The variables a, b, x, and y are positive integers, and D is the great

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The variables a, b, x, and y are positive integers, and D is the greatest common divisor of x and y. Is D greater than 20?

(1) x = 10a + 20b 
(2) y = 20a + 40b

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yashikaaggarwal · Answer

(1) x = 10a + 20 b
No information about y (not sufficient)

(2) y = 20a + 40 b
No information about x (not sufficient)

Combining both: common factor of X and Y 
=> 10a + 20 b & 20a + 40 b
=> (10a+20b) 2(10a+20b)
Both X and Y have 10a+20b common = GCD
10(a+2b) = GCD
Let say a and b are the least positive no.
10(1+2(1)) = 10(3) = 30 as GCD which is greater than 20
So any positive possible value of a and b will leads to a GCD greater than 20.
(Sufficient)

Answer is C

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QuantMadeEasy · Answer

Step 1: Understanding statement 1 alone 
x = 10 (a + 2b)
As the value of y is unknown, D cannot be determined
Insufficient

Step 2: Understanding statement 2 alone 
y = 20 (a + 2b)
As the value of x is unknown, D cannot be determined
Insufficient

Step 3: Clubbing statement 1 and 2 
D = HCF (x,y) = HCF (10 (a + 2b), 20 (a + 2b)) = 10(a + 2b)
As, minimum value of each a and b is 1, hence minimum value of D = 10 * 3 = 30
Sufficient

IMO C

HoneyLemon · Answer

imo  E 
The variables a, b, x, and y are positive integers, and D is the greatest common divisor of x and y. Is D greater than 20?

(1) x = 10a + 20 b 
-- no info about Y .. not sufficient .. 
(2) y = 20a + 40 b
-- no info about X .. not sufficient .. 
Combining X and Y .. D can be <20 or > 20 depending on value of a and b . 
So not sufficient .

Hence E .

minustark · Answer

The variables a, b, x, and y are positive integers, and D is the greatest common divisor of x and y. Is D greater than 20?

(1) x = 10a + 20 b
(2) y = 20a + 40 b

Statement 1 and 2 both give information about x and y respectively. They are not sufficient by themselves. When we take them together,we can draw several scenarios.

1# a = 1, b = 1 , so x = 30, y = 60. So the GCD, D > 20.
2# a = 1, b = 2, x = 50 and y = 90, here the GCD is 10, so D < 20.

No unique option. Together the statements are not sufficient. E is the answer.

exc4libur · Answer

d=gcf(x,y)>20?
(1) insufic
a,b=1,1: 10+20=30=x; y=1, gcf=1
a,b=1,1: 10+20=30=x; y=30, gcf=30

(2) insufic
a,b=1,1: 20+40=60=y; x=1, gcf=1
a,b=1,1: 20+40=60=y; x=30, gcf=30

(1/2) sufic
x=10a+20b, 10(a+2b)
y=20a+40b, 20(a+2b)
gcf(x,y)=10*(a+2b)
a,b≥1, gcf(x,y)≥10(3)=30

ans (C)

bidskamikaze · Answer

The variables a, b, x, and y are positive integers, and D is the greatest common divisor of x and y. Is D greater than 20?

(1) x = 10a + 20 b
(2) y = 20a + 40 b

Minimum value of a & b can be 1.
Individual statements are nt sufficient because in each statement, value of the second variable is not given.
combining, we get x= 10(a+2b) and y= 20(a+2b).

If we try to put to minimum values of a and b, we can see that GCD will be 30.
So in any case the GCD is more than 30.

Answer C.

The variables a, b, x, and y are positive integers, and D is the great

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