x and y are two positive integers. D is the greatest common divisor of

Question

x and y are two positive integers. D is the greatest common divisor of x and y. Is D > 20?

(1) x is a multiple of 4

(2) y is a multiple of 20

vrsthe1 · Answer

D is the GCD of X & Y. is D>20 --> factors of 20 = 2*2*5
for D > 20 X & Y should have atleast 1 factor more than that of 20.
X=4 --> factors 2 * 2 < 20
so statement 1 is not sufficient.
Y=20 --> 2*2*5 = factors of 20.
so statement 2 alone is not sufficient.

together with X being multiple of 4 & Y being multiple of 20 we can say that D is not greater than 20.
both statements together are sufficient.

Hence 'C'

GMATWhizTeam · Answer

Solution:

We are asked if GCD of  x	imes y > 20  or not. This is a yes-no question so we do not need actual GCD.

Individually both statements cannot be sufficient because they only talk about either  x  or  y . So, let's straight away get into combining the statements.

Combining the statements:

Statement 1:   x  is a multiple of  4 . So lets us assume  x=4k_1=2^2	imes k_1

Statement 2:   y  is a multiple of  20 . So lets us assume  y=20k_2=2^2	imes 5	imes k_2

Now we have  x=2^2	imes k_1  and  y=2^2	imes 5	imes k_2 .

We can infer that the least GCD that  xy  can be is  2^2=4 . For example when  x=4  and  y=20  or when  k_1=k_2=1 .

GCD can also be  2^2	imes 5=20 , when  x=y=20  or when  k_1=5  and  k_2=1 .

Or the GCD can even be greater than 20. This will happen when  k_1=k_2=10 . GCD of  xy = (40	imes 200)_{GCD}=40

Thus we see that GCD can be less than, equal to and greater than  20  and combining the statements is not sufficient to give exact answer.

Hence the right answer is    Option E   .

PaulLance · Answer

Hey, I'm new here and didn't really know how to reply to a post but saw an explanation by GMATWhiz on how 20 is the highest possible GCD.
What if X is 160 (multiple of 4) and Y is 400 (multiple of 20). Then the GCD would be 80, which is greater than 20. Hence, I chose E. 
What am I missing?

Posted from my mobile device

huongguyen · Answer

x and y are two positive integers. D is the greatest common divisor of x and y. Is D > 20?

(1) x is a multiple of 4
==>  x = 2^{2}k 
aparently, x alone can't be sufficient

(2) y is a multiple of 20
==>  y =2^{2}*5*m 
aparently, y alone can't be sufficient

(1) & (2):
GCD(x,y)  = 2^{2}  < 20 
=> Sufficient

IMO:   C

ankitpal10 · Answer

IMO it should be E.

(1) x is a multiple of 4

Given x is a multiple of 4, x can be 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...etc. Moreover, we do not have information about y. Insufficient.

(2) y is a multiple of 20

y can be 20, 40, 80, etc. Moreover, we do not have information about x. Insufficient.

(1) and (2) combined:

Case 1: If x = 4 and y = 20, then GCD = 4.
Case 2: If x = 20 and y = 20, then GCD = 20. No unique answer.

LamboWalker · Answer

Statement (1) 
x= 4 * something.
No info of y.
Insufficient.

Statement (2) 
y = 20 * something
No info of x.
Insufficient.

Statement (1) & (2) together

If x = 4 and y = 20, then GCD is less than 20 sure.
BUT if x= 40 and y = 800, GCD is more than 20.
Inconclusive and insufficient,

Therefore answer is  E

vrsthe1 · Answer

Hi  PaulLance ,

It is not needed to find what is the solution. 
we need to choose an option where either YES or NO for "is D>20 ?" can be evalulated.
so basis the question & options we cannot determine "is D>20?" with either statement 1 or statement 2 alone, but we can determine when using both the statements together.

Hence option 'C' (answer choices for Data Sufficiency (DS) questions are same you can read that at  https://gmatclub.com/forum/project-ds-butler-get-2-ds-questions-every-day-280918.html .)

firas92 · Answer

If x is 4, y is 20, GCD is 4 (D<20)

If x is 60, y is 60, GCD is 60 (D>20)

Answer is E

Posted from my mobile device

CrackverbalGMAT · Answer

Q.stem inputs - x and y are two positive integers. =>x & y can be from 1,2,3,4,........

(1) x is a multiple of 4

Thus x =4k where k is an integer.

There is no information of y. Insufficient.Eliminate A & D.

(2)y is a multiple of 20

Thus y = 20 k where n is an integer.

There is no information of y. Insufficient. Eliminate B.

Combining both 1 + 2
x =4m = 2^2*k 
and 
y = 20n =2^2*5^1 k

G.c.d of x and y :

Choose simple values on GMAT to prove sufficiency or insufficiency.

x=4 and y=20 would mean their G.cd is 4 and 4<20 (Answer to the question stem is a yes)

x=24 and y=120,gcd =24 24>20 (Answer to the question stem is a No).

There is no unique answer to the question stem even after combining.
 (option e)

D.S
GMAT SME

AndrewN · Answer

There is also a common-sense approach that you can use to see through the (C) trap within 30 seconds. Of course, Statement (1) tells us about one variable only, so it will NOT prove sufficient; the same can be said for Statement (2) on its own. But, when considering the two statements together, we can create a list of just what each statement  does  tell us.

(1) x = 4, 8, 12, 16,   20  , 24, 28, 32, 36,   40  ...
(2) y =   20  ,   40  , 60...

We can see as plain as day that, relative to our pivotal number 20, the answer to the question being asked could be YES or NO. Hence,  the answer must be (E) . Sometimes I think people follow algebra a bit too closely and miss the mark, either through a misinterpretation of the information or a mistake, or by spending more time than is probably necessary to answer a basic question.

Good luck with your studies, everyone.

- Andrew

GMATWhizTeam · Answer

Hey PaulLance , Thank you for pointing it out. We have edited the solution with the correct explanation

x and y are two positive integers. D is the greatest common divisor of

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