number of values that y can take and not for specific value of y.

Since we are dealing with three constants, A, B and C, so equation Ay+B=C tells us that y should also have just one value as there is no INEQUALITY or VARIABLES we are dealing with.

However, if A is 0, y can be any value as Ay will also be 0.

(1) C > B
Does not matter as y can be fraction, integer or decimal to satisfy the equation. 
Insufficient

(2) A > 1
So, we have only one value for y. 
Sufficient

B

Bunuel · Answer

The analysis for (1) is not precise. For (1), if A = 0, then no value of y can satisfy the equation. So, y cannot take any value.

Bunuel · Answer

This is a tricky algebra question, so I recommend studying it carefully.

chetan2u · Answer

Yes, you are correct. A=0 will give C=B, while statement I says that C>B. Thus, A=0 will not be valid for statement 1.
y=(C-B)/A

VenDeTa796 · Answer

IMO B.

According to the question. 
Ay+B=C
Ay=C-B

Case I
C>B
then we know that RHS>0
If A!=0, then 1 solution
if A=0, then 0 solutions

Case II
A>1
B-C will take a definitive value and y=(B-C)/A

Alternatively y=(B-C)/A, for y to have a value, A cannot be equal to 0

seikoholic · Answer

Will you provide a detailed solution and analysis?

Posted from my mobile device

TheWrongGrammer · Answer

Bunuel 
Can you please explain -
A> 1 signifies A can take any values greater than 1.
And if that’s the case then y will have multiple values based on A (and also B and C because even though the value B and C ate constant, their value have not been defined )
?

Posted from my mobile device

Bunuel · Answer

Official Solution:

If  a ,  b , and  c  are constants, how many different numbers  y  are there such that  a*y + b = c ? 
 
(1)  c >b 
 
Given  c - b > 0 , this means  a*y = some \ positive \ number .
 
If  a = 0 , then no value of  y  can satisfy this equation, as  0*y = positive\ number  has no solutions for  y .
 
If  a ≠ 0 , then only 1 value of  y  can satisfy this equation, since in this case  y = \frac{c - b}{a} .
 
Not sufficient.
 
(2)  a > 1 
 
 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} .
 
Sufficient.

Answer: B

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If a, b, and c are constants, how many different numbers y are there

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