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QANT Guide Q98

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Source: — Problem Solving |

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by Brent@GMATPrepNow » Fri May 10, 2013 10:03 pm
cpay3245 wrote:Which of the following CANNOT be the greatest common divisor of two positive integers x and y?

a) 1
b) x
c) y
d) x-y
e) x + y
APPROACH A:
We'll solve this by eliminating the answer choices that CAN be greatest common divisor (GCD) of two positive integers x and y.

A) x = 2 and y = 3, which means the GCD = 1. ELIMINATE A
B) x = 2 and y = 4, which means the GCD = 2 = x. ELIMINATE B
C) x = 4 and y = 2, which means the GCD = 2 = y. ELIMINATE C
D) x = 3 and y = 2, which means the GCD = 1 = x-y. ELIMINATE D

By the process of elimination, the correct answer must be E



APPROACH B:
Recognize that the GCD of x and y must be less than or equal to x and less than or equal to y.
Since x + y is greater than x and y, it could never be the GCD of x and y.

Answer = E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri May 10, 2013 10:23 pm, edited 1 time in total.
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by srcc25anu » Fri May 10, 2013 10:05 pm
The Greatest Common Divisor between any two numbers cannot be greater than the greater number itself (if both numbers are same)
For example, GCD of 4 and 4 cannot in any case be greater than the larger number itself that is 4. AND if two numbers are different, GCD will be less than the larger / largest number. for instance GCD of 3 and 9 will always be less than 9. GCD is 3 in this case.

So for the given question, GCD of X and Y cannot be X + Y (which is greater than either of the numbers)
Ans E

Also trying out numbers will help arrive at the correct solution.
A. x = 1, y = 3 GCD = 1
B. x = 2, y = 4 GCD = x = 2
C. x = 4, y = 2 GCD = y = 2
D. x = 6, y = 3 GCD = x - y = 6-3 = 3
E. NOT POSSIBLE
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by cpay3245 » Fri May 10, 2013 10:50 pm
srcc25anu wrote:The Greatest Common Divisor between any two numbers cannot be greater than the greater number itself (if both numbers are same)
For example, GCD of 4 and 4 cannot in any case be greater than the larger number itself that is 4. AND if two numbers are different, GCD will be less than the larger / largest number. for instance GCD of 3 and 9 will always be less than 9. GCD is 3 in this case.

So for the given question, GCD of X and Y cannot be X + Y (which is greater than either of the numbers)
Ans E

Also trying out numbers will help arrive at the correct solution.
A. x = 1, y = 3 GCD = 1
B. x = 2, y = 4 GCD = x = 2
C. x = 4, y = 2 GCD = y = 2
D. x = 6, y = 3 GCD = x - y = 6-3 = 3
E. NOT POSSIBLE
The answer is E...?
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by srcc25anu » Fri May 10, 2013 10:56 pm
cpay3245 wrote:The answer is E...?
E it is.
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by Jeff@TargetTestPrep » Tue Jan 02, 2018 7:31 am
cpay3245 wrote:Which of the following CANNOT be the greatest common divisor of two positive integers x and y?

a) 1
b) x
c) y
d) x-y
e) x + y
Since the greatest common divisor or greatest common factor (GCF) of any two positive integers must be no larger than the lesser of the two integers, the GCF can't be sum of the two integers. That is, the GCF of x and y can't be x + y.

Answer: E

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by Brent@GMATPrepNow » Tue Jan 02, 2018 8:32 am
cpay3245 wrote:Which of the following CANNOT be the greatest common divisor of two positive integers x and y?

a) 1
b) x
c) y
d) x-y
e) x + y
Jeff's approach (recognizing that the GCD of two values cannot be greater than each value) is perfect.
However, if you didn't spot that, you can always use the Process of Elimination.

The question asks "Which of the following CANNOT be the greatest common divisor of x and y?"
So, if we can find values for x and y such that an answer choice CAN be the greatest common divisor of x and y, then we can ELIMINATE that answer choice

For example, if x = 3 and y = 2, then the GCD of x and y is 1
So, we can ELIMINATE A.
We can also ELIMINATE D since x - y = 3 - 2 = 1

Next, if x = 2 and y = 4, then the GCD of x and y is 2 (aka x)
So, we can ELIMINATE B.

Similarly, if x = 4 and y = 2, then the GCD of x and y is 2 (aka y)
So, we can ELIMINATE C.

By the process of elimination, the correct answer must be E

Cheers,
Brent
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