GMATinsight wrote:

selim wrote:

When the positive integer x is divided by the positive integer y the quotient is 2 and the remainder is z. when x is divided by the positive integer a the quotient is 3 and the remainder is b. Is z>b ?

1)the ration of y to a is less than 3 to 2.

2)the ratio of y to a is greater than 2 to 3.

When the positive integer x is divided by the positive integer y the quotient is 2 and the remainder is z

i.e. x = 2y + z when x is divided by the positive integer a the quotient is 3 and the remainder is b

i.e. x = 3a + bi.e. 2y + z = 3a + b

Question : Is z > b ?Or

Question : Is 2y > 3a ?Statement 1: the ratio of y to a is less than 3 to 2.i.e. y / a < 3/2

i.e. 2y < 3a

SUFFICIENT

Statement 2: the ratio of y to a is greater than 2 to 3i.e. y / a > 2/3

i.e. 3y < 2a

NOT SUFFICIENT

Answer: Option A

Dear

GMATinsightWhile I have arrived to same conclusion for statement 1 as you did, I have arrived to different conclusion for statement 2.

Statement 2: the ratio of y to a is greater than 2 to 3i.e. y / a > 2/3

i.e. 3y < 2a

We are dealing with POSITIVE integers.....so 3a > 2a & 3y > 2y

But we have 2a > 3y Therefore:

3a > 2a > 3y > 2y......3a > 2y...same as statement 1...........Sufficient

Another way to plug positive integer numbers:

Let a =2 & y = 1.........2 (2) > 3(1)...... 2y + z = 3a + b..........2+z = 6+b.............z-b = 4...z must be greater than b

Let a =3 & y = 1.........2 (3) > 3(1)...... 2y + z = 3a + b..........2+z = 9+b.............z-b = 7...z must be greater than b

Let a =7 & y = 6.........2 (7) > 3(6)...... 2y + z = 3a + b..........12+z = 21+b.............z-b = 8...z must be greater than b

Sufficient

Where did I wrong in my solution?

Thanks