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Are both of the integers x and y divisible by 3?
(1) x + y and x – y are divisible by 3.
(2) x^2 and y^2 are divisible by 9.
DS20392
(1) x + y and x – y are divisible by 3.
(2) x^2 and y^2 are divisible by 9.
DS20392
23 May 2020, 09:25
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Bunuel
Are both of the integers x and y divisible by 3?
(1) x + y and x – y are divisible by 3.
(2) x^2 and y^2 are divisible by 9.
DS20392
(1) x + y and x – y are divisible by 3.
(2) x^2 and y^2 are divisible by 9.
DS20392
Question: Are both x and y divisible by 3?
Statement 1: x + y and x – y are divisible by 3.
x+y = 3a
x-y = 3b
Adding the equations
2x = 3(a+b)
ie.. x = 3(a+b)/2 SInce x is an Integer therefore x will be a multiple of 3
Similar will be the derivation of divisibility of y by 3 hence
SUFFICIENT
Statement 2: x^2 and y^2 are divisible by 9.
SInce x and y are Integers therefore x and y both will be multiples of 3
SUFFICIENT
Answer: Option D
23 May 2020, 10:25
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(1) x + y and x – y are divisible by 3.
x+y =3 Z : where Z is quotient
x-y = 3 P, where P is any quotient
Adding two : 2x = 3 (z+p),
As equation is multiple of 3, it will be divisible by 3.
Another way can be picking of numbers, But you will not find numbers whose difference and addition is divisible by 3, Only satisfied case would be when numbers are multiple of 3 e.g
10 -7 =3 : but 10+7 =17 not divisible, so doesn't satisfy equation 2
18-15 = 3: and 18 +15 =33, both equation satisfied. and individually numbers divisible by 3
Sufficient
(2) x^2 and y^2 are divisible by 9.
As per number theory, any number which is divisible by 9 is divisible by 3, So square of it will be also be divisible by 3,
Clearly sufficient
IMO D
x+y =3 Z : where Z is quotient
x-y = 3 P, where P is any quotient
Adding two : 2x = 3 (z+p),
As equation is multiple of 3, it will be divisible by 3.
Another way can be picking of numbers, But you will not find numbers whose difference and addition is divisible by 3, Only satisfied case would be when numbers are multiple of 3 e.g
10 -7 =3 : but 10+7 =17 not divisible, so doesn't satisfy equation 2
18-15 = 3: and 18 +15 =33, both equation satisfied. and individually numbers divisible by 3
Sufficient
(2) x^2 and y^2 are divisible by 9.
As per number theory, any number which is divisible by 9 is divisible by 3, So square of it will be also be divisible by 3,
Clearly sufficient
IMO D
