If a and b are different integers and |a| = square_root ab

Question

If  a  and  b  are different integers and  |a|=\sqrt{ab}  which of the following must be true?

1.  a=b  
2.  a=-b  
3.  a=0

A. 1 and 2
B. 1 and 3
C. 1 only
D. 2 only
E. 3 only

niks18 · Accepted Answer

|a| = \sqrt{ab} , Square both sides

a^2=ab=> a^2-ab=0

a(a-b)=0 . This implies either  a=0  or  a=b . but it is given that  a  &  b  are different integer. Hence  a=0

Option  E

GMATBusters · Answer

Another approach:
1.Since a and b are different integers. a can't be qual to b. Eliminate statement 1.
2.If a = -b, then a*b = -b^2 (negative) for which square root of ab is not defined, if both are not equal to 0. Eliminate statement 2.
3.Hence a has to be 0.

Answer E.

OC2910 · Answer

|a| = square_root ab
test the options that repeats the most 
1. a=b (not possible as question says they are different )

eliminate A,B,C options 
2. a=−b 
3. a=0 (putting zero satisfies the equation )
so eliminate D

a. 1 and 2
b. 1 and 3
c. 1 only
d. 2 only
e. 3 only (answer)

mysterymanrog · Answer

Notice that the absloute value of a and square root of ab must both return a non-negative value. 
This implies that a and b must have the same sign, as if they are opposing sign root(ab) will return a non-real value. 
Knowing the above and knowing that a and b are different integers, there is only 1 case: where a is 0, and b is any digit.

E

Kinshook · Answer

Asked: If  a  and  b  are different integers and  |a|=\sqrt{ab}  which of the following must be true?

a^2 = ab
a^2 - ab = 0
a(a-b) = 0

Either a =0
or
a-b=0 or a=b; Not true since a & b are different integers

a = 0

1.  a=b 
If a=0; May not be true 
2.  a=-b  
May not be true 
3.  a=0 
Must be true

A. 1 and 2
B. 1 and 3
C. 1 only
D. 2 only
E. 3 only

IMO E

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If a and b are different integers and |a| = square_root ab

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If a and b are different integers and |a| = square_root ab

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