If x and y are positive integers and y = 9 - x, what is the

Question

If x and y are positive integers and  y=\sqrt{9 - x} , what is the value of y?

(1) x < 8
(2) y > 1

Bunuel · Accepted Answer

Given:  x  and  y  are  positive integers  and  y=\sqrt{9-x}  -->  y^2=9-x  -->  y^2  is a  positive perfect square less than 9 : so  y^2=4=2^2  if  x=5  or  y^2=1=1^2  if  x=8 .

(1) x < 8 -->  x=5  and  y=2 . Sufficient.
(2) y > 1 -->  y=2 . Sufficient.

Answer: D.

ajit257 · Answer

Hi Bunuel,
 why is 2nd statement sufficient. why cant y be root 3 ..it is also greater than 1 or for that matter any integer greater than 1

Bunuel · Answer

You should read the stem carefully: "If x and y are  positive integers ..."

Also  y^2=9-x  --> as given that  y  is a positive integer then  y^2  is a  positive perfect square less than 9  (perfect square is a square of an integer): so  y^2=4=2^2  if  x=5  or  y^2=1=1^2  if  x=8 .

Bunuel · Answer

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WoundedTiger · Answer

For the given expression we have x,y are positive integers and therefore squaring both sides y^2= 9-x From St 1 we have x< 8 -----> so we have possible value of in the range 01 so we have y^2=9-x Now let us say y=2 so x=5 y=3, we get 9=9-x ----> x=0 which is not possible as "x" is a positive integer hence y=2 Ans should be D I messed it with choosing A as ans trying to beat the average time and not carefully solving the st2 :oops:

KarishmaB · Answer

y=\sqrt{9 - x}

x and y are positive integers. 
If x could be 0, y = 3
If x = 9, y = 0 (not allowed)

So y can be either 1 (x = 8) or 2 (x = 5)

(1) x < 8
So x cannot be 8. It must be 5 and y must be 2.
Sufficient alone.

(2) y > 1
So y cannot be 1. It must be 2. 
Sufficient alone.

Answer (D)

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 2 variables and 1 Equation: Let the original condition in a DS question contain 2 variables and 1 Equation. Now, 2 variables and 1 Equation would generally require 1 more equation for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 1 more equation to match the numbers of variables and equations in the original condition, the logical answer is D.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find the value of 'y'.

=> 'x' and 'y' are positive integers and y = \(\sqrt{9 - x}\)

=> y = \(\sqrt{9 - x}\) = \(y^2\) = 9 - x [\(y^2\) is a perfect square less than '9' for a value of 'x']

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x and y) and 1 Equation (y = \(\sqrt{9 - x}\)).To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take look at each condition separately.

Condition(1) tells us that x < 8.

=> For x = 5: \(y^2\) = 9 - 5 = 4 and hence y = 2

Since the answer is unique , Condition(1) is alone sufficient by CMT 2.

Condition(2) tells us that y > 1.

=> For y = 2: \(y^2\) = 9 - 5 = 4 [a perfect square]

Since the answer is unique , Condition(2) is alone sufficient by CMT 2.

Each condition alone is sufficient.

So, D is the correct answer.

Answer: D

SAVE TIME: By Variable Approach, when you know that value of Con(1) = Con(2), then 'D' is the correct answer.

bumpbot · Answer

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If x and y are positive integers and y = 9 - x, what is the

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