If © denotes one of three arithmetic operations, addition, subtraction

Question

If  ©  denotes one of three arithmetic operations, addition, subtraction, or division, and  2©x > x©2 , where  x  is a positive integer, what is the value of  x ?

A. 0
B. 1
C. 2
D. 3
E. Cannot be determined from the given information

Bunuel · Accepted Answer

Official Solution: If © denotes one of three arithmetic operations, addition, subtraction, or division, and 2©x > x©2 , where x is a positive integer, what is the value of x ? A. 0 B. 1 C. 2 D. 3 E. Cannot be determined from the given information If © represents addition, we'd have 2 + x > x + 2 , which is not true for any value of x . Hence, © is not addition. If © represents subtraction, we'd have 2 - x > x - 2 , simplifying to x < 2 . Given that x is a positive integer, if © is subtraction, then x must be 1. If © represents division, we'd have \frac{2}{x} > \frac{x}{2} . Cross-multiplying (we can safely do that since x is a positive integer) gives x^2 < 4 , which narrows down to -2 < x < 2 . As x is a positive integer, x must be 1. Therefore, if © is division, x is 1. In both viable cases (subtraction or division), x turns out to be 1. Answer: B

gmatophobia · Answer

The following operations are possible - 2 + x > x + 2 2 - x > x - 2 2 * x > x * 2 \frac{2 }{ x} > \frac{x }{ 2} Out of the following operations, the below are invalid 2 + x > x + 2 2 * x > x * 2 Case 1 : 2 - x > x - 2 2x < 4 x < 2 As x is positive, the value of x = 1 Case 2 : \frac{2 }{ x} > \frac{x }{ 2} x^2 < 4 -2 < x < 2 As x is positive, the value of x = 1 Option B

Nidzo · Answer

From  2©x>x©2  we can eliminate  ©  being addition as both sides would be equal to one another.

If  ©  is subtraction, for  2©x>x©2  to hold  x  must be smaller than  2 .

If  ©  is division, for  2©x>x©2  to hold  x  must be smaller than  2  and not be  0 , as dividing by zero is undefined.

From the answer choices, the only value which fits these parameters is B. 1.

ANSWER B

prantorboni · Answer

We need to find a value for x with appropriate operations among addition, subtraction and division that justify the equation,  2©x>x©2.
Now, keeping this in mind, after several trial of different numbers with addition and subtraction, we can easily figure out that addition and subtruction do not justify the quation, 2©x>x©2 i.e. 2+2>2+2 or 2-2>2-2.
However, if we consider division and the value of X equal 1, then euation becomes, 2>1/2, which is certainly true.
So, Answer B.

ablatt4 · Answer

There are 3 options here
1) 2+x>x+2
2) 2-x>x-2
3) 2/x>x/2

In option 1 we can see that no matter the value of x this equation cannot be true as both sides of the equation are identical. 
Option 2 and 3 are both viable so lets move toward the answer choices.
0 doesn't work because 2/0 is undefined
1 works because 2-1>1-2 AND 2/1>1/2
2 doesn't work because this would make the subtraction equation 0>0 and the division equation 1>1
3 doesn't work because 2-3=-1 and 3-2 =1 and -1>1 would be false
We can conclude the answer from these choices as only B (1) would allow both viable statements to be true

B is the answer

EthanTheTutor · Answer

You have to be careful with "Cannot be determined" - because that's in the answer choices, it's possible that in some case x=1 works, and in some other case x=4 works. Testing 0, 1, 2, 3 doesn't cover it.

If © denotes one of three arithmetic operations, addition, subtraction

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If © denotes one of three arithmetic operations, addition, subtraction

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