What is the greatest common factor of x and y ?

[BTGmoderatorDC]

What is the greatest common factor of x and y ?

(1) x and y are both divisible by 4
(2) x - y = 4

Can some experts determine whether the statements are sufficient?
Why is the statement 1 lack sufficiency?

OA C

[GMATGuruNY]

What is the greatest common factor of x and y ?

(1) x and y are both divisible by 4
(2) x - y = 4

Statement 1: x and y are both divisible by 4
Case 1: x=4, y=4
Here, the GCF of x and y is 4.
Case 2: x=8, y=8
Here, the GCF of x and y is 8.
Since the GCF can be different values, INSUFFICIENT.

Statement 2: x = y+4
Case 1: y=1, x=5
Here, the GCF of x and y is 1.
Case 2: y=2, x=6
Here, the GCF of x and y is 2.
Since the GCF can be different values, INSUFFICIENT.

Statements combined:
Case 1: y=4, x=8
Case 2: y=8, x=12
Case 3: y=12, x=16
Case 4: y=16, x=20
In every case, the GCF of x and y is 4.
SUFFICIENT.

The correct answer is C.

Rule:
For any two consecutive multiples of k, the GCF is k.'
To illustrate:
The GCF of 3 and 6 -- two consecutive multiples of 3 -- is 3.
The GCF of 15 and 20 -- two consecutive multiples of 5 -- is 5.
The GCF of 90 and 99 -- two consecutive multiples of 9 -- is 9.

Here, the statements combined imply that x and y are two consecutive multiples of 4, with the result that the GCF of x and y must be 4.

[Jay@ManhattanReview]

What is the greatest common factor of x and y ?

(1) x and y are both divisible by 4
(2) x - y = 4

Can some experts determine whether the statements are sufficient?
Why is the statement 1 lack sufficiency?

OA C

We have to determine the greatest common factor of x and y.

Statement 1: x and y are both divisible by 4.

If x and y are both divisible by factors of only 4, then GCD = 4.

If x and y are both divisible by factors of other than 4 also, then GCD ≠ 4. Insufficient.

Statement 2: x - y = 4

The equation means that the difference between the numbers is 4.

If say x = 20 and y = 16, then GCD = 4;
If say x = 10 and y = 6, then GCD = 2. No unique answer. Insufficient.

Statement 1 & 2:

From (1), we know that x and y are both divisible by 4; say x = 4m and y = 4n; where m and n are non-zero integers.

Thus, 4m - 4n = 4
m - n = 1

=> m and n are consecutive numbers and two consecutive numbers do not have any common factor except 1.

Thus, GCD of x and y = 4*1 = 4. Sufficient.

The correct answer: C

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

[BTGmoderatorDC]

What is the greatest common factor of x and y ?

(1) x and y are both divisible by 4
(2) x - y = 4

Statement 1: x and y are both divisible by 4
Case 1: x=4, y=4
Here, the GCF of x and y is 4.
Case 2: x=8, y=8
Here, the GCF of x and y is 8.
Since the GCF can be different values, INSUFFICIENT.

Statement 2: x = y+4
Case 1: y=1, x=5
Here, the GCF of x and y is 1.
Case 2: y=2, x=6
Here, the GCF of x and y is 2.
Since the GCF can be different values, INSUFFICIENT.

Statements combined:
Case 1: y=4, x=8
Case 2: y=8, x=12
Case 3: y=12, x=16
Case 4: y=16, x=20
In every case, the GCF of x and y is 4.
SUFFICIENT.

The correct answer is C.

Rule:
For any two consecutive multiples of k, the GCF is k.'
To illustrate:
The GCF of 3 and 6 -- two consecutive multiples of 3 -- is 3.
The GCF of 15 and 20 -- two consecutive multiples of 5 -- is 5.
The GCF of 90 and 99 -- two consecutive multiples of 9 -- is 9.

Here, the statements combined imply that x and y are two consecutive multiples of 4, with the result that the GCF of x and y must be 4.

Thanks for the answer!

[BTGmoderatorDC]

What is the greatest common factor of x and y ?

(1) x and y are both divisible by 4
(2) x - y = 4

Can some experts determine whether the statements are sufficient?
Why is the statement 1 lack sufficiency?

OA C

We have to determine the greatest common factor of x and y.

Statement 1: x and y are both divisible by 4.

If x and y are both divisible by factors of only 4, then GCD = 4.

If x and y are both divisible by factors of other than 4 also, then GCD ≠ 4. Insufficient.

Statement 2: x - y = 4

The equation means that the difference between the numbers is 4.

If say x = 20 and y = 16, then GCD = 4;
If say x = 10 and y = 6, then GCD = 2. No unique answer. Insufficient.

Statement 1 & 2:

From (1), we know that x and y are both divisible by 4; say x = 4m and y = 4n; where m and n are non-zero integers.

Thus, 4m - 4n = 4
m - n = 1

=> m and n are consecutive numbers and two consecutive numbers do not have any common factor except 1.

Thus, GCD of x and y = 4*1 = 4. Sufficient.

The correct answer: C

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Thanks for the help!

[Matt@VeritasPrep]

(1) x and y are both divisible by 4

Why is the statement 1 lack sufficiency?

With S1, we could have x = 8 and y = 32, or x = 256, y = 256, or whatever. They both divide by 4, so we know one common factor, but they may have an even GREATER common factor that we don't know.