x^2= 350y = 25*14*y.
as x is integer, y is multiple of 14.
a) x=4n. -> y has to be multiple of 4. thus y divisible by 18. (y is already multiple of 7)
Sufficient
b) x^2 or 350y is divisible by 28. 25y is divisible by 2. y is divisible by 2. y=14, is possible,
y not divisible by 28. y=56 also possible. y divisible by 28 now.
IMO A
Nice One
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pemdas
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number theory is built into DS
for x^2 to be right square of integer, we need 350y to be right square too. Hence y will be some number 350 is missing to be square
prime factorization of 350,
350 (2) 175
175 (5) 35
35 (5) 7
7 (7) 1 ==> 2*(5^2)*7, we need one 2 and one 7 at least ... next correct square would be (2^2)*(5^2)*(7^2) or (2*5*7)^2 multiplied by some other squared number
y with 350 can and cannot be divisible by 28, we deal only with y from 350y
let's turn to statements
st(1) x is divisible by 4, means that 350y square rooted would need to contain (2^2), hence our sqroot(350y) will be 2*5*7 multiplied by some other number containing 2, so that x and sqroot(350y) are divisible by 4. We answer Yes y is divisible by 28 and Sufficient.
st(2) x^2 is divisible by 28 means that y can and cannot be divisible by 28, depending on y's value. As y=2*7 it's not divisible by 28. But as y=2*7*(2^2)*(5^2)*(7^2) it's divisible by 28. Not Sufficient.
a
for x^2 to be right square of integer, we need 350y to be right square too. Hence y will be some number 350 is missing to be square
prime factorization of 350,
350 (2) 175
175 (5) 35
35 (5) 7
7 (7) 1 ==> 2*(5^2)*7, we need one 2 and one 7 at least ... next correct square would be (2^2)*(5^2)*(7^2) or (2*5*7)^2 multiplied by some other squared number
y with 350 can and cannot be divisible by 28, we deal only with y from 350y
let's turn to statements
st(1) x is divisible by 4, means that 350y square rooted would need to contain (2^2), hence our sqroot(350y) will be 2*5*7 multiplied by some other number containing 2, so that x and sqroot(350y) are divisible by 4. We answer Yes y is divisible by 28 and Sufficient.
st(2) x^2 is divisible by 28 means that y can and cannot be divisible by 28, depending on y's value. As y=2*7 it's not divisible by 28. But as y=2*7*(2^2)*(5^2)*(7^2) it's divisible by 28. Not Sufficient.
a
knight247 wrote:For positive integers x and y, x^2 = 350y. Is y divisible by 28?
(1) x is divisible by 4
(2) x^2 is divisible by 28
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tpr-becky
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the words "divisible by" suggest that factoring will be a big part of the problem
since x^2 = 350y - you have to factor 350 to 2(5)(5)(7) since x is an integer it means that 350y is a perfect square. Which means that y must contain a 2 and a 7 as factors (it can also have any other perfect square as a factor but we don't know that).
Statement 1 - x is divisible by 4 means that there are 4 2's as factors in 350y - we already know there are 2 of them but we still need 2 more 2's. This means that y must have a total of 3 2's for this to be true. Y must also have a 7 as stated above therefore we knwo that y will be divisible by 28 [ 4(7)] This is Sufficient - AD.
Statement 2 - x^2 is divisible by 28 - which means that x had a 2 and a 7 as factors - this is somethign we already knew from factoring 350 thus it doesn't tell us anything about y - this is insufficient.
The answer is A.
since x^2 = 350y - you have to factor 350 to 2(5)(5)(7) since x is an integer it means that 350y is a perfect square. Which means that y must contain a 2 and a 7 as factors (it can also have any other perfect square as a factor but we don't know that).
Statement 1 - x is divisible by 4 means that there are 4 2's as factors in 350y - we already know there are 2 of them but we still need 2 more 2's. This means that y must have a total of 3 2's for this to be true. Y must also have a 7 as stated above therefore we knwo that y will be divisible by 28 [ 4(7)] This is Sufficient - AD.
Statement 2 - x^2 is divisible by 28 - which means that x had a 2 and a 7 as factors - this is somethign we already knew from factoring 350 thus it doesn't tell us anything about y - this is insufficient.
The answer is A.
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thestartupguy
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IMO : A
x^2 = 350y; 350 = 2 x 5 x 5 x 7; y = 2 x 7 or y = 14 x 2 ^ 2a x 5 ^ 2b x 7 ^2c
St 1: If x has to be divisible by 4 then x ^ 2 should be divisible by 16.
As x and y should be integer y = 2 x 7 x 2^2 => Statement 1 holds true
St 2: x^2 is already divisible by 28 with y = 14, y <> 28 => N
But y can assume more values, which can have y = 28k.
Therefore, St 2 is NOT SUFFICIENT
IMO :A
x^2 = 350y; 350 = 2 x 5 x 5 x 7; y = 2 x 7 or y = 14 x 2 ^ 2a x 5 ^ 2b x 7 ^2c
St 1: If x has to be divisible by 4 then x ^ 2 should be divisible by 16.
As x and y should be integer y = 2 x 7 x 2^2 => Statement 1 holds true
St 2: x^2 is already divisible by 28 with y = 14, y <> 28 => N
But y can assume more values, which can have y = 28k.
Therefore, St 2 is NOT SUFFICIENT
IMO :A
