QANT Guide Q98

Question

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

Brent@GMATPrepNow · Answer

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.

Brent Hanneson - Creator of GMATPrepNow.com

srcc25anu · Answer

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

cpay3245 · Answer

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...?

srcc25anu · Answer

cpay3245 wrote:The answer is E...? E it is.

Jeff@TargetTestPrep · Answer

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Brent@GMATPrepNow · Answer

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.

Brent Hanneson - Creator of GMATPrepNow.com

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

QANT Guide Q98

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER