What is the value of xy? (1) y = x + 1 (2) y = x^2 + 1

Question

What is the value of xy?

(1) y = x + 1

(2) y = x^2 + 1

Praveenksinha · Accepted Answer

1) y = x + 1
Not sufficient

(2) y = x^2 + 1
Not Sufficient

combining both 1 and 2
X+1=X^2+1
X(X-1)=0
X=0,X=1
If X=0 then XY=0,but If X=1 then XY=Y clearly not sufficient

GMATinsight · Answer

Question : What is the value of xy?

Statement 1 :  y = x + 1

x and y both are unknown hence 
NOT SUFFICIENT

Statement 2 :  y = x^2 + 1

x and y both are unknown hence 
NOT SUFFICIENT

Combining the two statements

y = x+1 = x^2 + 1

i.e.  x = x^2 
i.e.   x = 0  and  y = 1    or   x = 1  and  y = 2  
i.e.  xy = 0  or  xy = 2

NOT SUFFICIENT

Answer: Option E

Pritishd · Answer

We need a single value of  xy  in order to conclude a statement sufficient

(1)  y = x + 1  -   Insufficient  
1. Replacing  y  with  x + 1  into  xy  we get  x(x+1) 
2. But, this statement does not help us arrive at a unique value for  xy

(2)  y = x^2 + 1  -   Insufficient  
1. Replacing  y  with  x^2 + 1  into  xy  we get  x(x^2+1) 
2. But, this statement does not help us arrive at a unique value for  xy

Combined  -   Insufficient  
1. Putting the values of  y  on either side we get,  x + 1 = x^2 + 1 
2.  x^2 - x = 0 
3.  x(x - 1) = 0 , we get  x = 0  or  x = 1 
4. Substituting the value of  x  we get  y = 1    @    x = 0  and  y = 2    @    x = 1 
5. Using the two sets of values we can get two different values of  xy = 0  and  2

Ans.  E

BrentGMATPrepNow · Answer

Target question :    What is the value of xy?

Statement 1 : y = x + 1  
There are several values of x and y that satisfy statement 1. Here are two: 
 Case a : x = 0 and y = 1. In this case, the answer to the target question is  xy = (0)(1) = 0 
 Case b : x = 1 and y = 2. In this case, the answer to the target question is  xy = (1)(2) = 2 
Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : y = x² + 1  
The statement doesn't feel sufficient either, so let's test some more values. 
  Strategy: When considering possible values to test for statement 2, you can save yourself some time by seeing if any of the values you used when testing statement 1 also work for statement 2.   
In this case, BOTH pairs of values that satisfied statement 1 also satisfy statement 2, which means we can repurpose them to get...
 Case a : x = 0 and y = 1. In this case, the answer to the target question is  xy = (0)(1) = 0 
 Case b : x = 1 and y = 2. In this case, the answer to the target question is  xy = (1)(2) = 2 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
  IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.   
In other words, 
 Case a : x = 0 and y = 1. In this case, the answer to the target question is  xy = (0)(1) = 0 
 Case b : x = 1 and y = 2. In this case, the answer to the target question is  xy = (1)(2) = 2 
Since we can’t answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Important: Some students will conclude that since the combined statements include 2 different equations with 2 variables, the combined statement should be sufficient. However, this rule applies only to situations in which the two equations are LINEAR equations.

Cheers,
Brent

KanikaJain · Answer

What is the value of xy?
(1) y = x + 1
(2) y = x^2 + 1

Statement 1:
xy = (x+1)x 
Value dependent on x

Statement 2:
xy = (x^2 + 1)x
Value dependent on x

on comparing values of y:
(x^2 + 1) = x + 1
thus x^2 = x

now x cannot be cancelled as if the value of x = 0.
thus x(x-1) = 0
thus x = 1, 0

and hence the value of y changes. 
thus xy value changes.

hence E

What is the value of xy? (1) y = x + 1 (2) y = x^2 + 1

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What is the value of xy? (1) y = x + 1 (2) y = x^2 + 1

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